Bibliographic Cross-References
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Metamath Proof Explorer Bibliographic Cross-References |
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| Bibliographic Reference | Description | Metamath Proof Explorer Page(s) |
|---|---|---|
| [Adamek] p. 21 | Definition 3.1 | df-cat 17571 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17571 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 17980 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17592 0funcg 49116 df-termc 49504 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49581 prsthinc 49495 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49609 df-mndtc 49609 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49605 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17615 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49597 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49622 oppgoppchom 49621 oppgoppcid 49623 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17685 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17673 invisoinvl 17694 |
| [Adamek] p. 28 | Example 3.13 | idinv 17693 idiso 17692 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17678 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17652 df-iso 17653 dfiso2 17676 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17659 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17710 cicerALT 49077 |
| [Adamek] p. 29 | Definition 3.15 | cic 17703 df-cic 17700 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17762 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17674 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17675 isoco 17681 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17762 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17785 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49335 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17778 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49605 discthing 49492 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49449 prsthinc 49495 thincciso 49484 thincciso2 49486 thincciso3 49487 thinccisod 49485 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49609 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17792 cofucla 49127 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49193 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18015 catcisoi 49431 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18070 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17811 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17810 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18070 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17835 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17841 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17840 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18055 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18055 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49163 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49154 funcoppc 17779 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18003 elcatchom 49428 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17829 fthoppf 49195 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17828 fulloppf 49194 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18012 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49116 df-catc 18003 |
| [Adamek] p. 45 | Exercise 3G | incat 49632 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49635 nelsubc3 49102 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49182 imasubc2 49183 imasubc3 49187 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17742 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17743 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49102 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17754 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17716 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49191 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49190 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49192 ressffth 17844 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49633 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17850 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17871 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17875 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17851 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17877 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49116 df-inito 17888 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49116 df-termc 49504 initc 49122 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21414 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17889 oppctermo 49267 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17916 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17920 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49268 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17890 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21415 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17923 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17651 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49500 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49499 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49464 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17686 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17688 |
| [Adamek] p. 185 | Section 10.67 | updjud 9824 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49676 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49676 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49676 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49677 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49677 |
| [Adamek] p. 478 | Item Rng | df-ringc 20559 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48579 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48601 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14475 df-pfx 14576 df-substr 14546 df-word 14418 lencl 14437 wrd0 14443 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24621 df-nmoo 30720 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32128 hmopidmchi 32126 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32176 pjcmul2i 32177 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31893 unoplin 31895 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31894 unopadj2 31913 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31988 lnopunii 31987 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32061 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27869 |
| [Alling] p. 184 | Axiom B | bdayfo 27614 |
| [Alling] p. 184 | Axiom O | sltso 27613 |
| [Alling] p. 184 | Axiom SD | nodense 27629 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27716 |
| [Alling] p. 185 | Theorem | conway 27738 |
| [Alling] p. 185 | Axiom FE | noeta 27680 |
| [Alling] p. 186 | Theorem 4 | slerec 27758 slerecd 27759 |
| [Alling], p. 2 | Definition | rp-brsslt 43455 |
| [Alling], p. 3 | Note | nla0001 43458 nla0002 43456 nla0003 43457 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11294 addcan2d 11314 addcan2i 11304 addcand 11313 addcani 11303 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11347 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11406 negsubd 11475 negsubi 11436 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11408 negnegd 11460 negnegi 11428 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11547 subdid 11570 subdii 11563 subdir 11548 subdird 11571 subdiri 11564 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11289 mul01d 11309 mul01i 11300 mul02 11288 mul02d 11308 mul02i 11299 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11751 mulcan2d 11748 mulcand 11747 mulcani 11753 |
| [Apostol] p. 18 | Theorem I.8 | receu 11759 xreceu 32897 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11789 divrecd 11897 divreci 11863 divreczi 11856 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11815 recreci 11850 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11754 mul0ord 11762 mul0ori 11761 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11553 mul2negd 11569 mul2negi 11562 mulneg1 11550 mulneg1d 11567 mulneg1i 11560 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11833 divadddivd 11938 divadddivi 11880 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11818 divmuldivd 11935 divmuldivi 11878 rdivmuldivd 20329 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11819 divdivdivd 11941 divdivdivi 11881 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12911 rpaddcld 12946 rpmulcl 12912 rpmulcld 12947 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12921 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12924 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11236 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11707 ltadd1dd 11725 ltadd1i 11668 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 11968 ltmul1a 11967 ltmul1i 12037 ltmul1ii 12047 ltmul2 11969 ltmul2d 12973 ltmul2dd 12987 ltmul2i 12040 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11634 msqgt0d 11681 msqgt0i 11651 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11636 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11620 lt0neg1d 11683 ltneg 11614 ltnegd 11692 ltnegi 11658 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11599 lt2addd 11737 lt2addi 11676 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12888 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11964 recgt0d 12053 recgt0i 12024 recgt0ii 12025 |
| [Apostol] p. 22 | Definition of integers | df-z 12466 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12136 |
| [Apostol] p. 22 | Definition of rationals | df-q 12844 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9338 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12374 |
| [Apostol] p. 26 | Theorem I.29 | arch 12375 archd 45198 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12573 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12376 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12842 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12841 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13095 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16247 zneo 12553 zneoALTV 47699 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26664 msqsqrtd 15347 resqrtth 15159 sqrtth 15269 sqrtthi 15275 sqsqrtd 15346 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12125 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12808 |
| [Apostol] p. 361 | Remark | crreczi 14132 |
| [Apostol] p. 363 | Remark | absgt0i 15304 |
| [Apostol] p. 363 | Example | abssubd 15360 abssubi 15308 |
| [ApostolNT] p. 7 | Remark | fmtno0 47570 fmtno1 47571 fmtno2 47580 fmtno3 47581 fmtno4 47582 fmtno5fac 47612 fmtnofz04prm 47607 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47558 |
| [ApostolNT] p. 8 | Definition | df-ppi 27035 |
| [ApostolNT] p. 14 | Definition | df-dvds 16161 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16177 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16202 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16197 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16190 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16192 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16178 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16179 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16184 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16219 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16221 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16223 |
| [ApostolNT] p. 15 | Definition | df-gcd 16403 dfgcd2 16454 |
| [ApostolNT] p. 16 | Definition | isprm2 16590 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16561 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16824 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16421 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16455 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16457 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16436 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16428 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16619 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16621 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16837 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16831 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16311 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16495 |
| [ApostolNT] p. 24 | Definition | df-mu 27036 |
| [ApostolNT] p. 25 | Definition | df-phi 16674 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27126 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16699 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16684 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16688 |
| [ApostolNT] p. 32 | Definition | df-vma 27033 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27128 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27152 |
| [ApostolNT] p. 38 | Remark | df-sgm 27037 |
| [ApostolNT] p. 38 | Definition | df-sgm 27037 |
| [ApostolNT] p. 75 | Definition | df-chp 27034 df-cht 27032 |
| [ApostolNT] p. 104 | Definition | congr 16572 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16164 |
| [ApostolNT] p. 106 | Definition | moddvds 16171 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16254 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16255 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13789 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13829 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14142 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16196 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16575 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 16983 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16577 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16691 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16710 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16692 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27007 |
| [ApostolNT] p. 179 | Definition | df-lgs 27231 lgsprme0 27275 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27276 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27252 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27267 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27324 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27343 2lgsoddprm 27352 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27310 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27319 |
| [ApostolNT] p. 188 | Definition | df-lgs 27231 lgs1 27277 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27268 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27270 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27278 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27279 |
| [Baer] p. 40 | Property (b) | mapdord 41676 |
| [Baer] p. 40 | Property (c) | mapd11 41677 |
| [Baer] p. 40 | Property (e) | mapdin 41700 mapdlsm 41702 |
| [Baer] p. 40 | Property (f) | mapd0 41703 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41663 mapd1o 41686 |
| [Baer] p. 41 | Property (g) | mapdat 41705 |
| [Baer] p. 44 | Part (1) | mapdpg 41744 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41839 mapdheq 41766 mapdheq2 41767 mapdheq2biN 41768 |
| [Baer] p. 45 | Part (3) | baerlem3 41751 |
| [Baer] p. 46 | Part (4) | mapdheq4 41770 mapdheq4lem 41769 |
| [Baer] p. 46 | Part (5) | baerlem5a 41752 baerlem5abmN 41756 baerlem5amN 41754 baerlem5b 41753 baerlem5bmN 41755 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41859 hdmap1l6a 41847 hdmap1l6e 41852 hdmap1l6f 41853 hdmap1l6g 41854 hdmap1l6lem1 41845 hdmap1l6lem2 41846 mapdh6N 41785 mapdh6aN 41773 mapdh6eN 41778 mapdh6fN 41779 mapdh6gN 41780 mapdh6lem1N 41771 mapdh6lem2N 41772 |
| [Baer] p. 48 | Part 9 | hdmapval 41866 |
| [Baer] p. 48 | Part 10 | hdmap10 41878 |
| [Baer] p. 48 | Part 11 | hdmapadd 41881 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41855 mapdh6hN 41781 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41791 mapdh75d 41792 mapdh75e 41790 mapdh75fN 41793 mapdh7cN 41787 mapdh7dN 41788 mapdh7eN 41786 mapdh7fN 41789 |
| [Baer] p. 48 | Part (8) | mapdh8 41826 mapdh8a 41813 mapdh8aa 41814 mapdh8ab 41815 mapdh8ac 41816 mapdh8ad 41817 mapdh8b 41818 mapdh8c 41819 mapdh8d 41821 mapdh8d0N 41820 mapdh8e 41822 mapdh8g 41823 mapdh8i 41824 mapdh8j 41825 |
| [Baer] p. 48 | Part (9) | mapdh9a 41827 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41807 |
| [Baer] p. 49 | Part 12 | hdmap11 41886 hdmapeq0 41882 hdmapf1oN 41903 hdmapneg 41884 hdmaprnN 41902 hdmaprnlem1N 41887 hdmaprnlem3N 41888 hdmaprnlem3uN 41889 hdmaprnlem4N 41891 hdmaprnlem6N 41892 hdmaprnlem7N 41893 hdmaprnlem8N 41894 hdmaprnlem9N 41895 hdmapsub 41885 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41906 hdmap14lem10 41915 hdmap14lem1a 41904 hdmap14lem2N 41907 hdmap14lem2a 41905 hdmap14lem3 41908 hdmap14lem8 41913 hdmap14lem9 41914 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41916 hdmap14lem12 41917 hdmap14lem13 41918 hdmap14lem14 41919 hdmap14lem15 41920 hgmapval 41925 |
| [Baer] p. 50 | Part 15 | hgmapadd 41932 hgmapmul 41933 hgmaprnlem2N 41935 hgmapvs 41929 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41939 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41955 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41956 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41957 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41958 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41960 hgmapvv 41964 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41959 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41961 |
| [Baer] p. 111 | Line 15 | hdmapg 41968 hdmapglem7 41967 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26665 2irrexpqALT 26735 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2564 |
| [BellMachover] p. 460 | Notation | df-mo 2535 |
| [BellMachover] p. 460 | Definition | mo3 2559 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2703 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2707 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5225 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5234 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37097 sepex 5238 |
| [BellMachover] p. 466 | Problem | axpow2 5305 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5306 |
| [BellMachover] p. 466 | Axiom Union | axun2 7670 |
| [BellMachover] p. 468 | Definition | df-ord 6309 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6324 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6331 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6326 |
| [BellMachover] p. 471 | Definition of N | df-om 7797 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7734 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6311 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9532 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7812 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9654 |
| [BellMachover] p. 478 | Definition | rankval2 9708 rankval2b 35103 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9672 r1ord3g 9669 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9482 |
| [BellMachover] p. 488 | Axiom AC | ac5 10365 dfac4 10010 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 9998 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39357 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32328 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32370 chirredi 32369 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32358 |
| [Beran] p. 3 | Definition of join | sshjval3 31329 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31591 cmcm2i 31568 cmcm2ii 31573 cmt2N 39288 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31592 lecmi 31577 lecmii 31578 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31566 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31595 cm2ji 31600 cm2mi 31601 |
| [Beran] p. 95 | Definition | df-sh 31182 issh2 31184 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31061 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31074 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31065 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31803 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31805 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31804 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31806 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31057 his1i 31075 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31058 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31059 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31060 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30943 dfhnorm2 31097 normval 31099 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31159 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30948 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31216 |
| [Beran] p. 96 | Definition of converge | df-hlim 30947 hlimi 31163 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31108 norm-i 31104 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31112 norm-ii 31113 normlem0 31084 normlem1 31085 normlem2 31086 normlem3 31087 normlem4 31088 normlem5 31089 normlem6 31090 normlem7 31091 normlem7tALT 31094 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31114 norm-iii 31115 |
| [Beran] p. 98 | Remark 3.4 | bcs 31156 bcsiALT 31154 bcsiHIL 31155 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31096 normpar 31130 normpari 31129 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31121 normpyth 31120 normpythi 31117 |
| [Beran] p. 99 | Remark | lnfn0 32022 lnfn0i 32017 lnop0 31941 lnop0i 31945 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32001 nmcfnex 32028 nmcfnexi 32026 nmcopex 32004 nmcopexi 32002 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32029 nmcfnlbi 32027 nmcoplb 32005 nmcoplbi 32003 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32031 lnfnconi 32030 lnopcon 32010 lnopconi 32009 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31131 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31128 norm3adifii 31123 norm3dif 31125 norm3difi 31122 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31276 pjhth 31368 pjhtheu 31369 pjpjhth 31400 pjpjhthi 31401 pjth 25364 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31381 ococi 31380 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32036 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32037 riesz4 32039 riesz4i 32038 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32054 cnlnadjeu 32053 cnlnadjeui 32052 cnlnadji 32051 cnlnadjlem1 32042 nmopadjlei 32063 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32066 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32065 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32067 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31911 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32077 nmopcoadji 32076 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32068 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32078 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32075 pjadj2coi 32179 pjadjcoi 32136 |
| [Beran] p. 107 | Definition | df-ch 31196 isch2 31198 |
| [Beran] p. 107 | Remark 3.12 | choccl 31281 isch3 31216 occl 31279 ocsh 31258 shoccl 31280 shocsh 31259 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31383 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31307 |
| [Beran] p. 109 | Property (i) | pjadj2 32162 pjadj3 32163 pjadji 31660 pjadjii 31649 |
| [Beran] p. 109 | Property (ii) | pjidmco 32156 pjidmcoi 32152 pjidmi 31648 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32148 |
| [Beran] p. 111 | Remark | ho0val 31725 pjch1 31645 |
| [Beran] p. 111 | Definition | df-hfmul 31709 df-hfsum 31708 df-hodif 31707 df-homul 31706 df-hosum 31705 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31646 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31669 pjchi 31407 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31414 pjoc2i 31413 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31655 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32140 pjssmii 31656 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32139 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32138 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32143 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32141 pjssge0ii 31657 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32142 pjdifnormii 31658 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1777 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1775 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1778 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1773 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34300 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34308 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34306 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34310 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34330 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34361 df-sitm 34339 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34361 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34338 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29024 isuhgrop 29046 isusgrop 29138 isuspgrop 29137 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47891 df-subgr 29244 uhgrspan1 29279 uhgrspansubgr 29267 |
| [Bollobas] p. 3 | Definition | df-gric 47911 gricuspgr 47948 isuspgrim 47926 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29431 df-clnbgr 47849 df-cusgr 29388 df-nbgr 29309 fusgrmaxsize 29441 |
| [Bollobas] p. 4 | Definition | df-upwlks 48164 df-wlks 29576 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29527 finsumvtxdgeven 29529 fusgr1th 29528 fusgrvtxdgonume 29531 vtxdgoddnumeven 29530 |
| [Bollobas] p. 5 | Notation | df-pths 29690 |
| [Bollobas] p. 5 | Definition | df-crcts 29762 df-cycls 29763 df-trls 29667 df-wlkson 29577 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29035 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48230 df-cllaw 48216 df-mgm 18545 df-mgm2 48249 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48231 df-asslaw 48218 df-sgrp 18624 df-sgrp2 48251 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48250 df-comlaw 48217 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18640 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33002 mndlactf1o 33006 mndractf1 33004 mndractf1o 33007 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20151 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20069 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33641 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33645 assarrginv 33644 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33686 fldextrspunfld 33684 fldextrspunlem1 33683 fldextrspunlem2 33685 fldextrspunlsp 33682 fldextrspunlsplem 33681 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33497 dfufd2 33510 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7221 fcofo 7222 |
| [BourbakiTop1] p. | Remark | xnegmnf 13106 xnegpnf 13105 |
| [BourbakiTop1] p. | Remark | rexneg 13107 |
| [BourbakiTop1] p. | Remark 3 | ust0 24133 ustfilxp 24126 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24003 |
| [BourbakiTop1] p. | Criterion | ishmeo 23672 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24196 iducn 24195 snfil 23777 |
| [BourbakiTop1] p. | Example 2 | neifil 23793 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23980 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24216 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33965 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23776 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24188 df-ust 24114 filintn0 23774 filn0 23775 istgp 23990 ucnprima 24194 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24199 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24210 df-usp 24170 df-utop 24144 trust 24142 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33864 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23029 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23182 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24119 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24122 |
| [BourbakiTop1] p. | Property V_ii | innei 23038 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23046 neissex 23040 |
| [BourbakiTop1] p. | Proposition 1 | neips 23026 neiss 23022 ucncn 24197 ustund 24135 ustuqtop 24159 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23180 neiptopreu 23046 utop2nei 24163 utop3cls 24164 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24204 uspreg 24186 utopreg 24165 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23604 imasncls 23605 imasnopn 23603 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23913 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24121 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24123 |
| [BourbakiTop1] p. | Property V_iii | elnei 23024 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24215 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24120 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24124 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23300 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23759 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22807 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33861 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46099 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46101 stoweid 46100 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46038 stoweidlem10 46047 stoweidlem14 46051 stoweidlem15 46052 stoweidlem35 46072 stoweidlem36 46073 stoweidlem37 46074 stoweidlem38 46075 stoweidlem40 46077 stoweidlem41 46078 stoweidlem43 46080 stoweidlem44 46081 stoweidlem46 46083 stoweidlem5 46042 stoweidlem50 46087 stoweidlem52 46089 stoweidlem53 46090 stoweidlem55 46092 stoweidlem56 46093 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46060 stoweidlem24 46061 stoweidlem27 46064 stoweidlem28 46065 stoweidlem30 46067 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46071 stoweidlem59 46096 stoweidlem60 46097 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46082 stoweidlem49 46086 stoweidlem7 46044 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46068 stoweidlem39 46076 stoweidlem42 46079 stoweidlem48 46085 stoweidlem51 46088 stoweidlem54 46091 stoweidlem57 46094 stoweidlem58 46095 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46062 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46054 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46048 stoweidlem13 46050 stoweidlem26 46063 stoweidlem61 46098 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46055 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48230 df-mgm 18545 df-mgm2 48249 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18624 df-sgrp2 48251 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18949 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5173 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30378 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30378 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30378 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30378 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30378 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30378 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30378 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30378 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30378 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30378 |
| [Clemente] p. 14 | Proof 5.11 | natded 30378 |
| [Clemente] p. 14 | Definition E` `n | natded 30378 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30380 ex-natded5.2 30379 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30383 ex-natded5.3 30382 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30385 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30387 ex-natded5.7 30386 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30389 ex-natded5.8 30388 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30391 ex-natded5.13 30390 |
| [Clemente] p. 32 | Definition I` `n | natded 30378 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30378 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30378 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30378 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30392 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30393 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30395 ex-natded9.26 30394 |
| [Cohen] p. 301 | Remark | relogoprlem 26525 |
| [Cohen] p. 301 | Property 2 | relogmul 26526 relogmuld 26559 |
| [Cohen] p. 301 | Property 3 | relogdiv 26527 relogdivd 26560 |
| [Cohen] p. 301 | Property 4 | relogexp 26530 |
| [Cohen] p. 301 | Property 1a | log1 26519 |
| [Cohen] p. 301 | Property 1b | loge 26520 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26722 |
| [Cohen4] p. 349 | Property | relogbf 26726 |
| [Cohen4] p. 352 | Definition | elogb 26705 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26712 |
| [Cohen4] p. 361 | Property 3 | logbrec 26717 relogbdiv 26714 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26710 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26715 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26703 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26704 |
| [Cohen4] p. 367 | Property | logbchbase 26706 |
| [Cohen4] p. 377 | Property 2 | logblt 26719 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34293 sxbrsigalem4 34295 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18460 acsinfd 18459 acsinfdimd 18461 acsmap2d 18458 acsmapd 18457 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34298 |
| [Connell] p. 57 | Definition | df-scmat 22404 df-scmatalt 48430 |
| [Conway] p. 4 | Definition | slerec 27758 slerecd 27759 |
| [Conway] p. 5 | Definition | addsval 27903 addsval2 27904 df-adds 27901 df-muls 28044 df-negs 27961 |
| [Conway] p. 7 | Theorem | 0slt1s 27771 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28380 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27814 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27813 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27700 |
| [Conway] p. 17 | Theorem 3 | addsass 27946 addsassd 27947 addscom 27907 addscomd 27908 addsrid 27905 addsridd 27906 |
| [Conway] p. 17 | Definition | df-0s 27766 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27984 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27981 negsidd 27982 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27930 sleadd1d 27936 |
| [Conway] p. 18 | Definition | df-1s 27767 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27976 negscld 27977 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27921 |
| [Conway] p. 19 | Note | mulsunif2 28107 |
| [Conway] p. 19 | Theorem 7 | addsdi 28092 addsdid 28093 addsdird 28094 mulnegs1d 28097 mulnegs2d 28098 mulsass 28103 mulsassd 28104 mulscom 28076 mulscomd 28077 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28071 mulscld 28072 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28075 sltmul 28073 sltmuld 28074 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28081 mulsgt0d 28082 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28154 |
| [Conway] p. 23 | Theorem 11 | eqscut3 27763 |
| [Conway] p. 24 | Definition | df-reno 28394 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28399 remulscl 28402 renegscl 28398 |
| [Conway] p. 27 | Definition | df-ons 28187 elons2 28193 |
| [Conway] p. 27 | Theorem 14 | sltonex 28197 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28199 onswe 28204 |
| [Conway] p. 29 | Remark | madebday 27843 newbday 27845 oldbday 27844 |
| [Conway] p. 29 | Definition | df-made 27786 df-new 27788 df-old 27787 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13762 |
| [Crawley] p. 1 | Definition of poset | df-poset 18216 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39424 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40228 dalaw 39924 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41999 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40028 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40144 df-ldil 40142 isldil 40148 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40143 df-trnN 40145 isltrn 40157 ltrnu 40159 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39829 cdlema2N 39830 exatleN 39442 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39514 cdlemb 39832 cdlemb2 40079 cdlemb3 40644 idltrn 40188 l1cvat 39093 lhpat 40081 lhpat2 40083 lshpat 39094 ltrnel 40177 ltrnmw 40189 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40229 cdlemc2 40230 ltrnnidn 40212 trlat 40207 trljat1 40204 trljat2 40205 trljat3 40206 trlne 40223 trlnidat 40211 trlnle 40224 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40029 |
| [Crawley] p. 113 | Lemma C | cdlemc 40235 cdlemc3 40231 cdlemc4 40232 |
| [Crawley] p. 113 | Lemma D | cdlemd 40245 cdlemd1 40236 cdlemd2 40237 cdlemd3 40238 cdlemd4 40239 cdlemd5 40240 cdlemd6 40241 cdlemd7 40242 cdlemd8 40243 cdlemd9 40244 cdleme31sde 40423 cdleme31se 40420 cdleme31se2 40421 cdleme31snd 40424 cdleme32a 40479 cdleme32b 40480 cdleme32c 40481 cdleme32d 40482 cdleme32e 40483 cdleme32f 40484 cdleme32fva 40475 cdleme32fva1 40476 cdleme32fvcl 40478 cdleme32le 40485 cdleme48fv 40537 cdleme4gfv 40545 cdleme50eq 40579 cdleme50f 40580 cdleme50f1 40581 cdleme50f1o 40584 cdleme50laut 40585 cdleme50ldil 40586 cdleme50lebi 40578 cdleme50rn 40583 cdleme50rnlem 40582 cdlemeg49le 40549 cdlemeg49lebilem 40577 |
| [Crawley] p. 113 | Lemma E | cdleme 40598 cdleme00a 40247 cdleme01N 40259 cdleme02N 40260 cdleme0a 40249 cdleme0aa 40248 cdleme0b 40250 cdleme0c 40251 cdleme0cp 40252 cdleme0cq 40253 cdleme0dN 40254 cdleme0e 40255 cdleme0ex1N 40261 cdleme0ex2N 40262 cdleme0fN 40256 cdleme0gN 40257 cdleme0moN 40263 cdleme1 40265 cdleme10 40292 cdleme10tN 40296 cdleme11 40308 cdleme11a 40298 cdleme11c 40299 cdleme11dN 40300 cdleme11e 40301 cdleme11fN 40302 cdleme11g 40303 cdleme11h 40304 cdleme11j 40305 cdleme11k 40306 cdleme11l 40307 cdleme12 40309 cdleme13 40310 cdleme14 40311 cdleme15 40316 cdleme15a 40312 cdleme15b 40313 cdleme15c 40314 cdleme15d 40315 cdleme16 40323 cdleme16aN 40297 cdleme16b 40317 cdleme16c 40318 cdleme16d 40319 cdleme16e 40320 cdleme16f 40321 cdleme16g 40322 cdleme19a 40341 cdleme19b 40342 cdleme19c 40343 cdleme19d 40344 cdleme19e 40345 cdleme19f 40346 cdleme1b 40264 cdleme2 40266 cdleme20aN 40347 cdleme20bN 40348 cdleme20c 40349 cdleme20d 40350 cdleme20e 40351 cdleme20f 40352 cdleme20g 40353 cdleme20h 40354 cdleme20i 40355 cdleme20j 40356 cdleme20k 40357 cdleme20l 40360 cdleme20l1 40358 cdleme20l2 40359 cdleme20m 40361 cdleme20y 40340 cdleme20zN 40339 cdleme21 40375 cdleme21d 40368 cdleme21e 40369 cdleme22a 40378 cdleme22aa 40377 cdleme22b 40379 cdleme22cN 40380 cdleme22d 40381 cdleme22e 40382 cdleme22eALTN 40383 cdleme22f 40384 cdleme22f2 40385 cdleme22g 40386 cdleme23a 40387 cdleme23b 40388 cdleme23c 40389 cdleme26e 40397 cdleme26eALTN 40399 cdleme26ee 40398 cdleme26f 40401 cdleme26f2 40403 cdleme26f2ALTN 40402 cdleme26fALTN 40400 cdleme27N 40407 cdleme27a 40405 cdleme27cl 40404 cdleme28c 40410 cdleme3 40275 cdleme30a 40416 cdleme31fv 40428 cdleme31fv1 40429 cdleme31fv1s 40430 cdleme31fv2 40431 cdleme31id 40432 cdleme31sc 40422 cdleme31sdnN 40425 cdleme31sn 40418 cdleme31sn1 40419 cdleme31sn1c 40426 cdleme31sn2 40427 cdleme31so 40417 cdleme35a 40486 cdleme35b 40488 cdleme35c 40489 cdleme35d 40490 cdleme35e 40491 cdleme35f 40492 cdleme35fnpq 40487 cdleme35g 40493 cdleme35h 40494 cdleme35h2 40495 cdleme35sn2aw 40496 cdleme35sn3a 40497 cdleme36a 40498 cdleme36m 40499 cdleme37m 40500 cdleme38m 40501 cdleme38n 40502 cdleme39a 40503 cdleme39n 40504 cdleme3b 40267 cdleme3c 40268 cdleme3d 40269 cdleme3e 40270 cdleme3fN 40271 cdleme3fa 40274 cdleme3g 40272 cdleme3h 40273 cdleme4 40276 cdleme40m 40505 cdleme40n 40506 cdleme40v 40507 cdleme40w 40508 cdleme41fva11 40515 cdleme41sn3aw 40512 cdleme41sn4aw 40513 cdleme41snaw 40514 cdleme42a 40509 cdleme42b 40516 cdleme42c 40510 cdleme42d 40511 cdleme42e 40517 cdleme42f 40518 cdleme42g 40519 cdleme42h 40520 cdleme42i 40521 cdleme42k 40522 cdleme42ke 40523 cdleme42keg 40524 cdleme42mN 40525 cdleme42mgN 40526 cdleme43aN 40527 cdleme43bN 40528 cdleme43cN 40529 cdleme43dN 40530 cdleme5 40278 cdleme50ex 40597 cdleme50ltrn 40595 cdleme51finvN 40594 cdleme51finvfvN 40593 cdleme51finvtrN 40596 cdleme6 40279 cdleme7 40287 cdleme7a 40281 cdleme7aa 40280 cdleme7b 40282 cdleme7c 40283 cdleme7d 40284 cdleme7e 40285 cdleme7ga 40286 cdleme8 40288 cdleme8tN 40293 cdleme9 40291 cdleme9a 40289 cdleme9b 40290 cdleme9tN 40295 cdleme9taN 40294 cdlemeda 40336 cdlemedb 40335 cdlemednpq 40337 cdlemednuN 40338 cdlemefr27cl 40441 cdlemefr32fva1 40448 cdlemefr32fvaN 40447 cdlemefrs32fva 40438 cdlemefrs32fva1 40439 cdlemefs27cl 40451 cdlemefs32fva1 40461 cdlemefs32fvaN 40460 cdlemesner 40334 cdlemeulpq 40258 |
| [Crawley] p. 114 | Lemma E | 4atex 40114 4atexlem7 40113 cdleme0nex 40328 cdleme17a 40324 cdleme17c 40326 cdleme17d 40536 cdleme17d1 40327 cdleme17d2 40533 cdleme18a 40329 cdleme18b 40330 cdleme18c 40331 cdleme18d 40333 cdleme4a 40277 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40363 cdleme21at 40366 cdleme21b 40364 cdleme21c 40365 cdleme21ct 40367 cdleme21f 40370 cdleme21g 40371 cdleme21h 40372 cdleme21i 40373 cdleme22gb 40332 |
| [Crawley] p. 116 | Lemma F | cdlemf 40601 cdlemf1 40599 cdlemf2 40600 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40605 cdlemg16 40695 cdlemg28 40742 cdlemg28a 40731 cdlemg28b 40741 cdlemg3a 40635 cdlemg42 40767 cdlemg43 40768 cdlemg44 40771 cdlemg44a 40769 cdlemg46 40773 cdlemg47 40774 cdlemg9 40672 ltrnco 40757 ltrncom 40776 tgrpabl 40789 trlco 40765 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40781 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40715 cdlemg17b 40700 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40794 df-edring 40795 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40798 |
| [Crawley] p. 118 | Remark | tendopltp 40818 |
| [Crawley] p. 118 | Lemma H | cdlemh 40855 cdlemh1 40853 cdlemh2 40854 |
| [Crawley] p. 118 | Lemma I | cdlemi 40858 cdlemi1 40856 cdlemi2 40857 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40859 cdlemj2 40860 cdlemj3 40861 tendocan 40862 |
| [Crawley] p. 118 | Lemma K | cdlemk 41012 cdlemk1 40869 cdlemk10 40881 cdlemk11 40887 cdlemk11t 40984 cdlemk11ta 40967 cdlemk11tb 40969 cdlemk11tc 40983 cdlemk11u-2N 40927 cdlemk11u 40909 cdlemk12 40888 cdlemk12u-2N 40928 cdlemk12u 40910 cdlemk13-2N 40914 cdlemk13 40890 cdlemk14-2N 40916 cdlemk14 40892 cdlemk15-2N 40917 cdlemk15 40893 cdlemk16-2N 40918 cdlemk16 40895 cdlemk16a 40894 cdlemk17-2N 40919 cdlemk17 40896 cdlemk18-2N 40924 cdlemk18-3N 40938 cdlemk18 40906 cdlemk19-2N 40925 cdlemk19 40907 cdlemk19u 41008 cdlemk1u 40897 cdlemk2 40870 cdlemk20-2N 40930 cdlemk20 40912 cdlemk21-2N 40929 cdlemk21N 40911 cdlemk22-3 40939 cdlemk22 40931 cdlemk23-3 40940 cdlemk24-3 40941 cdlemk25-3 40942 cdlemk26-3 40944 cdlemk26b-3 40943 cdlemk27-3 40945 cdlemk28-3 40946 cdlemk29-3 40949 cdlemk3 40871 cdlemk30 40932 cdlemk31 40934 cdlemk32 40935 cdlemk33N 40947 cdlemk34 40948 cdlemk35 40950 cdlemk36 40951 cdlemk37 40952 cdlemk38 40953 cdlemk39 40954 cdlemk39u 41006 cdlemk4 40872 cdlemk41 40958 cdlemk42 40979 cdlemk42yN 40982 cdlemk43N 41001 cdlemk45 40985 cdlemk46 40986 cdlemk47 40987 cdlemk48 40988 cdlemk49 40989 cdlemk5 40874 cdlemk50 40990 cdlemk51 40991 cdlemk52 40992 cdlemk53 40995 cdlemk54 40996 cdlemk55 40999 cdlemk55u 41004 cdlemk56 41009 cdlemk5a 40873 cdlemk5auN 40898 cdlemk5u 40899 cdlemk6 40875 cdlemk6u 40900 cdlemk7 40886 cdlemk7u-2N 40926 cdlemk7u 40908 cdlemk8 40876 cdlemk9 40877 cdlemk9bN 40878 cdlemki 40879 cdlemkid 40974 cdlemkj-2N 40920 cdlemkj 40901 cdlemksat 40884 cdlemksel 40883 cdlemksv 40882 cdlemksv2 40885 cdlemkuat 40904 cdlemkuel-2N 40922 cdlemkuel-3 40936 cdlemkuel 40903 cdlemkuv-2N 40921 cdlemkuv2-2 40923 cdlemkuv2-3N 40937 cdlemkuv2 40905 cdlemkuvN 40902 cdlemkvcl 40880 cdlemky 40964 cdlemkyyN 41000 tendoex 41013 |
| [Crawley] p. 120 | Remark | dva1dim 41023 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41014 cdleml2N 41015 cdleml3N 41016 cdleml4N 41017 cdleml5N 41018 cdleml6 41019 cdleml7 41020 cdleml8 41021 cdleml9 41022 dia1dim 41099 |
| [Crawley] p. 120 | Lemma M | dia11N 41086 diaf11N 41087 dialss 41084 diaord 41085 dibf11N 41199 djajN 41175 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41070 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41156 dia2dimlem1 41102 dia2dimlem2 41103 dia2dimlem3 41104 dia2dimlem4 41105 dia2dimlem5 41106 diaf1oN 41168 diarnN 41167 dvheveccl 41150 dvhopN 41154 |
| [Crawley] p. 121 | Lemma N | cdlemn 41250 cdlemn10 41244 cdlemn11 41249 cdlemn11a 41245 cdlemn11b 41246 cdlemn11c 41247 cdlemn11pre 41248 cdlemn2 41233 cdlemn2a 41234 cdlemn3 41235 cdlemn4 41236 cdlemn4a 41237 cdlemn5 41239 cdlemn5pre 41238 cdlemn6 41240 cdlemn7 41241 cdlemn8 41242 cdlemn9 41243 diclspsn 41232 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41211 |
| [Crawley] p. 122 | Lemma N | dih11 41303 dihf11 41305 dihjust 41255 dihjustlem 41254 dihord 41302 dihord1 41256 dihord10 41261 dihord11b 41260 dihord11c 41262 dihord2 41265 dihord2a 41257 dihord2b 41258 dihord2cN 41259 dihord2pre 41263 dihord2pre2 41264 dihordlem6 41251 dihordlem7 41252 dihordlem7b 41253 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41268 dihfval 41269 dihval 41270 |
| [Diestel] p. 3 | Definition | df-gric 47911 df-grim 47908 isuspgrim 47926 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29388 df-nbgr 29309 |
| [Diestel] p. 3 | Definition by | df-grisom 47907 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47891 df-subgr 29244 uhgrspan1 29279 uhgrspansubgr 29267 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29531 vtxdgoddnumeven 29530 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29035 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33872 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33884 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33876 zarcls1 33877 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33887 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33890 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33893 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3905 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9537 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8752 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9545 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9870 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10443 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5243 |
| [Enderton] p. 19 | Definition | df-tp 4581 |
| [Enderton] p. 26 | Exercise 5 | unissb 4891 |
| [Enderton] p. 26 | Exercise 10 | pwel 5319 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5509 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5027 iinin2 5026 iinun2 5021 iunin1 5020 iunin1f 32532 iunin2 5019 uniin1 32526 uniin2 32527 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5025 iundif2 5022 |
| [Enderton] p. 32 | Exercise 20 | unineq 4238 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5046 |
| [Enderton] p. 33 | Exercise 25 | iununi 5047 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5054 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7704 iunpwss 5055 |
| [Enderton] p. 36 | Definition | opthwiener 5454 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5391 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4896 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5410 rnex 7840 rnexg 7832 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5854 rnuni 6095 |
| [Enderton] p. 42 | Definition of a function | dffun7 6508 dffun8 6509 |
| [Enderton] p. 43 | Definition of function value | funfv2 6910 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6550 |
| [Enderton] p. 44 | Definition (d) | dfima2 6011 dfima3 6012 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6919 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10361 ac7g 10362 df-ac 10004 dfac2 10020 dfac2a 10018 dfac2b 10019 dfac3 10009 dfac7 10021 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7180 |
| [Enderton] p. 52 | Definition | df-map 8752 |
| [Enderton] p. 53 | Exercise 21 | coass 6213 |
| [Enderton] p. 53 | Exercise 27 | dmco 6202 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6557 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6051 |
| [Enderton] p. 54 | Remark | ixpf 8844 ixpssmap 8856 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8822 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10371 ac9s 10381 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38646 erref 8642 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38649 erthi 8678 |
| [Enderton] p. 57 | Definition | df-ec 8624 |
| [Enderton] p. 58 | Definition | df-qs 8628 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8624 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5850 |
| [Enderton] p. 68 | Definition of successor | df-suc 6312 |
| [Enderton] p. 71 | Definition | df-tr 5199 dftr4 5204 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6387 unisucg 6386 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6387 unisucg 6386 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5213 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5215 trintALT 44912 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8519 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8521 onasuc 8443 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7349 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8520 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8522 onmsuc 8444 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8537 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8524 nnacom 8532 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8538 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8539 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8541 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8525 nnmsucr 8540 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8553 |
| [Enderton] p. 129 | Definition | df-en 8870 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7300 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9903 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16119 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9116 |
| [Enderton] p. 135 | Corollary 6C | php3 9118 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9115 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9146 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9148 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9078 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9082 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9054 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10068 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10069 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10064 dju1en 10060 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9227 unifi 9228 unifi2 9229 |
| [Enderton] p. 144 | Corollary 6K | undif2 4427 unfi 9080 unfi2 9194 |
| [Enderton] p. 145 | Figure 38 | ffoss 7878 |
| [Enderton] p. 145 | Definition | df-dom 8871 |
| [Enderton] p. 146 | Example 1 | domen 8884 domeng 8885 |
| [Enderton] p. 146 | Example 3 | nndomo 9126 nnsdom 9544 nnsdomg 9183 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10072 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9055 xpdom1 8989 xpdom1g 8987 xpdom2g 8986 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9061 |
| [Enderton] p. 151 | Theorem 6M | zorn 10395 zorng 10392 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10380 dfac5 10017 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10463 |
| [Enderton] p. 164 | Example | infdif 10096 |
| [Enderton] p. 168 | Definition | df-po 5524 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6421 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6353 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6420 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6361 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7769 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7714 |
| [Enderton] p. 194 | Remark | onprc 7711 |
| [Enderton] p. 194 | Exercise 16 | suc11 6415 |
| [Enderton] p. 197 | Definition | df-card 9829 |
| [Enderton] p. 197 | Theorem 7P | carden 10439 |
| [Enderton] p. 200 | Exercise 25 | tfis 7785 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9666 |
| [Enderton] p. 202 | Definition | df-r1 9654 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9676 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9757 rankval4b 35104 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9496 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9747 rankprb 9741 rankpw 9733 rankpwi 9713 rankuniss 9756 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9508 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9509 |
| [Enderton] p. 212 | Definition of aleph | alephval3 9998 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9964 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 9978 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8261 |
| [Enderton] p. 222 | Definition of kard | karden 9785 kardex 9784 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8512 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8514 |
| [Enderton] p. 240 | Exercise 25 | oarec 8477 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10138 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17545 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17487 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18456 mrieqv2d 17542 mrieqvd 17541 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17546 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17551 mreexexlem2d 17548 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18462 mreexfidimd 17553 |
| [Frege1879] p. 11 | Statement | df3or2 43800 |
| [Frege1879] p. 12 | Statement | df3an2 43801 dfxor4 43798 dfxor5 43799 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43822 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43823 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43827 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43831 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43832 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43838 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43840 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43841 axfrege8 43839 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37478 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43844 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43852 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43846 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43845 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43854 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43855 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43858 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43848 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43853 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43850 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43856 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43860 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43859 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43851 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43857 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43847 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43849 rp-frege25 43837 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43842 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43862 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43843 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43863 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43866 axfrege31 43865 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43864 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43867 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43868 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43869 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43870 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43871 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43872 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43873 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43874 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43875 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43877 axfrege41 43876 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43878 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43879 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43880 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43881 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43882 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43883 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43884 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43885 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43886 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43889 ax-frege52c 43920 frege52aid 43890 frege52b 43921 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43894 ax-frege54c 43924 frege54b 43925 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43887 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3743 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43892 frege53aid 43891 frege53b 43922 frege53c 43946 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2731 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43900 frege55aid 43897 frege55b 43929 frege55c 43950 frege55cor1a 43901 frege55lem2a 43899 frege55lem2b 43928 frege55lem2c 43949 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43903 frege56aid 43902 frege56b 43930 frege56c 43951 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43907 ax-frege58b 43933 frege58bid 43934 frege58c 43953 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43905 frege57aid 43904 frege57b 43931 frege57c 43952 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3754 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43909 frege59b 43936 frege59c 43954 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43910 frege60b 43937 frege60c 43955 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43911 frege61b 43938 frege61c 43956 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43912 frege62b 43939 frege62c 43957 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43913 frege63b 43940 frege63c 43958 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43914 frege64b 43941 frege64c 43959 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43915 frege65b 43942 frege65c 43960 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43916 frege66b 43943 frege66c 43961 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43917 frege67b 43944 frege67c 43962 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43918 frege68b 43945 frege68c 43963 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43964 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43965 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43966 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43967 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43968 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43971 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43969 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43970 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43972 frege77d 43778 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43973 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43974 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43975 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43976 frege81d 43779 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43977 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43978 frege83d 43780 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43979 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43980 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43981 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43982 frege87d 43782 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43983 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43984 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43985 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43986 frege91d 43783 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43987 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43988 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43989 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43990 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43994 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43991 frege96d 43781 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43992 frege97d 43784 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43993 frege98d 43785 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43995 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43996 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43997 frege102d 43786 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43998 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43999 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44000 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44001 frege106d 43787 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44002 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44003 frege108d 43788 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44004 frege109d 43789 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44005 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44006 frege111d 43791 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44007 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44008 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44009 frege114d 43790 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44010 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44011 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44012 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44013 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44014 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44015 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44016 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44017 frege122d 43792 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44018 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44019 frege124d 43793 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44020 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44021 frege126d 43794 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44022 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44023 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44024 frege129d 43795 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44025 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44026 frege131d 43796 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44027 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44028 frege133d 43797 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46350 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46673 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46373 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46488 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46508 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46499 meadjunre 46513 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46500 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46501 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46497 meaiunle 46506 meaiunlelem 46505 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46518 meaiuninc2 46519 meaiuninc3 46522 meaiuninc3v 46521 meaiunincf 46520 meaiuninclem 46517 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46524 meaiininc2 46525 meaiininclem 46523 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46543 caragendifcl 46551 caratheodory 46565 omelesplit 46555 |
| [Fremlin1] p. 19 | Definition 113A | isome 46531 isomennd 46568 isomenndlem 46567 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46553 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46572 voncmpl 46658 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46535 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46560 carageniuncllem1 46558 carageniuncllem2 46559 caragenuncl 46550 caragenuncllem 46549 caragenunicl 46561 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46569 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46563 caratheodorylem2 46564 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46572 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46631 hoidmv1lelem1 46628 hoidmv1lelem2 46629 hoidmv1lelem3 46630 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46675 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46631 hoidmvle 46637 hoidmvlelem1 46632 hoidmvlelem2 46633 hoidmvlelem3 46634 hoidmvlelem4 46635 hoidmvlelem5 46636 hsphoidmvle2 46622 hsphoif 46613 hsphoival 46616 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46585 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46593 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46620 hoidmvn0val 46621 hoidmvval 46614 hoidmvval0 46624 hoidmvval0b 46627 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46625 hsphoidmvle 46623 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46574 df-voln 46576 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46641 ovn0 46603 ovn0lem 46602 ovnf 46600 ovnome 46610 ovnssle 46598 ovnsslelem 46597 ovnsupge0 46594 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46640 ovnhoilem1 46638 ovnhoilem2 46639 vonhoi 46704 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46657 hoidifhspf 46655 hoidifhspval 46645 hoidifhspval2 46652 hoidifhspval3 46656 hspmbl 46666 hspmbllem1 46663 hspmbllem2 46664 hspmbllem3 46665 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46658 vonmea 46611 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46609 ovnsubadd2 46683 ovnsubadd2lem 46682 ovnsubaddlem1 46607 ovnsubaddlem2 46608 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46668 hoimbl2 46702 hoimbllem 46667 hspdifhsp 46653 opnvonmbl 46671 opnvonmbllem2 46670 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46673 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46716 iccvonmbllem 46715 ioovonmbl 46714 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46722 vonicclem2 46721 vonioo 46719 vonioolem2 46718 vonn0icc 46725 vonn0icc2 46729 vonn0ioo 46724 vonn0ioo2 46727 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46726 snvonmbl 46723 vonct 46730 vonsn 46728 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46396 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46395 subsaliuncllem 46394 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46762 salpreimalegt 46746 salpreimaltle 46763 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46765 issmff 46771 issmflem 46764 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46782 issmflelem 46781 smfpreimale 46791 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46793 issmfgtlem 46792 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46733 issmf 46765 issmff 46771 issmfge 46807 issmfgelem 46806 issmfgt 46793 issmfgtlem 46792 issmfle 46782 issmflelem 46781 issmflem 46764 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46744 salpreimagtlt 46767 salpreimalelt 46766 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46807 issmfgelem 46806 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46790 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46788 cnfsmf 46777 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46804 decsmflem 46803 incsmf 46779 incsmflem 46778 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46738 pimconstlt1 46739 smfconst 46786 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46802 smfaddlem1 46800 smfaddlem2 46801 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46833 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46832 smfmullem1 46828 smfmullem2 46829 smfmullem3 46830 smfmullem4 46831 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46834 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46837 smfpimbor1lem2 46836 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46839 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46827 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46826 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46835 smfresal 46825 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46814 smflim2 46843 smflimlem1 46808 smflimlem2 46809 smflimlem3 46810 smflimlem4 46811 smflimlem5 46812 smflimlem6 46813 smflimmpt 46847 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46851 smfsuplem1 46848 smfsuplem2 46849 smfsuplem3 46850 smfsupmpt 46852 smfsupxr 46853 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46855 smfinflem 46854 smfinfmpt 46856 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46814 smflim2 46843 smflimmpt 46847 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46845 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46875 smfdivdmmbl2 46878 smfinfdmmbl 46886 smfinfdmmbllem 46885 smfsupdmmbl 46882 smfsupdmmbllem 46881 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46865 smflimsuplem2 46858 smflimsuplem6 46862 smflimsuplem7 46863 smflimsuplem8 46864 smflimsupmpt 46866 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46868 smfliminflem 46867 smfliminfmpt 46869 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46733 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46879 fsupdm2 46880 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46870 adddmmbl2 46871 finfdm 46883 finfdm2 46884 fsupdm 46879 fsupdm2 46880 muldmmbl 46872 muldmmbl2 46873 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46883 finfdm2 46884 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25462 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25505 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25515 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37737 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37740 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9528 inf1 9512 inf2 9513 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10799 enqer 10809 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10804 df-nq 10800 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10796 df-plq 10802 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7583 df-mpq 10797 df-mq 10803 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10805 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10863 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10864 ltbtwnnq 10866 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10859 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10860 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10867 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10869 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10881 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10883 |
| [Gleason] p. 122 | Definition | df-1p 10870 |
| [Gleason] p. 122 | Remark (1) | prub 10882 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10921 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10873 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10920 psslinpr 10919 supexpr 10942 suplem1pr 10940 suplem2pr 10941 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10906 addclprlem1 10904 addclprlem2 10905 df-plp 10871 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10910 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10909 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10922 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10931 ltexprlem1 10924 ltexprlem2 10925 ltexprlem3 10926 ltexprlem4 10927 ltexprlem5 10928 ltexprlem6 10929 ltexprlem7 10930 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10933 ltaprlem 10932 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10934 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10935 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10872 mulclpr 10908 mulclprlem 10907 reclem2pr 10936 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10917 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10912 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10911 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10916 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10939 reclem3pr 10937 reclem4pr 10938 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10943 enrer 10951 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10948 df-1r 10949 df-nr 10944 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10946 df-plr 10945 negexsr 10990 recexsr 10995 recexsrlem 10991 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10947 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12117 creur 12116 cru 12114 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11076 axcnre 11052 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15019 crimd 15136 crimi 15097 crre 15018 crred 15135 crrei 15096 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15021 remimd 15102 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15188 absval2d 15352 absval2i 15302 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15045 cjaddd 15124 cjaddi 15092 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15046 cjmuld 15125 cjmuli 15093 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15044 cjcjd 15103 cjcji 15075 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15043 cjreb 15027 cjrebd 15106 cjrebi 15078 cjred 15130 rere 15026 rereb 15024 rerebd 15105 rerebi 15077 rered 15128 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15052 addcjd 15116 addcji 15087 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15142 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15183 abscjd 15357 abscji 15306 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15193 abs00d 15353 abs00i 15303 absne0d 15354 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15226 releabsd 15358 releabsi 15307 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15198 absmuld 15361 absmuli 15309 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15186 sqabsaddi 15310 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15235 abstrid 15363 abstrii 15313 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13966 exp0 13969 expp1 13972 expp1d 14051 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26613 cxpaddd 26651 expadd 14008 expaddd 14052 expaddz 14010 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26622 cxpmuld 26671 expmul 14011 expmuld 14053 expmulz 14012 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26619 mulcxpd 26662 mulexp 14005 mulexpd 14065 mulexpz 14006 |
| [Gleason] p. 140 | Exercise 1 | znnen 16118 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13406 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15536 rlimadd 15547 rlimdiv 15550 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15538 rlimsub 15548 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15537 rlimmul 15549 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15541 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15487 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15508 climcj 15509 climim 15511 climre 15510 rlimabs 15513 rlimcj 15514 rlimim 15516 rlimre 15515 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11148 df-xr 11147 ltxr 13011 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15375 limsupval 15378 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15574 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15583 caucvgb 15584 caucvgbf 45526 caucvgr 15580 climcau 15575 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15720 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15787 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15240 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13729 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21283 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24256 xmet0 24255 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24272 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24263 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24265 mstri 24382 xmettri 24264 xmstri 24381 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24295 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23561 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25235 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24453 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24779 addcn2 15498 mulcn 24781 mulcn2 15500 subcn 24780 subcn2 15499 |
| [Gleason] p. 295 | Remark | bcval3 14210 bcval4 14211 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14225 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14208 df-bc 14207 |
| [Gleason] p. 296 | Remark | bcn0 14214 bcnn 14216 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15734 |
| [Gleason] p. 308 | Equation 2 | ef0 15995 |
| [Gleason] p. 308 | Equation 3 | efcj 15996 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16002 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16007 |
| [Gleason] p. 310 | Equation 14 | sinadd 16070 |
| [Gleason] p. 310 | Equation 15 | cosadd 16071 |
| [Gleason] p. 311 | Equation 17 | sincossq 16082 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16087 sinbnd 16086 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14120 sqeqori 14118 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 15976 |
| [Godowski] p. 730 | Equation SF | goeqi 32248 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31643 |
| [Golan] p. 1 | Remark | srgisid 20125 |
| [Golan] p. 1 | Definition | df-srg 20103 |
| [Golan] p. 149 | Definition | df-slmd 33165 |
| [Gonshor] p. 7 | Definition | df-scut 27721 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27758 slerecd 27759 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27862 cofcut1d 27863 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27864 cofcut2d 27865 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27866 cofcutr1d 27867 cofcutr2d 27868 |
| [Gonshor] p. 13 | Definition | df-adds 27901 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27917 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27943 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28067 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28087 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28376 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28378 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28377 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27958 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36192 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17485 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17487 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48218 df-cllaw 48216 df-comlaw 48217 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48230 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48251 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38802 dfmembpart2 38807 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32040 riesz2 32041 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31916 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32148 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32160 elpjidm 32159 pjnmopi 32123 |
| [Halmos] p. 44 | Remark | pjinormi 31662 pjinormii 31651 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32164 pjrn 31682 pjrni 31677 pjvec 31671 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31702 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32129 hmopidmpji 32127 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32166 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32155 pjocvec 31672 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32144 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32147 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32150 pjssdif2i 32149 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31830 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1796 |
| [Hatcher] p. 25 | Definition | df-phtpc 24916 df-phtpy 24895 |
| [Hatcher] p. 26 | Definition | df-pco 24930 df-pi1 24933 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24919 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24975 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22403 df-dmatalt 48429 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47847 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47832 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47844 bgoldbtbnd 47839 bgoldbtbnd 47839 tgblthelfgott 47845 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34650 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34651 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34665 hgt750lemb 34664 hgt750leme 34666 hgt750lemf 34661 hgt750lemg 34662 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47841 tgoldbachgt 34671 tgoldbachgtALTV 47842 tgoldbachgtd 34670 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34652 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30468 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18854 grpoideu 30484 mndideu 18650 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18884 grpoinveu 30494 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18915 grpo2inv 30506 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18928 grpoinvop 30508 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18950 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1769 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1770 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1772 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32395 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32408 cdj3i 32416 cdj3lem1 32409 cdjreui 32407 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32406 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41999 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41929 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41951 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41952 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41949 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41955 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41874 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41969 |
| [Holland95] p. 204 | Definition of involution | df-srng 20753 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39541 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41566 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41519 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39971 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41415 poml4N 39991 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41506 pexmidALTN 40016 pexmidN 40007 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41571 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39162 ldualset 39163 |
| [Holland95] p. 222 | Item 1 | df-lines 39539 df-pointsN 39540 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39941 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39985 omllaw4 39284 pol1N 39948 polcon3N 39955 |
| [Holland95] p. 223 | Definition | df-psubclN 39973 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39944 |
| [Holmes] p. 40 | Definition | df-xrn 38398 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31059 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32157 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31938 eigre 31810 eigrei 31809 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31939 eigorth 31813 eigorthi 31812 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31811 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30284 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30280 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30281 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30282 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30300 frgrregorufr0 30299 frgrregorufrg 30301 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30307 frrusgrord 30316 frrusgrord0 30315 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30063 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30290 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30293 frgrwopreg2 30294 frgrwopregasn 30291 frgrwopregbsn 30292 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30296 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30310 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30313 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30061 numclwlk1 30346 numclwlk1lem1 30344 numclwlk1lem2 30345 numclwwlk1 30336 numclwwlk8 30367 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30287 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29747 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30322 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30348 numclwwlkovh0 30347 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30356 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29953 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30360 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30363 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30366 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30378 natded 30378 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30378 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30378 natded 30378 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30378 |
| [Jech] p. 4 | Definition of class | cv 1540 cvjust 2725 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10467 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10465 alephmul 10466 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10464 infmap2 10105 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9704 |
| [Jech] p. 72 | Equation 9.3 | scott0 9776 scottex 9775 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9757 rankval4b 35104 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9781 |
| [Jech] p. 78 | Note | opthprc 5680 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42947 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43035 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43036 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42959 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42963 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42964 rmyp1 42965 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42966 rmym1 42967 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42957 rmx1 42958 rmxluc 42968 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42961 rmy1 42962 rmyluc 42969 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42971 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42972 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42992 jm2.17b 42993 jm2.17c 42994 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43025 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43029 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43020 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42995 jm2.24nn 42991 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43034 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43040 rmygeid 42996 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43052 |
| [Juillerat] p. 11 | Section *5 | etransc 46320 etransclem47 46318 etransclem48 46319 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46315 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46317 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46303 |
| [Juillerat] p. 13 | Proof | etransclem35 46306 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46309 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46295 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46312 |
| [Juillerat] p. 14 | Proof | etransclem23 46294 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1968 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2013 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2018 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2008 cbvaliw 2007 wl-cbvmotv 37546 wl-motae 37548 wl-moteq 37547 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1987 spimw 1971 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2034 spw 2035 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31491 chabs1i 31493 chabs2 31492 chabs2i 31494 chjass 31508 chjassi 31461 latabs1 18378 latabs2 18379 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32313 ela 32314 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32258 cvrval2 39312 |
| [Kalmbach] p. 16 | Definition | df-ol 39216 df-oml 39217 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31559 cmbri 31565 cmtvalN 39249 df-cm 31558 df-cmtN 39215 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39285 pjoml5 31588 pjoml5i 31563 |
| [Kalmbach] p. 22 | Definition | pjoml2 31586 pjoml2i 31560 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31589 cmcmi 31567 cmcmii 31572 cmtcomN 39287 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39283 omlsi 31379 pjoml 31411 pjomli 31410 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39282 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31571 cmcm3 31590 cmcm3i 31569 cmcm3ii 31574 cmcm4i 31570 cmt3N 39289 cmt4N 39290 cmtbr2N 39291 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31583 cmbr3i 31575 cmtbr3N 39292 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31593 fh1i 31596 fh2 31594 fh2i 31597 omlfh1N 39296 |
| [Kalmbach] p. 65 | Remark | chjatom 32332 chslej 31473 chsleji 31433 shslej 31355 shsleji 31345 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31470 chocini 31429 chsupcl 31315 chsupval2 31385 h0elch 31230 helch 31218 hsupval2 31384 ocin 31271 ococss 31268 shococss 31269 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31287 |
| [Kalmbach] p. 66 | Remark | df-pjh 31370 pjssmi 32140 pjssmii 31656 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31620 osumi 31617 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32175 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32375 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32285 |
| [Kalmbach] p. 140 | Remark | hatomic 32335 hatomici 32334 hatomistici 32337 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39357 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32356 lsatexch 39081 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32330 cvlcvr1 39377 cvr1 39448 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32349 cvexchi 32344 cvrexch 39458 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32339 hlrelat 39440 hlrelat5N 39439 lrelat 39052 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21076 lsmsatcv 39048 spansncv 31628 spansncvi 31627 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39067 spansncv2 32268 |
| [Kalmbach] p. 266 | Definition | df-st 32186 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31824 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10534 fpwwe2 10531 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10535 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10542 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10537 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10539 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10552 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10556 gchxpidm 10557 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10568 gchhar 10567 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10103 unxpwdom 9475 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10558 |
| [Kreyszig] p. 3 | Property M1 | metcl 24245 xmetcl 24244 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24252 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24485 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11835 muleqadd 11758 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24351 |
| [Kreyszig] p. 19 | Remark | mopntopon 24352 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24411 mopnm 24357 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24409 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24414 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24455 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23171 lmmbr 25183 lmmbr2 25184 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23293 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25238 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25201 iscmet2 25219 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25241 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23374 metelcls 25230 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25231 metcld2 25232 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25024 lmodvneg1 20836 nvinv 30614 vcm 30551 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25020 lmod0vs 20826 slmd0vs 33188 vc0 30549 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20827 slmdvs0 33189 vcz 30550 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30666 ngpmet 24516 nrmmetd 24487 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30661 imsdval2 30662 ncvspds 25086 ngpds 24517 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24502 nvnd 30663 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24531 nmge0 24530 nvge0 30648 nvz 30644 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24537 nvabs 30647 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30776 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30720 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30782 blocni 30780 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30781 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25129 ipeq0 21573 ipz 30694 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25141 pythi 30825 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30829 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25163 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15760 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25361 minveco 30859 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30725 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25254 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30848 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32098 leopg 32097 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32116 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30893 |
| [Kulpa] p. 547 | Theorem | poimir 37692 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37691 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37690 |
| [Kulpa] p. 548 | Theorem | broucube 37693 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37685 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37686 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2383 axnul 5243 |
| [Kunen] p. 11 | Axiom 3 | axnul 5243 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7887 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8762 mapvalg 8760 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10410 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7871 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9654 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9696 r1elssi 9695 |
| [Kunen] p. 107 | Exercise 4 | rankop 9748 rankopb 9742 rankuni 9753 rankxplim 9769 rankxpsuc 9772 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44986 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44994 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44993 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44995 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45000 rexabso 45001 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45007 n0abso 45008 ssabso 45006 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45009 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45019 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45014 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45017 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45018 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45013 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45025 wfaxpr 45030 wfaxreg 45032 wfaxrep 45026 wfaxsep 45027 wfaxun 45031 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45016 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45029 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45025 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45024 omelaxinf2 45021 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45034 wfaxinf2 45033 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45047 permaxext 45037 permaxinf2 45045 permaxnul 45040 permaxpow 45041 permaxpr 45042 permaxrep 45038 permaxsep 45039 permaxun 45043 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45035 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45046 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4954 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33673 |
| [Lang] p. | Definition | df-rn 5627 |
| [Lang] p. 3 | Statement | lidrideqd 18574 mndbn0 18655 |
| [Lang] p. 3 | Definition | df-mnd 18640 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18592 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18746 |
| [Lang] p. 5 | Equation | gsumreidx 19827 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48212 |
| [Lang] p. 6 | Example | nn0mnd 48209 |
| [Lang] p. 6 | Equation | gsumxp2 19890 |
| [Lang] p. 6 | Statement | cycsubm 19112 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18990 |
| [Lang] p. 6 | Observation | mndlsmidm 19580 |
| [Lang] p. 7 | Definition | dfgrp2e 18873 |
| [Lang] p. 30 | Definition | df-tocyc 33071 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33116 |
| [Lang] p. 32 | Property (b) | cyc3conja 33121 cycpmconjv 33106 |
| [Lang] p. 53 | Definition | df-cat 17571 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18001 cat1lem 18000 |
| [Lang] p. 54 | Definition | df-iso 17653 |
| [Lang] p. 57 | Definition | df-inito 17888 df-termo 17889 |
| [Lang] p. 58 | Example | irinitoringc 21414 |
| [Lang] p. 58 | Statement | initoeu1 17915 termoeu1 17922 |
| [Lang] p. 62 | Definition | df-func 17762 |
| [Lang] p. 65 | Definition | df-nat 17850 |
| [Lang] p. 91 | Note | df-ringc 20559 |
| [Lang] p. 92 | Statement | mxidlprm 33430 |
| [Lang] p. 92 | Definition | isprmidlc 33407 |
| [Lang] p. 128 | Remark | dsmmlmod 21680 |
| [Lang] p. 129 | Proof | lincscm 48461 lincscmcl 48463 lincsum 48460 lincsumcl 48462 |
| [Lang] p. 129 | Statement | lincolss 48465 |
| [Lang] p. 129 | Observation | dsmmfi 21673 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33635 qusdimsum 33636 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33615 |
| [Lang] p. 147 | Definition | snlindsntor 48502 |
| [Lang] p. 504 | Statement | mat1 22360 matring 22356 |
| [Lang] p. 504 | Definition | df-mamu 22304 |
| [Lang] p. 505 | Statement | mamuass 22315 mamutpos 22371 matassa 22357 mattposvs 22368 tposmap 22370 |
| [Lang] p. 513 | Definition | mdet1 22514 mdetf 22508 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22604 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22500 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22524 |
| [Lang] p. 515 | Definition | df-minmar1 22548 smadiadetr 22588 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22523 mdetralt 22521 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22536 |
| [Lang] p. 518 | Definition | df-madu 22547 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22558 madurid 22557 matinv 22590 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22803 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33702 finextalg 33706 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33671 fedgmul 33639 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33733 |
| [Lang], p. 561 | Remark | chpmatply1 22745 |
| [Lang], p. 561 | Definition | df-chpmat 22740 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44366 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44361 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44367 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5243 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2710 |
| [Levy] p. 59 | Definition | df-ttrcl 9598 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9641 |
| [Levy] p. 338 | Axiom | df-clel 2806 df-cleq 2723 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2806 df-cleq 2723 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2710 |
| [Levy] p. 358 | Axiom | df-clab 2710 |
| [Levy58] p. 2 | Definition I | isfin1-3 10274 |
| [Levy58] p. 2 | Definition II | df-fin2 10174 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10173 |
| [Levy58] p. 2 | Definition III | df-fin3 10176 |
| [Levy58] p. 3 | Definition V | df-fin5 10177 |
| [Levy58] p. 3 | Definition IV | df-fin4 10175 |
| [Levy58] p. 4 | Definition VI | df-fin6 10178 |
| [Levy58] p. 4 | Definition VII | df-fin7 10179 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10303 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27623 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27634 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27666 nosupbnd1 27651 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27668 nosupbnd2 27653 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27672 noetasuplem4 27673 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27669 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1769 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1770 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1772 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32383 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32387 mdsymi 32386 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32381 mdsymlem6 32383 mdsymlem7 32384 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32385 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32288 ssdmd2 32289 ssmd1 32286 ssmd2 32287 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32284 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32256 df-md 32255 mdbr 32269 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32306 mdslj1i 32294 mdslj2i 32295 mdslle1i 32292 mdslle2i 32293 mdslmd1i 32304 mdslmd2i 32305 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32296 mdsl2bi 32298 mdsl2i 32297 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32310 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32307 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32308 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32285 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32290 mdsl3 32291 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32309 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32404 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39359 hlrelat1 39438 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39077 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32311 cvmdi 32299 cvnbtwn4 32264 cvrnbtwn4 39317 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32312 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39378 cvp 32350 cvrp 39454 lcvp 39078 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32374 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32373 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39371 hlexch4N 39430 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32376 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39481 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39787 atpsubN 39791 df-pointsN 39540 pointpsubN 39789 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39542 pmap11 39800 pmaple 39799 pmapsub 39806 pmapval 39795 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39803 pmap1N 39805 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39808 pmapglb2N 39809 pmapglb2xN 39810 pmapglbx 39807 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39890 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39515 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39834 paddclN 39880 paddidm 39879 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39516 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39876 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39515 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39516 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19585 lsmmod2 19586 lssats 39050 shatomici 32333 shatomistici 32336 shmodi 31365 shmodsi 31364 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32275 mdsymlem7 32384 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31564 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31468 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32390 |
| [Margaris] p. 40 | Rule C | exlimiv 1931 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1781 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30375 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44946 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44947 |
| [Margaris] p. 79 | Rule C | exinst01 44657 exinst11 44658 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1977 19.2g 2191 r19.2z 4445 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2205 rr19.3v 3622 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2162 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1827 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1782 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2184 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2208 19.9h 2288 exlimd 2221 exlimdh 2292 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2165 excomim 2166 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2328 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30376 conventions-labels 30376 conventions-labels 30376 conventions-labels 30376 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1828 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44410 albi 1819 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2228 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2229 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44412 exbi 1848 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2232 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44409 2alimdv 1919 alimd 2215 alimdh 1818 alimdv 1917 ax-4 1810 ralimdaa 3233 ralimdv 3146 ralimdva 3144 ralimdvva 3179 sbcimdv 3810 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2210 19.21h 2289 19.21t 2209 19.21vv 44408 alrimd 2218 alrimdd 2217 alrimdh 1864 alrimdv 1930 alrimi 2216 alrimih 1825 alrimiv 1928 alrimivv 1929 hbralrimi 3122 r19.21be 3225 r19.21bi 3224 ralrimd 3237 ralrimdv 3130 ralrimdva 3132 ralrimdvv 3176 ralrimdvva 3187 ralrimi 3230 ralrimia 3231 ralrimiv 3123 ralrimiva 3124 ralrimivv 3173 ralrimivva 3175 ralrimivvva 3178 ralrimivw 3128 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44411 2eximdv 1920 exim 1835 eximd 2219 eximdh 1865 eximdv 1918 rexim 3073 reximd2a 3242 reximdai 3234 reximdd 45184 reximddv 3148 reximddv2 3191 reximddv3 3149 reximdv 3147 reximdv2 3142 reximdva 3145 reximdvai 3143 reximdvva 3180 reximi2 3065 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2214 19.23bi 2194 19.23h 2290 19.23t 2213 exlimdv 1934 exlimdvv 1935 exlimexi 44556 exlimiv 1931 exlimivv 1933 rexlimd3 45180 rexlimdv 3131 rexlimdv3a 3137 rexlimdva 3133 rexlimdva2 3135 rexlimdvaa 3134 rexlimdvv 3188 rexlimdvva 3189 rexlimdvvva 3190 rexlimdvw 3138 rexlimiv 3126 rexlimiva 3125 rexlimivv 3174 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1992 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1881 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1871 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2230 r19.27z 4455 r19.27zv 4456 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2231 19.28vv 44418 r19.28z 4448 r19.28zf 45195 r19.28zv 4451 rr19.28v 3623 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1874 r19.29d2r 3119 r19.29imd 3097 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1882 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2237 19.31vv 44416 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2236 r19.32 47128 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44414 19.33 1885 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1993 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1878 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2233 19.36vv 44415 r19.36zv 4457 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2235 19.37vv 44417 r19.37zv 4452 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1840 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1991 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1888 19.40 1887 r19.40 3098 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2238 19.41rg 44582 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2239 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1883 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2240 r19.44zv 4454 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2241 r19.45zv 4453 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2605 |
| [Mayet] p. 370 | Remark | jpi 32245 largei 32242 stri 32232 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32187 ishst 32189 |
| [Mayet3] p. 10 | Theorem | hstrbi 32241 hstri 32240 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31703 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31704 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32253 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31307 chsupcl 31315 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32335 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32329 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32356 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40021 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18390 latj32 18388 latjass 18386 |
| [Megill] p. 444 | Axiom C5 | ax-5 1911 ax5ALT 38945 |
| [Megill] p. 444 | Section 7 | conventions 30375 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38939 ax-c11n 38926 axc11n 2426 |
| [Megill] p. 446 | Lemma L17 | equtrr 2023 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38934 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38966 hbnae 2432 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2481 sbid 2258 sbidd-misc 49750 sbidd 49749 |
| [Megill] p. 448 | Remark 9.6 | axc14 2463 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38922 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38921 sp 2186 |
| [Megill] p. 448 | Scheme C6' | ax-11 2160 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38923 |
| [Megill] p. 448 | Scheme C8' | ax-7 2009 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38928 |
| [Megill] p. 448 | Scheme C10' | ax-6 1968 ax-c10 38924 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38925 |
| [Megill] p. 448 | Scheme C12' | ax-8 2113 |
| [Megill] p. 448 | Scheme C13' | ax-9 2121 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38929 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38927 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38930 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38942 dral1 2439 dral2-o 38968 dral2 2438 drex1 2441 drex2 2442 drsb1 2495 drsb2 2269 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2176 sbequ 2086 sbid2v 2509 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38935 hba1 2295 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46922 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3830 rspsbca 3831 stdpc4 2071 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38922 ra4 3837 stdpc5 2211 |
| [Mendelson] p. 81 | Rule C | exlimiv 1931 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2029 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2253 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3739 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5454 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4348 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4349 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4227 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4284 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4228 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4091 |
| [Mendelson] p. 231 | Definition of union | dfun3 4226 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5392 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4856 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5507 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4568 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5508 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4883 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5766 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6216 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7708 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6312 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8510 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9053 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8974 xpsneng 8975 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 8981 xpcomeng 8982 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 8984 |
| [Mendelson] p. 255 | Definition | brsdom 8897 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8977 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8754 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8959 mapsnend 8958 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9059 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9058 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8806 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8962 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 8978 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10067 djucomen 10066 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10071 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10065 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8446 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8473 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10447 |
| [Mendelson] p. 281 | Definition | df-r1 9654 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9703 |
| [Mendelson] p. 287 | Axiom system MK | ru 3739 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30234 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30269 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30271 vdgn1frgrv3 30272 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30273 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30266 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30259 2pthfrgrrn 30257 2pthfrgrrn2 30258 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31227 |
| [Monk1] p. 22 | Remark | conventions 30375 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30375 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4189 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5723 ssrelf 32593 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5724 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5154 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6210 coi2 6211 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5860 rn0 5866 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6088 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5634 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5869 rnxp 6117 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5715 xp0 6105 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6026 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6023 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7844 imaexg 7843 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6020 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7008 funfvop 6983 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6876 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6887 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6527 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7188 dff13f 7189 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7153 funrnex 7886 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7181 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6174 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4914 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7938 df-1st 7921 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7939 df-2nd 7922 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9744 ranksnb 9717 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9745 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9746 rankunb 9740 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9728 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9654 r1val2 9727 |
| [Monk1] p. 117 | Lemma | zorn2 10394 zorn2g 10391 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9876 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10449 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9871 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1810 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2009 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2180 ax-c15 38927 ax12v2 2182 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38922 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2160 |
| [Monk2] p. 109 | Lemma 15 | equvini 2455 equvinv 2030 eqvinop 5427 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1911 ax5ALT 38945 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2144 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2160 |
| [Monk2] p. 114 | Lemma 21 | sp 2186 |
| [Monk2] p. 114 | Lemma 22 | axc4 2322 hba1-o 38935 hba1 2295 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2156 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2179 nfra2 3342 nfra2w 3268 |
| [Moore] p. 53 | Part I | df-mre 17485 |
| [Munkres] p. 77 | Example 2 | distop 22908 indistop 22915 indistopon 22914 |
| [Munkres] p. 77 | Example 3 | fctop 22917 fctop2 22918 |
| [Munkres] p. 77 | Example 4 | cctop 22919 |
| [Munkres] p. 78 | Definition of basis | df-bases 22859 isbasis3g 22862 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17344 tgval2 22869 |
| [Munkres] p. 79 | Remark | tgcl 22882 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22876 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22900 tgss3 22899 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22901 basgen2 22902 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37382 topdifinfeq 37383 topdifinffin 37381 topdifinfindis 37379 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23073 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22951 topcld 22948 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22952 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22954 |
| [Munkres] p. 94 | Definition of closure | clsval 22950 |
| [Munkres] p. 94 | Definition of interior | ntrval 22949 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22988 elcls 22986 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22996 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23061 neindisj 23030 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23063 |
| [Munkres] p. 97 | Definition of limit point | islp2 23058 lpval 23052 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23228 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23140 iscn 23148 iscn2 23151 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23193 cncnp2 23194 cncnpi 23191 df-cnp 23141 iscnp 23150 iscnp2 23152 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24456 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25236 |
| [Nathanson] p. 123 | Remark | reprgt 34629 reprinfz1 34630 reprlt 34627 |
| [Nathanson] p. 123 | Definition | df-repr 34617 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34649 |
| [Nathanson] p. 123 | Proposition | breprexp 34641 breprexpnat 34642 itgexpif 34614 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32079 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47840 |
| [Pfenning] p. 17 | Definition XM | natded 30378 |
| [Pfenning] p. 17 | Definition NNC | natded 30378 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30378 |
| [Pfenning] p. 18 | Rule" | natded 30378 |
| [Pfenning] p. 18 | Definition /\I | natded 30378 |
| [Pfenning] p. 18 | Definition ` `E | natded 30378 natded 30378 natded 30378 natded 30378 natded 30378 |
| [Pfenning] p. 18 | Definition ` `I | natded 30378 natded 30378 natded 30378 natded 30378 natded 30378 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30378 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30378 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30378 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30378 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30378 |
| [Pfenning] p. 127 | Definition =E | natded 30378 |
| [Pfenning] p. 127 | Definition =I | natded 30378 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25127 df-dip 30676 dip0l 30693 ip0l 21571 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25168 ipval 30678 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30689 ipcj 21569 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25130 dipdir 30817 ipdir 21574 ipdiri 30805 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30685 nmsq 25119 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30800 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30802 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30803 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25136 dipass 30820 ipass 21580 ipassi 30816 |
| [Prugovecki] p. 186 | Definition of bra | braval 31919 df-bra 31825 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31826 kbval 31929 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32357 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39926 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32371 atcvat4i 32372 cvrat3 39480 cvrat4 39481 lsatcvat3 39090 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32257 cvrval 39307 df-cv 32254 df-lcv 39057 lspsncv0 21081 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39938 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39939 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2710 rabid 3416 rabidd 45191 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2281 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2723 |
| [Quine] p. 19 | Definition 2.9 | conventions 30375 df-v 3438 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2870 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2867 abid2f 2925 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2278 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2088 sbalex 2245 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2806 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2731 eqid1 30442 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2738 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3742 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3743 dfsbcq2 3744 |
| [Quine] p. 43 | Theorem 6.8 | vex 3440 |
| [Quine] p. 43 | Theorem 6.9 | isset 3450 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3546 spcgv 3551 spcimgf 3505 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3754 spsbcd 3755 |
| [Quine] p. 44 | Theorem 6.12 | elex 3457 |
| [Quine] p. 44 | Theorem 6.13 | elab 3635 elabg 3632 elabgf 3630 |
| [Quine] p. 44 | Theorem 6.14 | noel 4288 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4670 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4579 df-sn 4577 |
| [Quine] p. 49 | Theorem 7.4 | snss 4737 snssg 4736 |
| [Quine] p. 49 | Theorem 7.5 | prss 4772 prssg 4771 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4715 prid1g 4713 prid2 4716 prid2g 4714 snid 4615 snidg 4613 |
| [Quine] p. 51 | Theorem 7.12 | snex 5374 |
| [Quine] p. 51 | Theorem 7.13 | prex 5375 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4878 unisnALT 44957 unisng 4877 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4882 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4889 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4887 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6451 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47116 dfiota2 6438 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47125 iotaval 6455 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6461 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6457 |
| [Quine] p. 58 | Definition 9.1 | df-op 4583 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5465 opabidw 5464 opelopab 5482 opelopaba 5476 opelopabaf 5484 opelopabf 5485 opelopabg 5478 opelopabga 5473 opelopabgf 5480 oprabid 7378 oprabidw 7377 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5622 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5624 |
| [Quine] p. 64 | Definition 9.15 | df-id 5511 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6546 |
| [Quine] p. 65 | Theorem 10.4 | funi 6513 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6534 funsng 6532 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6483 |
| [Quine] p. 65 | Definition 10.2 | args 6041 dffv4 6819 |
| [Quine] p. 68 | Definition 10.11 | conventions 30375 df-fv 6489 fv2 6817 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14176 nn0opth2i 14175 nn0opthi 14174 omopthi 8576 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8329 |
| [Quine] p. 232 | Equation i | carddom 10442 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6569 funimaexg 6568 |
| [Quine] p. 331 | Axiom system NF | ru 3739 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31059 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30676 polid 31134 polid2i 31132 polidi 31133 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30788 |
| [ReedSimon] p. 195 | Remark | lnophm 31994 lnophmi 31993 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32107 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32109 leopmuli 32108 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32112 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31827 leoppos 32101 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32111 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32100 |
| [Roman] p. 4 | Definition | df-dmat 22403 df-dmatalt 48429 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20069 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20151 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48516 |
| [Roman] p. 112 | Note | isldepslvec2 48516 ldepsnlinc 48539 zlmodzxznm 48528 |
| [Roman] p. 112 | Example | zlmodzxzequa 48527 zlmodzxzequap 48530 zlmodzxzldep 48535 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22803 |
| [Rosenlicht] p. 80 | Theorem | heicant 37694 |
| [Rosser] p. 281 | Definition | df-op 4583 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34653 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34654 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48396 pmtr3ncom 19385 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19381 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19324 cayleyth 19325 |
| [Rudin] p. 164 | Equation 27 | efcan 16000 |
| [Rudin] p. 164 | Equation 30 | efzval 16008 |
| [Rudin] p. 167 | Equation 48 | absefi 16102 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1772 |
| [Sanford] p. 39 | Rule 4 | mptxor 1770 |
| [Sanford] p. 40 | Rule 1 | mptnan 1769 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6062 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6065 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6061 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6059 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17485 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17486 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17486 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17488 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10025 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43094 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10334 axdc3 10342 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20153 isrngo 37936 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31517 |
| [Schechter] p. 276 | Definition of span | df-span 31284 spanval 31308 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22906 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6331 onelord 43283 ordelon 6330 ordelord 6328 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43284 sucidg 6389 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6361 onsuc 7743 ord0 6360 ordsuci 7741 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43285 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5202 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43060 elon2 6317 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6312 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5519 epelg 5517 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9485 epirron 43286 ordirr 6324 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43288 oneptr 43287 ontr1 6353 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6349 oneptri 43289 ordtri3or 6338 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8416 ord0eln0 6362 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6375 onsucss 43298 trsucss 6396 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7748 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6402 ordnbtwn 6401 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43300 ordnexbtwnsuc 43299 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10289 onsucf1lem 43301 onsucf1o 43304 onsucf1olem 43302 onsucrn 43303 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43305 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7775 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43294 ordne0gt0 43293 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43296 limnsuc 43297 onsucelab 43295 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9533 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7790 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9536 ordom 7806 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9537 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8555 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7713 ssorduni 7712 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8446 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9540 limom 7812 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8385 df1o2 8392 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8431 oa0suclim 43307 oalim 8447 oasuc 8439 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8432 om0suclim 43308 omlim 8448 omsuc 8441 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8437 oe0m1 8436 oe0suclim 43309 oelim 8449 oesuc 8442 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43261 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43311 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43312 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43313 limexissupab 43315 limiun 43314 limuni 6368 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8453 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8457 om1om1r 43316 om1r 8458 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8450 oaomoecl 43310 oecl 8452 omcl 8451 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43263 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8459 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8460 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43317 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43318 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8526 nnamecl 43319 nnecl 8528 nnmcl 8527 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43320 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8467 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8468 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8475 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43322 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43323 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43325 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8474 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43329 omword1 8488 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43328 oaordnrex 43327 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43324 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43330 omword2 8489 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43331 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43332 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43333 omordi 8481 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8483 omord2com 43334 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43335 df-2o 8386 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43338 oewordi 8506 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43339 oeworde 8508 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43340 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43341 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43337 omnord1ex 43336 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43342 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43344 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43348 oenord1ex 43347 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43349 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8476 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43343 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8494 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8495 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43351 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8512 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43352 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43353 cantnfub2 43354 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43357 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28890 axtgcgrrflx 28438 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28891 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28892 axtgcgrid 28439 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28424 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28903 axtgsegcon 28440 df-trkgcb 28426 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28914 axtg5seg 28441 df-trkgcb 28426 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28915 axtgbtwnid 28442 df-trkgb 28425 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28917 axtgpasch 28443 df-trkgb 28425 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28936 df-trkg2d 34673 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28446 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28447 df-trkg2d 34673 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28939 axtgeucl 28448 df-trkge 28427 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28952 axtgcont 28445 axtgcont1 28444 df-trkgb 28425 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36020 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36022 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36025 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36029 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36030 tgcgrcomimp 28453 tgcgrcoml 28455 tgcgrcomr 28454 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36035 tgcgrtriv 28460 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36039 tg5segofs 34681 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34678 df-ofs 36016 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36041 tgcgrextend 28461 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36043 tgsegconeq 28462 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36055 btwntriv2 36045 tgbtwntriv2 28463 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36046 tgbtwncom 28464 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36049 tgbtwntriv1 28467 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36050 tgbtwnswapid 28468 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36056 btwnintr 36052 tgbtwnexch2 28472 tgbtwnintr 28469 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36058 btwnexch3 36053 tgbtwnexch 28474 tgbtwnexch3 28470 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36057 tgbtwnouttr 28473 tgbtwnouttr2 28471 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28935 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36060 tgbtwndiff 28482 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28475 trisegint 36061 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36077 tgifscgr 28484 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28534 colrot1 28535 colrot2 28536 lncom 28598 lnrot1 28599 lnrot2 28600 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36073 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36078 tgcgrsub 28485 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36088 tgcgrxfr 28494 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28493 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36074 df-cgrg 28487 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28487 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36089 tgbtwnxfr 28506 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36095 colinearperm2 36097 colinearperm3 36096 colinearperm4 36098 colinearperm5 36099 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28509 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36072 tgellng 28529 tglng 28522 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36100 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36108 lnxfr 28542 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36109 lnext 28543 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36113 tgfscgr 28544 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36114 lncgr 28545 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36075 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36116 lnid 28546 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36117 tgidinside 28547 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36134 tgbtwnconn1 28551 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36135 tgbtwnconn2 28552 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36136 tgbtwnconn3 28553 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36142 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36140 legov 28561 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28562 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28575 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36143 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36145 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36147 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36148 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36149 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36146 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36151 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28563 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28565 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28566 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28567 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28568 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36158 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36159 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36154 df-outsideof 36153 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36155 ishlg 28578 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28583 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28585 outsideofrflx 36160 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28579 hlcomd 28580 outsideofcom 36161 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28586 outsideoftr 36162 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28594 outsideofeu 36164 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36171 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36172 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36165 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36180 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36181 tglineelsb2 28608 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36183 linerflx1 36182 linerflx2 36184 tglinecom 28611 tglinerflx1 28609 tglinerflx2 28610 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36186 tglinethru 28612 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36170 tglng 28522 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28570 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36189 tglinethrueu 28615 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36190 tglineineq 28619 tglineinteq 28621 tglineintmo 28618 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28625 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28626 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28627 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28642 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28638 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28630 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28629 ismir 28635 mirbtwn 28634 mircgr 28633 mirfv 28632 mirval 28631 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28640 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28641 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28642 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28645 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28646 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28651 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28648 mirbtwni 28647 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28649 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28661 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28665 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28662 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28663 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28664 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28667 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28668 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28674 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28670 israg 28673 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28675 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28676 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28678 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28679 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28680 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28681 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28682 ragncol 28685 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28683 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28689 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28693 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28690 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28672 isperp 28688 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28691 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28698 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28706 colperpexlem2 28707 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28709 colperpexlem3 28708 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28714 midex 28713 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28711 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28720 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28715 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28724 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28727 opphllem6 28728 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28730 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28443 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28731 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28739 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28734 hpgbr 28736 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28741 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28740 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28742 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28743 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28744 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28745 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28746 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28760 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28750 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28764 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28765 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28766 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28767 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28768 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28771 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28773 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28751 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28774 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28777 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28778 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28779 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28780 trgcopyeu 28782 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28806 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28785 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28794 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28792 cgrahl2 28793 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28795 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28796 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28798 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28799 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28802 cgrahl 28803 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28807 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28808 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28809 acopyeu 28810 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28817 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28821 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28814 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28829 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28822 isleag 28823 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28831 tgsas1 28830 tgsas2 28832 tgsas3 28833 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28835 tgasa1 28834 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28836 tgsss2 28837 tgsss3 28838 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27207 dchrsum 27205 dchrsum2 27204 sumdchr 27208 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27209 sum2dchr 27210 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19978 ablfacrp2 19979 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27152 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27153 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27160 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27418 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27421 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27475 vmalogdivsum2 27474 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27465 dirith2 27464 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27463 rpvmasum 27462 rpvmasum2 27448 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27423 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27461 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27428 dchrisumlem1 27425 dchrisumlem2 27426 dchrisumlem3 27427 dchrisumlema 27424 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27431 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27460 dchrmusumlem 27458 dchrvmasumlem 27459 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27430 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27432 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27456 dchrisum0re 27449 dchrisumn0 27457 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27442 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27446 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27447 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27502 pntrsumbnd2 27503 pntrsumo1 27501 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27466 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27468 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27470 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27473 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27478 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27479 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27484 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27486 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27487 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27495 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27496 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27493 selberg3lem2 27494 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27497 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27491 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27504 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27505 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27506 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27520 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27532 pntlemb 27533 pntlemc 27531 pntlemd 27530 pntlemg 27534 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27532 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27524 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27529 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27532 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27545 pntleml 27547 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33751 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33738 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33770 constrinvcl 33781 constrmulcl 33779 constrnegcl 33771 constrsqrtcl 33787 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33757 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33767 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33789 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33799 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4256 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4355 dif0 4328 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4442 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4425 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4247 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4248 |
| [Stoll] p. 20 | Remark | invdif 4229 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4585 |
| [Stoll] p. 43 | Definition | uniiun 5007 |
| [Stoll] p. 44 | Definition | intiin 5008 |
| [Stoll] p. 45 | Definition | df-iin 4944 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4943 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4256 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44367 |
| [Suppes] p. 22 | Theorem 2 | eq0 4300 eq0f 4297 |
| [Suppes] p. 22 | Theorem 4 | eqss 3950 eqssd 3952 eqssi 3951 |
| [Suppes] p. 23 | Theorem 5 | ss0 4352 ss0b 4351 |
| [Suppes] p. 23 | Theorem 6 | sstr 3943 sstrALT2 44866 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4053 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4054 |
| [Suppes] p. 23 | Theorem 9 | psstr 4057 |
| [Suppes] p. 23 | Theorem 10 | pssss 4048 |
| [Suppes] p. 25 | Theorem 12 | elin 3918 elun 4103 |
| [Suppes] p. 26 | Theorem 15 | inidm 4177 |
| [Suppes] p. 26 | Theorem 16 | in0 4345 |
| [Suppes] p. 27 | Theorem 23 | unidm 4107 |
| [Suppes] p. 27 | Theorem 24 | un0 4344 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4128 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4136 |
| [Suppes] p. 27 | Theorem 27 | unss 4140 |
| [Suppes] p. 27 | Theorem 28 | indir 4236 |
| [Suppes] p. 27 | Theorem 29 | undir 4237 |
| [Suppes] p. 28 | Theorem 32 | difid 4326 |
| [Suppes] p. 29 | Theorem 33 | difin 4222 |
| [Suppes] p. 29 | Theorem 34 | indif 4230 |
| [Suppes] p. 29 | Theorem 35 | undif1 4426 |
| [Suppes] p. 29 | Theorem 36 | difun2 4431 |
| [Suppes] p. 29 | Theorem 37 | difin0 4424 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4422 |
| [Suppes] p. 29 | Theorem 39 | difundi 4240 |
| [Suppes] p. 29 | Theorem 40 | difindi 4242 |
| [Suppes] p. 30 | Theorem 41 | nalset 5251 |
| [Suppes] p. 39 | Theorem 61 | uniss 4867 |
| [Suppes] p. 39 | Theorem 65 | uniop 5455 |
| [Suppes] p. 41 | Theorem 70 | intsn 4934 |
| [Suppes] p. 42 | Theorem 71 | intpr 4932 intprg 4931 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5411 |
| [Suppes] p. 42 | Theorem 78 | intun 4930 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4982 dfiun2g 4980 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4983 |
| [Suppes] p. 47 | Theorem 86 | elpw 4554 elpw2 5272 elpw2g 5271 elpwg 4553 elpwgdedVD 44948 |
| [Suppes] p. 47 | Theorem 87 | pwid 4572 |
| [Suppes] p. 47 | Theorem 89 | pw0 4764 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4765 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5631 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5773 xpindir 5774 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5685 xpundir 5686 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9483 |
| [Suppes] p. 58 | Theorem 2 | relss 5722 |
| [Suppes] p. 59 | Theorem 4 | eldm 5840 eldm2 5841 eldm2g 5839 eldmg 5838 |
| [Suppes] p. 59 | Definition 3 | df-dm 5626 |
| [Suppes] p. 60 | Theorem 6 | dmin 5851 |
| [Suppes] p. 60 | Theorem 8 | rnun 6092 |
| [Suppes] p. 60 | Theorem 9 | rnin 6093 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5828 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5822 brcnvg 5819 |
| [Suppes] p. 62 | Equation 5 | elcnv 5816 elcnv2 5817 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6053 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6091 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6089 |
| [Suppes] p. 63 | Definition | dftrrels2 38611 |
| [Suppes] p. 63 | Theorem 20 | co02 6208 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5914 |
| [Suppes] p. 63 | Definition 7 | df-co 5625 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5825 |
| [Suppes] p. 64 | Theorem 27 | coass 6213 |
| [Suppes] p. 65 | Theorem 31 | resundi 5942 |
| [Suppes] p. 65 | Theorem 34 | elima 6014 elima2 6015 elima3 6016 elimag 6013 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6096 |
| [Suppes] p. 66 | Theorem 40 | dminss 6100 |
| [Suppes] p. 66 | Theorem 41 | imainss 6101 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6104 |
| [Suppes] p. 81 | Definition 34 | dfec2 8625 |
| [Suppes] p. 82 | Theorem 72 | elec 8668 elecALTV 38300 elecg 8666 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38647 erth 8676 erth2 8677 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38650 erdisj 8679 |
| [Suppes] p. 83 | Definition 35, | df-parts 38802 dfmembpart2 38807 |
| [Suppes] p. 89 | Theorem 96 | map0b 8807 |
| [Suppes] p. 89 | Theorem 97 | map0 8811 map0g 8808 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8812 mapsnd 8810 |
| [Suppes] p. 89 | Theorem 99 | mapss 8813 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9956 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9955 |
| [Suppes] p. 92 | Theorem 1 | enref 8907 enrefg 8906 |
| [Suppes] p. 92 | Theorem 2 | ensym 8925 ensymb 8924 ensymi 8926 |
| [Suppes] p. 92 | Theorem 3 | entr 8928 |
| [Suppes] p. 92 | Theorem 4 | unen 8967 |
| [Suppes] p. 94 | Theorem 15 | endom 8901 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8922 |
| [Suppes] p. 94 | Theorem 17 | domtr 8929 |
| [Suppes] p. 95 | Theorem 18 | sbth 9010 |
| [Suppes] p. 97 | Theorem 23 | canth2 9043 canth2g 9044 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9014 df-sdom 8872 dfsdom2 9013 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9027 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9016 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9015 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9025 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8904 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9028 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9023 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8953 fundmeng 8954 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 8988 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9024 |
| [Suppes] p. 104 | Theorem 37 | fofi 9197 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9203 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9203 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10439 |
| [Suppes] p. 130 | Definition 3 | df-tr 5199 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7713 |
| [Suppes] p. 134 | Definition 6 | df-suc 6312 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7830 finds 7826 finds1 7829 finds2 7828 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9542 isfinite2 9182 isfiniteg 9184 unbnn 9180 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10806 df-ltpq 10798 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7793 tfinds 7790 tfinds2 7794 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8466 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8468 |
| [Suppes] p. 211 | Theorem 25 | oaass 8476 |
| [Suppes] p. 225 | Definition 8 | iscard2 9866 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10451 |
| [Suppes] p. 228 | Theorem 59 | harcard 9868 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9954 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6358 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7726 onminsb 7727 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10460 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9958 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9965 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9959 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9830 |
| [Suppes] p. 242 | Theorem 6 | weth 10383 |
| [Suppes] p. 242 | Theorem 8 | entric 10445 |
| [Suppes] p. 242 | Theorem 9 | carden 10439 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35728 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35732 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2703 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2723 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2806 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2725 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2751 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7350 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3739 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5359 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4601 elpr2 4603 elpr2g 4602 elprg 4599 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4591 elsn2 4618 elsn2g 4617 elsng 4590 velsn 4592 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5407 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4586 sneqr 4792 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4597 dfsn2 4589 dfsn2ALT 4598 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7674 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5416 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5404 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5389 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7677 unexg 7676 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4644 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4860 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3909 df-un 3907 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4876 uniprg 4875 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5315 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4642 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6378 elsucg 6376 sstr2 3941 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4108 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4159 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4122 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4178 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4234 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4235 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3922 df-ss 3919 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4552 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4137 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3920 sseqin2 4173 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3957 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4187 inss2 4188 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3999 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4870 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5390 sspwimp 44949 sspwimpALT 44956 sspwimpALT2 44959 sspwimpcf 44951 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5397 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5217 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3396 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5245 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3905 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4286 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4326 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4303 n0f 4299 neq0 4302 neq0f 4298 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9482 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9622 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9624 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3438 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5253 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4350 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5259 ssexg 5261 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5255 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9491 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9485 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4316 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4085 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4250 undif3VD 44913 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4086 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4093 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3048 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3057 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7686 xpexg 7683 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5623 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6552 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6728 fun11 6555 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6494 svrelfun 6553 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5827 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5829 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5628 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5629 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5625 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6141 dfrel2 6136 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5632 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5751 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5758 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5771 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5954 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5934 opelresi 5936 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5961 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5950 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5955 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6523 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6057 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6521 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6730 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2604 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30375 df-fv 6489 fv3 6840 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7855 cnvexg 7854 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7839 dmexg 7831 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7840 rnexg 7832 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44485 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7850 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6835 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47204 tz6.12-1-afv2 47271 tz6.12-1 6845 tz6.12-afv 47203 tz6.12-afv2 47270 tz6.12 6846 tz6.12c-afv2 47272 tz6.12c 6844 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47267 tz6.12-2 6809 tz6.12i-afv2 47273 tz6.12i 6848 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6484 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6485 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6487 wfo 6479 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6486 wf1 6478 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6488 wf1o 6480 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6964 eqfnfv2 6965 eqfnfv2f 6968 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6920 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7151 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7149 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6569 funimaexg 6568 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5092 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5525 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5577 dffr3 6048 eliniseg 6043 iniseg 6046 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5516 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5593 fr3nr 7705 frirr 5592 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5569 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7707 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5580 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5602 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6294 tz6.26i 6295 wefrc 5610 wereu2 5613 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6296 wfii 6297 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6490 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7263 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7264 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7270 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7271 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7272 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7276 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7283 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7285 |
| [TakeutiZaring] p. 35 | Notation | wtr 5198 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44486 tz7.2 5599 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5203 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6319 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6327 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6328 ordelordALT 44569 ordelordALTVD 44898 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6334 ordelssne 6333 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6332 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6336 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7715 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7716 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6310 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6338 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44581 ordon 7710 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7711 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7783 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6354 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5200 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7725 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7761 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6412 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6411 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7712 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4889 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6312 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6388 sucidg 6389 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7743 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6402 ordnbtwn 6401 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7758 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6311 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7811 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7816 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7771 ordelsuc 7750 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7752 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7781 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7798 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7819 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7820 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7821 |
| [TakeutiZaring] p. 43 | Remark | omon 7808 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9525 omex 9533 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7806 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7825 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7822 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7823 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7801 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4912 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5216 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4913 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5282 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7728 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6357 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4898 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9550 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7723 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8295 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8316 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8317 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8318 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8325 tz7.44-2 8326 tz7.44-3 8327 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8287 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8282 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8266 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8364 tz7.49c 8365 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8362 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8361 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8363 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2651 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9899 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9900 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8447 oasuc 8439 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7791 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8450 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8431 oa0r 8453 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8451 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8463 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8534 nnaordi 8533 oaord 8462 oaordi 8461 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4998 uniss2 4892 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8465 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8470 oawordex 8472 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8526 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8563 |
| [TakeutiZaring] p. 60 | Remark | oancom 9541 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8475 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8531 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8467 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8434 omlim 8448 omsuc 8441 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8432 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8528 nnmcl 8527 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8547 nnmordi 8546 omord 8483 omordi 8481 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8484 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8551 omwordri 8487 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8454 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8457 om1r 8458 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8490 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8492 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8493 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8494 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8495 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8523 oe0 8437 oelim 8449 oesuc 8442 onesuc 8445 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8435 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8501 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8502 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8436 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8460 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8503 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8509 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8507 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8508 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8512 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8514 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9618 tz9.1 9619 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9654 r10 9658 r1lim 9662 r1limg 9661 r1suc 9660 r1sucg 9659 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9670 r1ord2 9671 r1ordg 9668 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9680 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9705 tz9.13 9681 tz9.13g 9682 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9655 rankval 9706 rankvalb 9687 rankvalg 9707 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9729 rankelb 9714 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9743 rankval3 9730 rankval3b 9716 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9719 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9685 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9724 rankr1c 9711 rankr1g 9722 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9725 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9739 rankssb 9738 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9732 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9731 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10363 dfac3 10009 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9918 numth 10360 numth2 10359 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10434 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10435 cardid2 9843 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9850 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10439 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9849 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9834 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9855 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9847 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9063 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8940 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9068 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 8992 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9853 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 9986 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9115 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9123 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 9987 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9120 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 9976 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9954 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9862 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10104 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9207 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8873 isfi 8898 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9124 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10422 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 8985 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10414 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10074 unxpdom 9143 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9864 cardsdomelir 9863 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9145 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9902 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8752 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10450 infxpidm2 9905 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10095 infxp 10102 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 8997 pw2f1o 8995 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9056 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10375 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10370 ac6s5 10379 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10431 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10432 uniimadomf 10433 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10162 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10157 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10142 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10139 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10145 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10152 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10161 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10470 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10140 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10164 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 9985 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 9984 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 9996 alephfp2 9997 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10587 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10000 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10457 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10471 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10472 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38921 |
| [Tarski] p. 67 | Scheme B5 | sp 2186 |
| [Tarski] p. 68 | Lemma 6 | avril1 30438 equid 2013 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2018 |
| [Tarski] p. 70 | Lemma 14 | spim 2387 spime 2389 spimew 1972 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2180 ax-c15 38927 ax12i 1967 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2088 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1969 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1911 ax5ALT 38945 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2009 ax-8 2113 ax-9 2121 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28440 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28441 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28443 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28443 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28444 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16149 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37698 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37700 |
| [Weierstrass] p. 272 | Definition | df-mdet 22498 mdetuni 22535 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 903 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 919 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 969 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37478 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43832 imim2 58 wl-luk-imim2 37473 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47049 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2658 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37476 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 894 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 44958 wl-luk-notnotr 37477 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43862 axfrege28 43861 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 924 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37470 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 889 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 941 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30376 pm2.27 42 wl-luk-pm2.27 37468 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 922 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38390 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 923 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 971 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 970 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1087 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 944 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 881 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 942 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 891 pm2.67 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 898 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 900 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 802 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 962 pm3.44 961 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 965 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 904 pm4.25 905 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1009 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 870 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 921 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 917 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 978 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1088 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1007 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1053 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1024 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 998 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1000 pm4.45 999 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 853 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 985 pm4.56 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 991 pm4.57 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 856 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 951 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 936 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 963 pm4.77 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 934 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1005 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1025 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 843 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 946 pm5.11g 945 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 947 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 949 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 948 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1013 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 901 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 955 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1006 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 950 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1002 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1029 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1030 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44390 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44391 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1871 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44392 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44393 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44394 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1894 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44395 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44396 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44397 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44398 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44399 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44401 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44402 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44403 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44400 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2093 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44406 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44407 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2073 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2163 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1830 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1831 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44408 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44409 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44410 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44411 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44413 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44412 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1888 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44415 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44416 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44414 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1829 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44417 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44418 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1847 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44419 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2346 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1861 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44424 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44420 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44421 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44422 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44423 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44428 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44425 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44426 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44427 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44429 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2564 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44439 pm13.13b 44440 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44441 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3009 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3010 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3621 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44447 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44448 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44442 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44584 pm13.193 44443 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44444 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44445 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44446 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44453 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44452 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44451 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3804 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44454 pm14.122b 44455 pm14.122c 44456 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44457 pm14.123b 44458 pm14.123c 44459 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44461 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44460 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44462 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6462 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44463 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6463 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44464 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44466 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2628 eupickbi 2631 sbaniota 44467 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44465 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2579 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44468 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30375 df-fv 6489 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9891 pm54.43lem 9890 |
| [Young] p. 141 | Definition of operator ordering | leop2 32099 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32105 idleop 32106 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42860 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42867 pellexlem1 42861 |