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 17609 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17609 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18018 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17630 0funcg 49067 df-termc 49455 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49532 prsthinc 49446 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49560 df-mndtc 49560 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49556 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17653 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49548 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49573 oppgoppchom 49572 oppgoppcid 49574 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17723 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17711 invisoinvl 17732 |
| [Adamek] p. 28 | Example 3.13 | idinv 17731 idiso 17730 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17716 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17690 df-iso 17691 dfiso2 17714 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17697 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17748 cicerALT 49028 |
| [Adamek] p. 29 | Definition 3.15 | cic 17741 df-cic 17738 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17800 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17712 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17713 isoco 17719 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17800 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17823 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49286 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17816 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49556 discthing 49443 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49400 prsthinc 49446 thincciso 49435 thincciso2 49437 thincciso3 49438 thinccisod 49436 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49560 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17830 cofucla 49078 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49144 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18053 catcisoi 49382 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18108 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17849 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17848 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18108 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17873 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17879 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17878 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18093 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18093 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49114 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49105 funcoppc 17817 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18041 elcatchom 49379 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17867 fthoppf 49146 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17866 fulloppf 49145 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18050 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49067 df-catc 18041 |
| [Adamek] p. 45 | Exercise 3G | incat 49583 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49586 nelsubc3 49053 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49133 imasubc2 49134 imasubc3 49138 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17780 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17781 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49053 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17792 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17754 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49142 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49141 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49143 ressffth 17882 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49584 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17888 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17909 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17913 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17889 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17915 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49067 df-inito 17926 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49067 df-termc 49455 initc 49073 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21421 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17927 oppctermo 49218 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17954 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17958 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49219 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17928 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21422 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17961 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17689 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49451 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49450 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49415 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17724 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17726 |
| [Adamek] p. 185 | Section 10.67 | updjud 9863 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49627 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49627 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49627 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49628 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49628 |
| [Adamek] p. 478 | Item Rng | df-ringc 20566 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48530 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48552 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14512 df-pfx 14612 df-substr 14582 df-word 14455 lencl 14474 wrd0 14480 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24629 df-nmoo 30724 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32132 hmopidmchi 32130 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32180 pjcmul2i 32181 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31897 unoplin 31899 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31898 unopadj2 31917 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31992 lnopunii 31991 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32065 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27875 |
| [Alling] p. 184 | Axiom B | bdayfo 27622 |
| [Alling] p. 184 | Axiom O | sltso 27621 |
| [Alling] p. 184 | Axiom SD | nodense 27637 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27724 |
| [Alling] p. 185 | Theorem | conway 27745 |
| [Alling] p. 185 | Axiom FE | noeta 27688 |
| [Alling] p. 186 | Theorem 4 | slerec 27765 slerecd 27766 |
| [Alling], p. 2 | Definition | rp-brsslt 43405 |
| [Alling], p. 3 | Note | nla0001 43408 nla0002 43406 nla0003 43407 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11334 addcan2d 11354 addcan2i 11344 addcand 11353 addcani 11343 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11387 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11446 negsubd 11515 negsubi 11476 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11448 negnegd 11500 negnegi 11468 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11587 subdid 11610 subdii 11603 subdir 11588 subdird 11611 subdiri 11604 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11329 mul01d 11349 mul01i 11340 mul02 11328 mul02d 11348 mul02i 11339 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11791 mulcan2d 11788 mulcand 11787 mulcani 11793 |
| [Apostol] p. 18 | Theorem I.8 | receu 11799 xreceu 32892 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11829 divrecd 11937 divreci 11903 divreczi 11896 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11855 recreci 11890 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11794 mul0ord 11802 mul0ori 11801 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11593 mul2negd 11609 mul2negi 11602 mulneg1 11590 mulneg1d 11607 mulneg1i 11600 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11873 divadddivd 11978 divadddivi 11920 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11858 divmuldivd 11975 divmuldivi 11918 rdivmuldivd 20333 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11859 divdivdivd 11981 divdivdivi 11921 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12951 rpaddcld 12986 rpmulcl 12952 rpmulcld 12987 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12961 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12964 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11276 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11747 ltadd1dd 11765 ltadd1i 11708 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12008 ltmul1a 12007 ltmul1i 12077 ltmul1ii 12087 ltmul2 12009 ltmul2d 13013 ltmul2dd 13027 ltmul2i 12080 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11674 msqgt0d 11721 msqgt0i 11691 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11676 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11660 lt0neg1d 11723 ltneg 11654 ltnegd 11732 ltnegi 11698 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11639 lt2addd 11777 lt2addi 11716 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12928 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12004 recgt0d 12093 recgt0i 12064 recgt0ii 12065 |
| [Apostol] p. 22 | Definition of integers | df-z 12506 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12176 |
| [Apostol] p. 22 | Definition of rationals | df-q 12884 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9381 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12414 |
| [Apostol] p. 26 | Theorem I.29 | arch 12415 archd 45149 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12613 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12416 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12882 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12881 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13135 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16285 zneo 12593 zneoALTV 47663 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26672 msqsqrtd 15385 resqrtth 15197 sqrtth 15307 sqrtthi 15313 sqsqrtd 15384 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12165 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12848 |
| [Apostol] p. 361 | Remark | crreczi 14169 |
| [Apostol] p. 363 | Remark | absgt0i 15342 |
| [Apostol] p. 363 | Example | abssubd 15398 abssubi 15346 |
| [ApostolNT] p. 7 | Remark | fmtno0 47534 fmtno1 47535 fmtno2 47544 fmtno3 47545 fmtno4 47546 fmtno5fac 47576 fmtnofz04prm 47571 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47522 |
| [ApostolNT] p. 8 | Definition | df-ppi 27043 |
| [ApostolNT] p. 14 | Definition | df-dvds 16199 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16215 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16240 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16235 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16230 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16216 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16217 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16222 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16257 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16259 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16261 |
| [ApostolNT] p. 15 | Definition | df-gcd 16441 dfgcd2 16492 |
| [ApostolNT] p. 16 | Definition | isprm2 16628 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16599 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16862 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16459 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16493 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16495 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16474 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16466 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16657 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16659 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16875 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16869 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16349 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16533 |
| [ApostolNT] p. 24 | Definition | df-mu 27044 |
| [ApostolNT] p. 25 | Definition | df-phi 16712 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27134 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16737 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16722 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16726 |
| [ApostolNT] p. 32 | Definition | df-vma 27041 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27136 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27160 |
| [ApostolNT] p. 38 | Remark | df-sgm 27045 |
| [ApostolNT] p. 38 | Definition | df-sgm 27045 |
| [ApostolNT] p. 75 | Definition | df-chp 27042 df-cht 27040 |
| [ApostolNT] p. 104 | Definition | congr 16610 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16202 |
| [ApostolNT] p. 106 | Definition | moddvds 16209 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16292 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16293 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13826 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13866 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14179 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16234 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16613 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17021 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16615 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16729 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16748 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16730 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27015 |
| [ApostolNT] p. 179 | Definition | df-lgs 27239 lgsprme0 27283 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27284 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27260 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27275 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27332 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27351 2lgsoddprm 27360 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27318 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27327 |
| [ApostolNT] p. 188 | Definition | df-lgs 27239 lgs1 27285 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27276 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27278 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27286 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27287 |
| [Baer] p. 40 | Property (b) | mapdord 41625 |
| [Baer] p. 40 | Property (c) | mapd11 41626 |
| [Baer] p. 40 | Property (e) | mapdin 41649 mapdlsm 41651 |
| [Baer] p. 40 | Property (f) | mapd0 41652 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41612 mapd1o 41635 |
| [Baer] p. 41 | Property (g) | mapdat 41654 |
| [Baer] p. 44 | Part (1) | mapdpg 41693 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41788 mapdheq 41715 mapdheq2 41716 mapdheq2biN 41717 |
| [Baer] p. 45 | Part (3) | baerlem3 41700 |
| [Baer] p. 46 | Part (4) | mapdheq4 41719 mapdheq4lem 41718 |
| [Baer] p. 46 | Part (5) | baerlem5a 41701 baerlem5abmN 41705 baerlem5amN 41703 baerlem5b 41702 baerlem5bmN 41704 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41808 hdmap1l6a 41796 hdmap1l6e 41801 hdmap1l6f 41802 hdmap1l6g 41803 hdmap1l6lem1 41794 hdmap1l6lem2 41795 mapdh6N 41734 mapdh6aN 41722 mapdh6eN 41727 mapdh6fN 41728 mapdh6gN 41729 mapdh6lem1N 41720 mapdh6lem2N 41721 |
| [Baer] p. 48 | Part 9 | hdmapval 41815 |
| [Baer] p. 48 | Part 10 | hdmap10 41827 |
| [Baer] p. 48 | Part 11 | hdmapadd 41830 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41804 mapdh6hN 41730 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41740 mapdh75d 41741 mapdh75e 41739 mapdh75fN 41742 mapdh7cN 41736 mapdh7dN 41737 mapdh7eN 41735 mapdh7fN 41738 |
| [Baer] p. 48 | Part (8) | mapdh8 41775 mapdh8a 41762 mapdh8aa 41763 mapdh8ab 41764 mapdh8ac 41765 mapdh8ad 41766 mapdh8b 41767 mapdh8c 41768 mapdh8d 41770 mapdh8d0N 41769 mapdh8e 41771 mapdh8g 41772 mapdh8i 41773 mapdh8j 41774 |
| [Baer] p. 48 | Part (9) | mapdh9a 41776 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41756 |
| [Baer] p. 49 | Part 12 | hdmap11 41835 hdmapeq0 41831 hdmapf1oN 41852 hdmapneg 41833 hdmaprnN 41851 hdmaprnlem1N 41836 hdmaprnlem3N 41837 hdmaprnlem3uN 41838 hdmaprnlem4N 41840 hdmaprnlem6N 41841 hdmaprnlem7N 41842 hdmaprnlem8N 41843 hdmaprnlem9N 41844 hdmapsub 41834 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41855 hdmap14lem10 41864 hdmap14lem1a 41853 hdmap14lem2N 41856 hdmap14lem2a 41854 hdmap14lem3 41857 hdmap14lem8 41862 hdmap14lem9 41863 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41865 hdmap14lem12 41866 hdmap14lem13 41867 hdmap14lem14 41868 hdmap14lem15 41869 hgmapval 41874 |
| [Baer] p. 50 | Part 15 | hgmapadd 41881 hgmapmul 41882 hgmaprnlem2N 41884 hgmapvs 41878 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41888 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41904 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41905 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41906 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41907 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41909 hgmapvv 41913 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41908 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41910 |
| [Baer] p. 111 | Line 15 | hdmapg 41917 hdmapglem7 41916 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26673 2irrexpqALT 26743 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2562 |
| [BellMachover] p. 460 | Notation | df-mo 2533 |
| [BellMachover] p. 460 | Definition | mo3 2557 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2701 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2705 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5237 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5246 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37045 sepex 5250 |
| [BellMachover] p. 466 | Problem | axpow2 5317 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5318 |
| [BellMachover] p. 466 | Axiom Union | axun2 7693 |
| [BellMachover] p. 468 | Definition | df-ord 6323 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6338 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6345 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6340 |
| [BellMachover] p. 471 | Definition of N | df-om 7823 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7757 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6325 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9571 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7838 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9693 |
| [BellMachover] p. 478 | Definition | rankval2 9747 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9711 r1ord3g 9708 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9524 |
| [BellMachover] p. 488 | Axiom AC | ac5 10406 dfac4 10051 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10039 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39305 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32332 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32374 chirredi 32373 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32362 |
| [Beran] p. 3 | Definition of join | sshjval3 31333 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31595 cmcm2i 31572 cmcm2ii 31577 cmt2N 39236 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31596 lecmi 31581 lecmii 31582 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31570 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31599 cm2ji 31604 cm2mi 31605 |
| [Beran] p. 95 | Definition | df-sh 31186 issh2 31188 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31065 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31078 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31069 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31807 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31809 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31808 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31810 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31061 his1i 31079 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31062 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31063 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31064 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30947 dfhnorm2 31101 normval 31103 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31163 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30952 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31220 |
| [Beran] p. 96 | Definition of converge | df-hlim 30951 hlimi 31167 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31112 norm-i 31108 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31116 norm-ii 31117 normlem0 31088 normlem1 31089 normlem2 31090 normlem3 31091 normlem4 31092 normlem5 31093 normlem6 31094 normlem7 31095 normlem7tALT 31098 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31118 norm-iii 31119 |
| [Beran] p. 98 | Remark 3.4 | bcs 31160 bcsiALT 31158 bcsiHIL 31159 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31100 normpar 31134 normpari 31133 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31125 normpyth 31124 normpythi 31121 |
| [Beran] p. 99 | Remark | lnfn0 32026 lnfn0i 32021 lnop0 31945 lnop0i 31949 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32005 nmcfnex 32032 nmcfnexi 32030 nmcopex 32008 nmcopexi 32006 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32033 nmcfnlbi 32031 nmcoplb 32009 nmcoplbi 32007 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32035 lnfnconi 32034 lnopcon 32014 lnopconi 32013 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31135 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31132 norm3adifii 31127 norm3dif 31129 norm3difi 31126 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31280 pjhth 31372 pjhtheu 31373 pjpjhth 31404 pjpjhthi 31405 pjth 25372 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31385 ococi 31384 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32040 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32041 riesz4 32043 riesz4i 32042 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32058 cnlnadjeu 32057 cnlnadjeui 32056 cnlnadji 32055 cnlnadjlem1 32046 nmopadjlei 32067 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32070 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32069 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32071 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31915 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32081 nmopcoadji 32080 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32072 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32082 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32079 pjadj2coi 32183 pjadjcoi 32140 |
| [Beran] p. 107 | Definition | df-ch 31200 isch2 31202 |
| [Beran] p. 107 | Remark 3.12 | choccl 31285 isch3 31220 occl 31283 ocsh 31262 shoccl 31284 shocsh 31263 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31387 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31311 |
| [Beran] p. 109 | Property (i) | pjadj2 32166 pjadj3 32167 pjadji 31664 pjadjii 31653 |
| [Beran] p. 109 | Property (ii) | pjidmco 32160 pjidmcoi 32156 pjidmi 31652 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32152 |
| [Beran] p. 111 | Remark | ho0val 31729 pjch1 31649 |
| [Beran] p. 111 | Definition | df-hfmul 31713 df-hfsum 31712 df-hodif 31711 df-homul 31710 df-hosum 31709 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31650 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31673 pjchi 31411 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31418 pjoc2i 31417 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31659 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32144 pjssmii 31660 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32143 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32142 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32147 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32145 pjssge0ii 31661 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32146 pjdifnormii 31662 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1776 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1774 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1777 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1772 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34276 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34284 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34282 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34286 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34306 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34337 df-sitm 34315 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34337 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34314 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29028 isuhgrop 29050 isusgrop 29142 isuspgrop 29141 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47854 df-subgr 29248 uhgrspan1 29283 uhgrspansubgr 29271 |
| [Bollobas] p. 3 | Definition | df-gric 47874 gricuspgr 47911 isuspgrim 47889 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29435 df-clnbgr 47813 df-cusgr 29392 df-nbgr 29313 fusgrmaxsize 29445 |
| [Bollobas] p. 4 | Definition | df-upwlks 48115 df-wlks 29580 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29531 finsumvtxdgeven 29533 fusgr1th 29532 fusgrvtxdgonume 29535 vtxdgoddnumeven 29534 |
| [Bollobas] p. 5 | Notation | df-pths 29694 |
| [Bollobas] p. 5 | Definition | df-crcts 29766 df-cycls 29767 df-trls 29671 df-wlkson 29581 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29039 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48181 df-cllaw 48167 df-mgm 18549 df-mgm2 48200 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48182 df-asslaw 48169 df-sgrp 18628 df-sgrp2 48202 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48201 df-comlaw 48168 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18644 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33010 mndlactf1o 33014 mndractf1 33012 mndractf1o 33015 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20155 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20073 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33622 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33626 assarrginv 33625 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33666 fldextrspunfld 33664 fldextrspunlem1 33663 fldextrspunlem2 33665 fldextrspunlsp 33662 fldextrspunlsplem 33661 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33501 dfufd2 33514 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7244 fcofo 7245 |
| [BourbakiTop1] p. | Remark | xnegmnf 13146 xnegpnf 13145 |
| [BourbakiTop1] p. | Remark | rexneg 13147 |
| [BourbakiTop1] p. | Remark 3 | ust0 24140 ustfilxp 24133 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24010 |
| [BourbakiTop1] p. | Criterion | ishmeo 23679 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24204 iducn 24203 snfil 23784 |
| [BourbakiTop1] p. | Example 2 | neifil 23800 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23987 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24224 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33940 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23783 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24196 df-ust 24121 filintn0 23781 filn0 23782 istgp 23997 ucnprima 24202 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24207 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24218 df-usp 24178 df-utop 24152 trust 24150 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33839 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23036 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23189 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24126 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24129 |
| [BourbakiTop1] p. | Property V_ii | innei 23045 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23053 neissex 23047 |
| [BourbakiTop1] p. | Proposition 1 | neips 23033 neiss 23029 ucncn 24205 ustund 24142 ustuqtop 24167 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23187 neiptopreu 23053 utop2nei 24171 utop3cls 24172 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24212 uspreg 24194 utopreg 24173 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23611 imasncls 23612 imasnopn 23610 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23920 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24128 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24130 |
| [BourbakiTop1] p. | Property V_iii | elnei 23031 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24223 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24127 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24131 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23307 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23766 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22814 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33836 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46053 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46055 stoweid 46054 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45992 stoweidlem10 46001 stoweidlem14 46005 stoweidlem15 46006 stoweidlem35 46026 stoweidlem36 46027 stoweidlem37 46028 stoweidlem38 46029 stoweidlem40 46031 stoweidlem41 46032 stoweidlem43 46034 stoweidlem44 46035 stoweidlem46 46037 stoweidlem5 45996 stoweidlem50 46041 stoweidlem52 46043 stoweidlem53 46044 stoweidlem55 46046 stoweidlem56 46047 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46014 stoweidlem24 46015 stoweidlem27 46018 stoweidlem28 46019 stoweidlem30 46021 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46025 stoweidlem59 46050 stoweidlem60 46051 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46036 stoweidlem49 46040 stoweidlem7 45998 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46022 stoweidlem39 46030 stoweidlem42 46033 stoweidlem48 46039 stoweidlem51 46042 stoweidlem54 46045 stoweidlem57 46048 stoweidlem58 46049 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46016 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46008 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46002 stoweidlem13 46004 stoweidlem26 46017 stoweidlem61 46052 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46009 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48181 df-mgm 18549 df-mgm2 48200 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18628 df-sgrp2 48202 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18953 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5184 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30382 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30382 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30382 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30382 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30382 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30382 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30382 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30382 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30382 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30382 |
| [Clemente] p. 14 | Proof 5.11 | natded 30382 |
| [Clemente] p. 14 | Definition E` `n | natded 30382 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30384 ex-natded5.2 30383 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30387 ex-natded5.3 30386 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30389 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30391 ex-natded5.7 30390 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30393 ex-natded5.8 30392 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30395 ex-natded5.13 30394 |
| [Clemente] p. 32 | Definition I` `n | natded 30382 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30382 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30382 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30382 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30396 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30397 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30399 ex-natded9.26 30398 |
| [Cohen] p. 301 | Remark | relogoprlem 26533 |
| [Cohen] p. 301 | Property 2 | relogmul 26534 relogmuld 26567 |
| [Cohen] p. 301 | Property 3 | relogdiv 26535 relogdivd 26568 |
| [Cohen] p. 301 | Property 4 | relogexp 26538 |
| [Cohen] p. 301 | Property 1a | log1 26527 |
| [Cohen] p. 301 | Property 1b | loge 26528 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26730 |
| [Cohen4] p. 349 | Property | relogbf 26734 |
| [Cohen4] p. 352 | Definition | elogb 26713 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26720 |
| [Cohen4] p. 361 | Property 3 | logbrec 26725 relogbdiv 26722 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26718 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26723 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26711 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26712 |
| [Cohen4] p. 367 | Property | logbchbase 26714 |
| [Cohen4] p. 377 | Property 2 | logblt 26727 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34269 sxbrsigalem4 34271 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18498 acsinfd 18497 acsinfdimd 18499 acsmap2d 18496 acsmapd 18495 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34274 |
| [Connell] p. 57 | Definition | df-scmat 22411 df-scmatalt 48381 |
| [Conway] p. 4 | Definition | slerec 27765 slerecd 27766 |
| [Conway] p. 5 | Definition | addsval 27909 addsval2 27910 df-adds 27907 df-muls 28050 df-negs 27967 |
| [Conway] p. 7 | Theorem | 0slt1s 27778 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27820 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27819 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27708 |
| [Conway] p. 17 | Theorem 3 | addsass 27952 addsassd 27953 addscom 27913 addscomd 27914 addsrid 27911 addsridd 27912 |
| [Conway] p. 17 | Definition | df-0s 27773 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27990 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27987 negsidd 27988 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27936 sleadd1d 27942 |
| [Conway] p. 18 | Definition | df-1s 27774 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27982 negscld 27983 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27927 |
| [Conway] p. 19 | Note | mulsunif2 28113 |
| [Conway] p. 19 | Theorem 7 | addsdi 28098 addsdid 28099 addsdird 28100 mulnegs1d 28103 mulnegs2d 28104 mulsass 28109 mulsassd 28110 mulscom 28082 mulscomd 28083 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28077 mulscld 28078 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28081 sltmul 28079 sltmuld 28080 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28087 mulsgt0d 28088 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28160 |
| [Conway] p. 23 | Theorem 11 | eqscut3 27770 |
| [Conway] p. 24 | Definition | df-reno 28398 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28403 remulscl 28406 renegscl 28402 |
| [Conway] p. 27 | Definition | df-ons 28193 elons2 28199 |
| [Conway] p. 27 | Theorem 14 | sltonex 28203 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28205 onswe 28210 |
| [Conway] p. 29 | Remark | madebday 27849 newbday 27851 oldbday 27850 |
| [Conway] p. 29 | Definition | df-made 27792 df-new 27794 df-old 27793 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13799 |
| [Crawley] p. 1 | Definition of poset | df-poset 18254 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39373 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40177 dalaw 39873 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41948 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39977 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40093 df-ldil 40091 isldil 40097 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40092 df-trnN 40094 isltrn 40106 ltrnu 40108 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39778 cdlema2N 39779 exatleN 39391 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39463 cdlemb 39781 cdlemb2 40028 cdlemb3 40593 idltrn 40137 l1cvat 39041 lhpat 40030 lhpat2 40032 lshpat 39042 ltrnel 40126 ltrnmw 40138 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40178 cdlemc2 40179 ltrnnidn 40161 trlat 40156 trljat1 40153 trljat2 40154 trljat3 40155 trlne 40172 trlnidat 40160 trlnle 40173 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39978 |
| [Crawley] p. 113 | Lemma C | cdlemc 40184 cdlemc3 40180 cdlemc4 40181 |
| [Crawley] p. 113 | Lemma D | cdlemd 40194 cdlemd1 40185 cdlemd2 40186 cdlemd3 40187 cdlemd4 40188 cdlemd5 40189 cdlemd6 40190 cdlemd7 40191 cdlemd8 40192 cdlemd9 40193 cdleme31sde 40372 cdleme31se 40369 cdleme31se2 40370 cdleme31snd 40373 cdleme32a 40428 cdleme32b 40429 cdleme32c 40430 cdleme32d 40431 cdleme32e 40432 cdleme32f 40433 cdleme32fva 40424 cdleme32fva1 40425 cdleme32fvcl 40427 cdleme32le 40434 cdleme48fv 40486 cdleme4gfv 40494 cdleme50eq 40528 cdleme50f 40529 cdleme50f1 40530 cdleme50f1o 40533 cdleme50laut 40534 cdleme50ldil 40535 cdleme50lebi 40527 cdleme50rn 40532 cdleme50rnlem 40531 cdlemeg49le 40498 cdlemeg49lebilem 40526 |
| [Crawley] p. 113 | Lemma E | cdleme 40547 cdleme00a 40196 cdleme01N 40208 cdleme02N 40209 cdleme0a 40198 cdleme0aa 40197 cdleme0b 40199 cdleme0c 40200 cdleme0cp 40201 cdleme0cq 40202 cdleme0dN 40203 cdleme0e 40204 cdleme0ex1N 40210 cdleme0ex2N 40211 cdleme0fN 40205 cdleme0gN 40206 cdleme0moN 40212 cdleme1 40214 cdleme10 40241 cdleme10tN 40245 cdleme11 40257 cdleme11a 40247 cdleme11c 40248 cdleme11dN 40249 cdleme11e 40250 cdleme11fN 40251 cdleme11g 40252 cdleme11h 40253 cdleme11j 40254 cdleme11k 40255 cdleme11l 40256 cdleme12 40258 cdleme13 40259 cdleme14 40260 cdleme15 40265 cdleme15a 40261 cdleme15b 40262 cdleme15c 40263 cdleme15d 40264 cdleme16 40272 cdleme16aN 40246 cdleme16b 40266 cdleme16c 40267 cdleme16d 40268 cdleme16e 40269 cdleme16f 40270 cdleme16g 40271 cdleme19a 40290 cdleme19b 40291 cdleme19c 40292 cdleme19d 40293 cdleme19e 40294 cdleme19f 40295 cdleme1b 40213 cdleme2 40215 cdleme20aN 40296 cdleme20bN 40297 cdleme20c 40298 cdleme20d 40299 cdleme20e 40300 cdleme20f 40301 cdleme20g 40302 cdleme20h 40303 cdleme20i 40304 cdleme20j 40305 cdleme20k 40306 cdleme20l 40309 cdleme20l1 40307 cdleme20l2 40308 cdleme20m 40310 cdleme20y 40289 cdleme20zN 40288 cdleme21 40324 cdleme21d 40317 cdleme21e 40318 cdleme22a 40327 cdleme22aa 40326 cdleme22b 40328 cdleme22cN 40329 cdleme22d 40330 cdleme22e 40331 cdleme22eALTN 40332 cdleme22f 40333 cdleme22f2 40334 cdleme22g 40335 cdleme23a 40336 cdleme23b 40337 cdleme23c 40338 cdleme26e 40346 cdleme26eALTN 40348 cdleme26ee 40347 cdleme26f 40350 cdleme26f2 40352 cdleme26f2ALTN 40351 cdleme26fALTN 40349 cdleme27N 40356 cdleme27a 40354 cdleme27cl 40353 cdleme28c 40359 cdleme3 40224 cdleme30a 40365 cdleme31fv 40377 cdleme31fv1 40378 cdleme31fv1s 40379 cdleme31fv2 40380 cdleme31id 40381 cdleme31sc 40371 cdleme31sdnN 40374 cdleme31sn 40367 cdleme31sn1 40368 cdleme31sn1c 40375 cdleme31sn2 40376 cdleme31so 40366 cdleme35a 40435 cdleme35b 40437 cdleme35c 40438 cdleme35d 40439 cdleme35e 40440 cdleme35f 40441 cdleme35fnpq 40436 cdleme35g 40442 cdleme35h 40443 cdleme35h2 40444 cdleme35sn2aw 40445 cdleme35sn3a 40446 cdleme36a 40447 cdleme36m 40448 cdleme37m 40449 cdleme38m 40450 cdleme38n 40451 cdleme39a 40452 cdleme39n 40453 cdleme3b 40216 cdleme3c 40217 cdleme3d 40218 cdleme3e 40219 cdleme3fN 40220 cdleme3fa 40223 cdleme3g 40221 cdleme3h 40222 cdleme4 40225 cdleme40m 40454 cdleme40n 40455 cdleme40v 40456 cdleme40w 40457 cdleme41fva11 40464 cdleme41sn3aw 40461 cdleme41sn4aw 40462 cdleme41snaw 40463 cdleme42a 40458 cdleme42b 40465 cdleme42c 40459 cdleme42d 40460 cdleme42e 40466 cdleme42f 40467 cdleme42g 40468 cdleme42h 40469 cdleme42i 40470 cdleme42k 40471 cdleme42ke 40472 cdleme42keg 40473 cdleme42mN 40474 cdleme42mgN 40475 cdleme43aN 40476 cdleme43bN 40477 cdleme43cN 40478 cdleme43dN 40479 cdleme5 40227 cdleme50ex 40546 cdleme50ltrn 40544 cdleme51finvN 40543 cdleme51finvfvN 40542 cdleme51finvtrN 40545 cdleme6 40228 cdleme7 40236 cdleme7a 40230 cdleme7aa 40229 cdleme7b 40231 cdleme7c 40232 cdleme7d 40233 cdleme7e 40234 cdleme7ga 40235 cdleme8 40237 cdleme8tN 40242 cdleme9 40240 cdleme9a 40238 cdleme9b 40239 cdleme9tN 40244 cdleme9taN 40243 cdlemeda 40285 cdlemedb 40284 cdlemednpq 40286 cdlemednuN 40287 cdlemefr27cl 40390 cdlemefr32fva1 40397 cdlemefr32fvaN 40396 cdlemefrs32fva 40387 cdlemefrs32fva1 40388 cdlemefs27cl 40400 cdlemefs32fva1 40410 cdlemefs32fvaN 40409 cdlemesner 40283 cdlemeulpq 40207 |
| [Crawley] p. 114 | Lemma E | 4atex 40063 4atexlem7 40062 cdleme0nex 40277 cdleme17a 40273 cdleme17c 40275 cdleme17d 40485 cdleme17d1 40276 cdleme17d2 40482 cdleme18a 40278 cdleme18b 40279 cdleme18c 40280 cdleme18d 40282 cdleme4a 40226 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40312 cdleme21at 40315 cdleme21b 40313 cdleme21c 40314 cdleme21ct 40316 cdleme21f 40319 cdleme21g 40320 cdleme21h 40321 cdleme21i 40322 cdleme22gb 40281 |
| [Crawley] p. 116 | Lemma F | cdlemf 40550 cdlemf1 40548 cdlemf2 40549 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40554 cdlemg16 40644 cdlemg28 40691 cdlemg28a 40680 cdlemg28b 40690 cdlemg3a 40584 cdlemg42 40716 cdlemg43 40717 cdlemg44 40720 cdlemg44a 40718 cdlemg46 40722 cdlemg47 40723 cdlemg9 40621 ltrnco 40706 ltrncom 40725 tgrpabl 40738 trlco 40714 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40730 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40664 cdlemg17b 40649 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40743 df-edring 40744 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40747 |
| [Crawley] p. 118 | Remark | tendopltp 40767 |
| [Crawley] p. 118 | Lemma H | cdlemh 40804 cdlemh1 40802 cdlemh2 40803 |
| [Crawley] p. 118 | Lemma I | cdlemi 40807 cdlemi1 40805 cdlemi2 40806 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40808 cdlemj2 40809 cdlemj3 40810 tendocan 40811 |
| [Crawley] p. 118 | Lemma K | cdlemk 40961 cdlemk1 40818 cdlemk10 40830 cdlemk11 40836 cdlemk11t 40933 cdlemk11ta 40916 cdlemk11tb 40918 cdlemk11tc 40932 cdlemk11u-2N 40876 cdlemk11u 40858 cdlemk12 40837 cdlemk12u-2N 40877 cdlemk12u 40859 cdlemk13-2N 40863 cdlemk13 40839 cdlemk14-2N 40865 cdlemk14 40841 cdlemk15-2N 40866 cdlemk15 40842 cdlemk16-2N 40867 cdlemk16 40844 cdlemk16a 40843 cdlemk17-2N 40868 cdlemk17 40845 cdlemk18-2N 40873 cdlemk18-3N 40887 cdlemk18 40855 cdlemk19-2N 40874 cdlemk19 40856 cdlemk19u 40957 cdlemk1u 40846 cdlemk2 40819 cdlemk20-2N 40879 cdlemk20 40861 cdlemk21-2N 40878 cdlemk21N 40860 cdlemk22-3 40888 cdlemk22 40880 cdlemk23-3 40889 cdlemk24-3 40890 cdlemk25-3 40891 cdlemk26-3 40893 cdlemk26b-3 40892 cdlemk27-3 40894 cdlemk28-3 40895 cdlemk29-3 40898 cdlemk3 40820 cdlemk30 40881 cdlemk31 40883 cdlemk32 40884 cdlemk33N 40896 cdlemk34 40897 cdlemk35 40899 cdlemk36 40900 cdlemk37 40901 cdlemk38 40902 cdlemk39 40903 cdlemk39u 40955 cdlemk4 40821 cdlemk41 40907 cdlemk42 40928 cdlemk42yN 40931 cdlemk43N 40950 cdlemk45 40934 cdlemk46 40935 cdlemk47 40936 cdlemk48 40937 cdlemk49 40938 cdlemk5 40823 cdlemk50 40939 cdlemk51 40940 cdlemk52 40941 cdlemk53 40944 cdlemk54 40945 cdlemk55 40948 cdlemk55u 40953 cdlemk56 40958 cdlemk5a 40822 cdlemk5auN 40847 cdlemk5u 40848 cdlemk6 40824 cdlemk6u 40849 cdlemk7 40835 cdlemk7u-2N 40875 cdlemk7u 40857 cdlemk8 40825 cdlemk9 40826 cdlemk9bN 40827 cdlemki 40828 cdlemkid 40923 cdlemkj-2N 40869 cdlemkj 40850 cdlemksat 40833 cdlemksel 40832 cdlemksv 40831 cdlemksv2 40834 cdlemkuat 40853 cdlemkuel-2N 40871 cdlemkuel-3 40885 cdlemkuel 40852 cdlemkuv-2N 40870 cdlemkuv2-2 40872 cdlemkuv2-3N 40886 cdlemkuv2 40854 cdlemkuvN 40851 cdlemkvcl 40829 cdlemky 40913 cdlemkyyN 40949 tendoex 40962 |
| [Crawley] p. 120 | Remark | dva1dim 40972 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40963 cdleml2N 40964 cdleml3N 40965 cdleml4N 40966 cdleml5N 40967 cdleml6 40968 cdleml7 40969 cdleml8 40970 cdleml9 40971 dia1dim 41048 |
| [Crawley] p. 120 | Lemma M | dia11N 41035 diaf11N 41036 dialss 41033 diaord 41034 dibf11N 41148 djajN 41124 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41019 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41105 dia2dimlem1 41051 dia2dimlem2 41052 dia2dimlem3 41053 dia2dimlem4 41054 dia2dimlem5 41055 diaf1oN 41117 diarnN 41116 dvheveccl 41099 dvhopN 41103 |
| [Crawley] p. 121 | Lemma N | cdlemn 41199 cdlemn10 41193 cdlemn11 41198 cdlemn11a 41194 cdlemn11b 41195 cdlemn11c 41196 cdlemn11pre 41197 cdlemn2 41182 cdlemn2a 41183 cdlemn3 41184 cdlemn4 41185 cdlemn4a 41186 cdlemn5 41188 cdlemn5pre 41187 cdlemn6 41189 cdlemn7 41190 cdlemn8 41191 cdlemn9 41192 diclspsn 41181 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41160 |
| [Crawley] p. 122 | Lemma N | dih11 41252 dihf11 41254 dihjust 41204 dihjustlem 41203 dihord 41251 dihord1 41205 dihord10 41210 dihord11b 41209 dihord11c 41211 dihord2 41214 dihord2a 41206 dihord2b 41207 dihord2cN 41208 dihord2pre 41212 dihord2pre2 41213 dihordlem6 41200 dihordlem7 41201 dihordlem7b 41202 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41217 dihfval 41218 dihval 41219 |
| [Diestel] p. 3 | Definition | df-gric 47874 df-grim 47871 isuspgrim 47889 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29392 df-nbgr 29313 |
| [Diestel] p. 3 | Definition by | df-grisom 47870 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47854 df-subgr 29248 uhgrspan1 29283 uhgrspansubgr 29271 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29535 vtxdgoddnumeven 29534 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29039 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33847 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33859 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33851 zarcls1 33852 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33862 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33865 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33868 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3914 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9576 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8778 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9584 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9909 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10484 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5255 |
| [Enderton] p. 19 | Definition | df-tp 4590 |
| [Enderton] p. 26 | Exercise 5 | unissb 4899 |
| [Enderton] p. 26 | Exercise 10 | pwel 5331 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5524 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5038 iinin2 5037 iinun2 5032 iunin1 5031 iunin1f 32536 iunin2 5030 uniin1 32530 uniin2 32531 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5036 iundif2 5033 |
| [Enderton] p. 32 | Exercise 20 | unineq 4247 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5057 |
| [Enderton] p. 33 | Exercise 25 | iununi 5058 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5065 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7727 iunpwss 5066 |
| [Enderton] p. 36 | Definition | opthwiener 5469 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5405 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4905 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5425 rnex 7866 rnexg 7858 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5868 rnuni 6109 |
| [Enderton] p. 42 | Definition of a function | dffun7 6527 dffun8 6528 |
| [Enderton] p. 43 | Definition of function value | funfv2 6931 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6569 |
| [Enderton] p. 44 | Definition (d) | dfima2 6022 dfima3 6023 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6940 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10402 ac7g 10403 df-ac 10045 dfac2 10061 dfac2a 10059 dfac2b 10060 dfac3 10050 dfac7 10062 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7202 |
| [Enderton] p. 52 | Definition | df-map 8778 |
| [Enderton] p. 53 | Exercise 21 | coass 6226 |
| [Enderton] p. 53 | Exercise 27 | dmco 6215 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6576 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6062 |
| [Enderton] p. 54 | Remark | ixpf 8870 ixpssmap 8882 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8848 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10412 ac9s 10422 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38594 erref 8668 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38597 erthi 8704 |
| [Enderton] p. 57 | Definition | df-ec 8650 |
| [Enderton] p. 58 | Definition | df-qs 8654 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8650 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5864 |
| [Enderton] p. 68 | Definition of successor | df-suc 6326 |
| [Enderton] p. 71 | Definition | df-tr 5210 dftr4 5216 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6401 unisucg 6400 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6401 unisucg 6400 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5225 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5227 trintALT 44863 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8545 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8547 onasuc 8469 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7372 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8546 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8548 onmsuc 8470 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8563 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8550 nnacom 8558 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8564 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8565 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8567 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8551 nnmsucr 8566 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8579 |
| [Enderton] p. 129 | Definition | df-en 8896 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7323 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9944 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16157 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9148 |
| [Enderton] p. 135 | Corollary 6C | php3 9150 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9147 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9179 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9181 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9109 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9114 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9082 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10109 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10110 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10105 dju1en 10101 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9270 unifi 9271 unifi2 9272 |
| [Enderton] p. 144 | Corollary 6K | undif2 4436 unfi 9112 unfi2 9235 |
| [Enderton] p. 145 | Figure 38 | ffoss 7904 |
| [Enderton] p. 145 | Definition | df-dom 8897 |
| [Enderton] p. 146 | Example 1 | domen 8910 domeng 8911 |
| [Enderton] p. 146 | Example 3 | nndomo 9158 nnsdom 9583 nnsdomg 9222 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10113 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9083 xpdom1 9017 xpdom1g 9015 xpdom2g 9014 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9089 |
| [Enderton] p. 151 | Theorem 6M | zorn 10436 zorng 10433 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10421 dfac5 10058 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10504 |
| [Enderton] p. 164 | Example | infdif 10137 |
| [Enderton] p. 168 | Definition | df-po 5539 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6436 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6367 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6435 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6375 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7794 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7737 |
| [Enderton] p. 194 | Remark | onprc 7734 |
| [Enderton] p. 194 | Exercise 16 | suc11 6429 |
| [Enderton] p. 197 | Definition | df-card 9868 |
| [Enderton] p. 197 | Theorem 7P | carden 10480 |
| [Enderton] p. 200 | Exercise 25 | tfis 7811 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9705 |
| [Enderton] p. 202 | Definition | df-r1 9693 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9715 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9796 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9535 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9786 rankprb 9780 rankpw 9772 rankpwi 9752 rankuniss 9795 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9547 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9548 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10039 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10005 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10019 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8287 |
| [Enderton] p. 222 | Definition of kard | karden 9824 kardex 9823 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8538 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8540 |
| [Enderton] p. 240 | Exercise 25 | oarec 8503 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10179 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17583 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17525 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18494 mrieqv2d 17580 mrieqvd 17579 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17584 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17589 mreexexlem2d 17586 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18500 mreexfidimd 17591 |
| [Frege1879] p. 11 | Statement | df3or2 43750 |
| [Frege1879] p. 12 | Statement | df3an2 43751 dfxor4 43748 dfxor5 43749 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43772 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43773 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43777 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43781 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43782 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43788 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43790 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43791 axfrege8 43789 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37426 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43794 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43802 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43796 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43795 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43804 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43805 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43808 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43798 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43803 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43800 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43806 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43810 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43809 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43801 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43807 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43797 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43799 rp-frege25 43787 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43792 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43812 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43793 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43813 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43816 axfrege31 43815 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43814 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43817 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43818 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43819 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43820 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43821 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43822 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43823 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43824 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43825 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43827 axfrege41 43826 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43828 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43829 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43830 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43831 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43832 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43833 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43834 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43835 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43836 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43839 ax-frege52c 43870 frege52aid 43840 frege52b 43871 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43844 ax-frege54c 43874 frege54b 43875 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43837 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3752 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43842 frege53aid 43841 frege53b 43872 frege53c 43896 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2729 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43850 frege55aid 43847 frege55b 43879 frege55c 43900 frege55cor1a 43851 frege55lem2a 43849 frege55lem2b 43878 frege55lem2c 43899 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43853 frege56aid 43852 frege56b 43880 frege56c 43901 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43857 ax-frege58b 43883 frege58bid 43884 frege58c 43903 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43855 frege57aid 43854 frege57b 43881 frege57c 43902 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3763 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43859 frege59b 43886 frege59c 43904 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43860 frege60b 43887 frege60c 43905 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43861 frege61b 43888 frege61c 43906 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43862 frege62b 43889 frege62c 43907 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43863 frege63b 43890 frege63c 43908 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43864 frege64b 43891 frege64c 43909 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43865 frege65b 43892 frege65c 43910 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43866 frege66b 43893 frege66c 43911 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43867 frege67b 43894 frege67c 43912 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43868 frege68b 43895 frege68c 43913 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43914 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43915 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43916 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43917 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43918 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43921 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43919 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43920 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43922 frege77d 43728 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43923 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43924 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43925 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43926 frege81d 43729 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43927 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43928 frege83d 43730 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43929 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43930 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43931 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43932 frege87d 43732 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43933 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43934 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43935 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43936 frege91d 43733 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43937 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43938 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43939 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43940 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43944 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43941 frege96d 43731 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43942 frege97d 43734 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43943 frege98d 43735 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43945 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43946 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43947 frege102d 43736 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43948 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43949 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43950 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43951 frege106d 43737 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43952 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43953 frege108d 43738 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43954 frege109d 43739 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43955 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43956 frege111d 43741 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43957 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43958 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43959 frege114d 43740 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43960 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43961 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43962 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43963 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43964 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43965 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43966 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43967 frege122d 43742 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43968 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43969 frege124d 43743 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43970 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43971 frege126d 43744 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43972 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43973 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43974 frege129d 43745 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43975 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43976 frege131d 43746 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43977 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43978 frege133d 43747 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46304 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46627 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46327 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46442 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46462 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46453 meadjunre 46467 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46454 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46455 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46451 meaiunle 46460 meaiunlelem 46459 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46472 meaiuninc2 46473 meaiuninc3 46476 meaiuninc3v 46475 meaiunincf 46474 meaiuninclem 46471 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46478 meaiininc2 46479 meaiininclem 46477 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46497 caragendifcl 46505 caratheodory 46519 omelesplit 46509 |
| [Fremlin1] p. 19 | Definition 113A | isome 46485 isomennd 46522 isomenndlem 46521 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46507 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46526 voncmpl 46612 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46489 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46514 carageniuncllem1 46512 carageniuncllem2 46513 caragenuncl 46504 caragenuncllem 46503 caragenunicl 46515 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46523 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46517 caratheodorylem2 46518 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46526 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46585 hoidmv1lelem1 46582 hoidmv1lelem2 46583 hoidmv1lelem3 46584 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46629 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46585 hoidmvle 46591 hoidmvlelem1 46586 hoidmvlelem2 46587 hoidmvlelem3 46588 hoidmvlelem4 46589 hoidmvlelem5 46590 hsphoidmvle2 46576 hsphoif 46567 hsphoival 46570 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46539 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46547 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46574 hoidmvn0val 46575 hoidmvval 46568 hoidmvval0 46578 hoidmvval0b 46581 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46579 hsphoidmvle 46577 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46528 df-voln 46530 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46595 ovn0 46557 ovn0lem 46556 ovnf 46554 ovnome 46564 ovnssle 46552 ovnsslelem 46551 ovnsupge0 46548 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46594 ovnhoilem1 46592 ovnhoilem2 46593 vonhoi 46658 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46611 hoidifhspf 46609 hoidifhspval 46599 hoidifhspval2 46606 hoidifhspval3 46610 hspmbl 46620 hspmbllem1 46617 hspmbllem2 46618 hspmbllem3 46619 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46612 vonmea 46565 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46563 ovnsubadd2 46637 ovnsubadd2lem 46636 ovnsubaddlem1 46561 ovnsubaddlem2 46562 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46622 hoimbl2 46656 hoimbllem 46621 hspdifhsp 46607 opnvonmbl 46625 opnvonmbllem2 46624 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46627 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46670 iccvonmbllem 46669 ioovonmbl 46668 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46676 vonicclem2 46675 vonioo 46673 vonioolem2 46672 vonn0icc 46679 vonn0icc2 46683 vonn0ioo 46678 vonn0ioo2 46681 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46680 snvonmbl 46677 vonct 46684 vonsn 46682 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46350 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46349 subsaliuncllem 46348 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46716 salpreimalegt 46700 salpreimaltle 46717 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46719 issmff 46725 issmflem 46718 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46736 issmflelem 46735 smfpreimale 46745 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46747 issmfgtlem 46746 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46687 issmf 46719 issmff 46725 issmfge 46761 issmfgelem 46760 issmfgt 46747 issmfgtlem 46746 issmfle 46736 issmflelem 46735 issmflem 46718 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46698 salpreimagtlt 46721 salpreimalelt 46720 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46761 issmfgelem 46760 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46744 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46742 cnfsmf 46731 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46758 decsmflem 46757 incsmf 46733 incsmflem 46732 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46692 pimconstlt1 46693 smfconst 46740 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46756 smfaddlem1 46754 smfaddlem2 46755 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46787 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46786 smfmullem1 46782 smfmullem2 46783 smfmullem3 46784 smfmullem4 46785 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46788 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46791 smfpimbor1lem2 46790 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46793 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46781 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46780 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46789 smfresal 46779 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46768 smflim2 46797 smflimlem1 46762 smflimlem2 46763 smflimlem3 46764 smflimlem4 46765 smflimlem5 46766 smflimlem6 46767 smflimmpt 46801 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46805 smfsuplem1 46802 smfsuplem2 46803 smfsuplem3 46804 smfsupmpt 46806 smfsupxr 46807 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46809 smfinflem 46808 smfinfmpt 46810 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46768 smflim2 46797 smflimmpt 46801 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46799 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46829 smfdivdmmbl2 46832 smfinfdmmbl 46840 smfinfdmmbllem 46839 smfsupdmmbl 46836 smfsupdmmbllem 46835 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46819 smflimsuplem2 46812 smflimsuplem6 46816 smflimsuplem7 46817 smflimsuplem8 46818 smflimsupmpt 46820 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46822 smfliminflem 46821 smfliminfmpt 46823 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46687 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46833 fsupdm2 46834 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46824 adddmmbl2 46825 finfdm 46837 finfdm2 46838 fsupdm 46833 fsupdm2 46834 muldmmbl 46826 muldmmbl2 46827 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46837 finfdm2 46838 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25470 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25513 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25523 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37685 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37688 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9567 inf1 9551 inf2 9552 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10840 enqer 10850 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10845 df-nq 10841 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10837 df-plq 10843 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7606 df-mpq 10838 df-mq 10844 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10846 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10904 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10905 ltbtwnnq 10907 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10900 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10901 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10908 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10910 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10922 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10924 |
| [Gleason] p. 122 | Definition | df-1p 10911 |
| [Gleason] p. 122 | Remark (1) | prub 10923 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10962 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10914 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10961 psslinpr 10960 supexpr 10983 suplem1pr 10981 suplem2pr 10982 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10947 addclprlem1 10945 addclprlem2 10946 df-plp 10912 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10951 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10950 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10963 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10972 ltexprlem1 10965 ltexprlem2 10966 ltexprlem3 10967 ltexprlem4 10968 ltexprlem5 10969 ltexprlem6 10970 ltexprlem7 10971 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10974 ltaprlem 10973 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10975 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10976 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10913 mulclpr 10949 mulclprlem 10948 reclem2pr 10977 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10958 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10953 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10952 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10957 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10980 reclem3pr 10978 reclem4pr 10979 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10984 enrer 10992 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10989 df-1r 10990 df-nr 10985 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10987 df-plr 10986 negexsr 11031 recexsr 11036 recexsrlem 11032 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10988 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12157 creur 12156 cru 12154 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11117 axcnre 11093 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15057 crimd 15174 crimi 15135 crre 15056 crred 15173 crrei 15134 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15059 remimd 15140 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15226 absval2d 15390 absval2i 15340 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15083 cjaddd 15162 cjaddi 15130 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15084 cjmuld 15163 cjmuli 15131 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15082 cjcjd 15141 cjcji 15113 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15081 cjreb 15065 cjrebd 15144 cjrebi 15116 cjred 15168 rere 15064 rereb 15062 rerebd 15143 rerebi 15115 rered 15166 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15090 addcjd 15154 addcji 15125 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15180 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15221 abscjd 15395 abscji 15344 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15231 abs00d 15391 abs00i 15341 absne0d 15392 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15264 releabsd 15396 releabsi 15345 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15236 absmuld 15399 absmuli 15347 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15224 sqabsaddi 15348 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15273 abstrid 15401 abstrii 15351 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14003 exp0 14006 expp1 14009 expp1d 14088 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26621 cxpaddd 26659 expadd 14045 expaddd 14089 expaddz 14047 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26630 cxpmuld 26679 expmul 14048 expmuld 14090 expmulz 14049 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26627 mulcxpd 26670 mulexp 14042 mulexpd 14102 mulexpz 14043 |
| [Gleason] p. 140 | Exercise 1 | znnen 16156 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13446 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15574 rlimadd 15585 rlimdiv 15588 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15576 rlimsub 15586 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15575 rlimmul 15587 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15579 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15525 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15546 climcj 15547 climim 15549 climre 15548 rlimabs 15551 rlimcj 15552 rlimim 15554 rlimre 15553 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11189 df-xr 11188 ltxr 13051 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15413 limsupval 15416 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15612 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15621 caucvgb 15622 caucvgbf 45478 caucvgr 15618 climcau 15613 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15758 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15825 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15278 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13766 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21290 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24264 xmet0 24263 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24280 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24271 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24273 mstri 24390 xmettri 24272 xmstri 24389 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24303 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23568 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25243 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24461 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24787 addcn2 15536 mulcn 24789 mulcn2 15538 subcn 24788 subcn2 15537 |
| [Gleason] p. 295 | Remark | bcval3 14247 bcval4 14248 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14262 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14245 df-bc 14244 |
| [Gleason] p. 296 | Remark | bcn0 14251 bcnn 14253 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15772 |
| [Gleason] p. 308 | Equation 2 | ef0 16033 |
| [Gleason] p. 308 | Equation 3 | efcj 16034 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16040 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16045 |
| [Gleason] p. 310 | Equation 14 | sinadd 16108 |
| [Gleason] p. 310 | Equation 15 | cosadd 16109 |
| [Gleason] p. 311 | Equation 17 | sincossq 16120 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16125 sinbnd 16124 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14157 sqeqori 14155 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16014 |
| [Godowski] p. 730 | Equation SF | goeqi 32252 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31647 |
| [Golan] p. 1 | Remark | srgisid 20129 |
| [Golan] p. 1 | Definition | df-srg 20107 |
| [Golan] p. 149 | Definition | df-slmd 33170 |
| [Gonshor] p. 7 | Definition | df-scut 27729 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27765 slerecd 27766 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27868 cofcut1d 27869 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27870 cofcut2d 27871 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27872 cofcutr1d 27873 cofcutr2d 27874 |
| [Gonshor] p. 13 | Definition | df-adds 27907 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27923 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27949 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28073 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28093 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28381 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28383 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28382 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27964 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36140 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17523 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17525 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48169 df-cllaw 48167 df-comlaw 48168 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48181 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48202 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38750 dfmembpart2 38755 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32044 riesz2 32045 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31920 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32152 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32164 elpjidm 32163 pjnmopi 32127 |
| [Halmos] p. 44 | Remark | pjinormi 31666 pjinormii 31655 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32168 pjrn 31686 pjrni 31681 pjvec 31675 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31706 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32133 hmopidmpji 32131 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32170 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32159 pjocvec 31676 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32148 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32151 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32154 pjssdif2i 32153 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31834 |
| [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 1795 |
| [Hatcher] p. 25 | Definition | df-phtpc 24924 df-phtpy 24903 |
| [Hatcher] p. 26 | Definition | df-pco 24938 df-pi1 24941 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24927 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24983 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22410 df-dmatalt 48380 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47811 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47796 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47808 bgoldbtbnd 47803 bgoldbtbnd 47803 tgblthelfgott 47809 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34626 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34627 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34641 hgt750lemb 34640 hgt750leme 34642 hgt750lemf 34637 hgt750lemg 34638 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47805 tgoldbachgt 34647 tgoldbachgtALTV 47806 tgoldbachgtd 34646 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34628 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30472 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18858 grpoideu 30488 mndideu 18654 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18888 grpoinveu 30498 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18919 grpo2inv 30510 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18932 grpoinvop 30512 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18954 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1768 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1769 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1771 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32399 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32412 cdj3i 32420 cdj3lem1 32413 cdjreui 32411 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32410 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41948 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41878 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41900 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41901 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41898 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41904 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41823 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41918 |
| [Holland95] p. 204 | Definition of involution | df-srng 20760 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39490 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41515 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41468 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39920 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41364 poml4N 39940 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41455 pexmidALTN 39965 pexmidN 39956 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41520 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39110 ldualset 39111 |
| [Holland95] p. 222 | Item 1 | df-lines 39488 df-pointsN 39489 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39890 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39934 omllaw4 39232 pol1N 39897 polcon3N 39904 |
| [Holland95] p. 223 | Definition | df-psubclN 39922 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39893 |
| [Holmes] p. 40 | Definition | df-xrn 38346 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31063 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32161 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31942 eigre 31814 eigrei 31813 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31943 eigorth 31817 eigorthi 31816 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31815 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30288 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30284 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30285 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30286 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30304 frgrregorufr0 30303 frgrregorufrg 30305 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30311 frrusgrord 30320 frrusgrord0 30319 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30067 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30294 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30297 frgrwopreg2 30298 frgrwopregasn 30295 frgrwopregbsn 30296 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30300 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30314 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30317 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30065 numclwlk1 30350 numclwlk1lem1 30348 numclwlk1lem2 30349 numclwwlk1 30340 numclwwlk8 30371 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30291 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29751 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30326 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30352 numclwwlkovh0 30351 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30360 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29957 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30364 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30367 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30370 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30382 natded 30382 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30382 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30382 natded 30382 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30382 |
| [Jech] p. 4 | Definition of class | cv 1539 cvjust 2723 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10508 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10506 alephmul 10507 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10505 infmap2 10146 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9743 |
| [Jech] p. 72 | Equation 9.3 | scott0 9815 scottex 9814 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9796 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9820 |
| [Jech] p. 78 | Note | opthprc 5695 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42897 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42985 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42986 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42909 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42913 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42914 rmyp1 42915 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42916 rmym1 42917 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42907 rmx1 42908 rmxluc 42918 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42911 rmy1 42912 rmyluc 42919 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42921 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42922 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42942 jm2.17b 42943 jm2.17c 42944 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42975 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42979 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42970 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42945 jm2.24nn 42941 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42984 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42990 rmygeid 42946 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43002 |
| [Juillerat] p. 11 | Section *5 | etransc 46274 etransclem47 46272 etransclem48 46273 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46269 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46271 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46257 |
| [Juillerat] p. 13 | Proof | etransclem35 46260 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46263 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46249 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46266 |
| [Juillerat] p. 14 | Proof | etransclem23 46248 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1967 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2012 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2017 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2007 cbvaliw 2006 wl-cbvmotv 37494 wl-motae 37496 wl-moteq 37495 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1986 spimw 1970 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2033 spw 2034 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31495 chabs1i 31497 chabs2 31496 chabs2i 31498 chjass 31512 chjassi 31465 latabs1 18416 latabs2 18417 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32317 ela 32318 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32262 cvrval2 39260 |
| [Kalmbach] p. 16 | Definition | df-ol 39164 df-oml 39165 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31563 cmbri 31569 cmtvalN 39197 df-cm 31562 df-cmtN 39163 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39233 pjoml5 31592 pjoml5i 31567 |
| [Kalmbach] p. 22 | Definition | pjoml2 31590 pjoml2i 31564 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31593 cmcmi 31571 cmcmii 31576 cmtcomN 39235 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39231 omlsi 31383 pjoml 31415 pjomli 31414 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39230 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31575 cmcm3 31594 cmcm3i 31573 cmcm3ii 31578 cmcm4i 31574 cmt3N 39237 cmt4N 39238 cmtbr2N 39239 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31587 cmbr3i 31579 cmtbr3N 39240 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31597 fh1i 31600 fh2 31598 fh2i 31601 omlfh1N 39244 |
| [Kalmbach] p. 65 | Remark | chjatom 32336 chslej 31477 chsleji 31437 shslej 31359 shsleji 31349 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31474 chocini 31433 chsupcl 31319 chsupval2 31389 h0elch 31234 helch 31222 hsupval2 31388 ocin 31275 ococss 31272 shococss 31273 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31291 |
| [Kalmbach] p. 66 | Remark | df-pjh 31374 pjssmi 32144 pjssmii 31660 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31624 osumi 31621 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32179 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32379 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32289 |
| [Kalmbach] p. 140 | Remark | hatomic 32339 hatomici 32338 hatomistici 32341 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39305 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32360 lsatexch 39029 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32334 cvlcvr1 39325 cvr1 39397 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32353 cvexchi 32348 cvrexch 39407 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32343 hlrelat 39389 hlrelat5N 39388 lrelat 39000 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21083 lsmsatcv 38996 spansncv 31632 spansncvi 31631 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39015 spansncv2 32272 |
| [Kalmbach] p. 266 | Definition | df-st 32190 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31828 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10575 fpwwe2 10572 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10576 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10583 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10578 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10580 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10593 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10597 gchxpidm 10598 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10609 gchhar 10608 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10144 unxpwdom 9518 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10599 |
| [Kreyszig] p. 3 | Property M1 | metcl 24253 xmetcl 24252 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24260 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24493 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11875 muleqadd 11798 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24359 |
| [Kreyszig] p. 19 | Remark | mopntopon 24360 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24419 mopnm 24365 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24417 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24422 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24463 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23178 lmmbr 25191 lmmbr2 25192 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23300 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25246 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25209 iscmet2 25227 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25249 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23381 metelcls 25238 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25239 metcld2 25240 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25032 lmodvneg1 20843 nvinv 30618 vcm 30555 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25028 lmod0vs 20833 slmd0vs 33193 vc0 30553 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20834 slmdvs0 33194 vcz 30554 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30670 ngpmet 24524 nrmmetd 24495 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30665 imsdval2 30666 ncvspds 25094 ngpds 24525 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24510 nvnd 30667 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24539 nmge0 24538 nvge0 30652 nvz 30648 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24545 nvabs 30651 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30780 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30724 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30786 blocni 30784 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30785 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25137 ipeq0 21580 ipz 30698 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25149 pythi 30829 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30833 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25171 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15798 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25369 minveco 30863 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30729 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25262 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30852 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32102 leopg 32101 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32120 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30897 |
| [Kulpa] p. 547 | Theorem | poimir 37640 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37639 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37638 |
| [Kulpa] p. 548 | Theorem | broucube 37641 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37633 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37634 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2381 axnul 5255 |
| [Kunen] p. 11 | Axiom 3 | axnul 5255 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7913 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8788 mapvalg 8786 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10451 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7897 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9693 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9735 r1elssi 9734 |
| [Kunen] p. 107 | Exercise 4 | rankop 9787 rankopb 9781 rankuni 9792 rankxplim 9808 rankxpsuc 9811 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44937 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44945 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44944 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44946 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 44951 rexabso 44952 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 44958 n0abso 44959 ssabso 44957 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44960 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 44970 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44965 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 44968 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 44969 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44964 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 44976 wfaxpr 44981 wfaxreg 44983 wfaxrep 44977 wfaxsep 44978 wfaxun 44982 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 44967 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 44980 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 44976 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 44975 omelaxinf2 44972 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 44985 wfaxinf2 44984 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 44998 permaxext 44988 permaxinf2 44996 permaxnul 44991 permaxpow 44992 permaxpr 44993 permaxrep 44989 permaxsep 44990 permaxun 44994 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 44986 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 44997 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4964 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33653 |
| [Lang] p. | Definition | df-rn 5642 |
| [Lang] p. 3 | Statement | lidrideqd 18578 mndbn0 18659 |
| [Lang] p. 3 | Definition | df-mnd 18644 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18596 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18750 |
| [Lang] p. 5 | Equation | gsumreidx 19831 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48163 |
| [Lang] p. 6 | Example | nn0mnd 48160 |
| [Lang] p. 6 | Equation | gsumxp2 19894 |
| [Lang] p. 6 | Statement | cycsubm 19116 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18994 |
| [Lang] p. 6 | Observation | mndlsmidm 19584 |
| [Lang] p. 7 | Definition | dfgrp2e 18877 |
| [Lang] p. 30 | Definition | df-tocyc 33079 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33124 |
| [Lang] p. 32 | Property (b) | cyc3conja 33129 cycpmconjv 33114 |
| [Lang] p. 53 | Definition | df-cat 17609 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18039 cat1lem 18038 |
| [Lang] p. 54 | Definition | df-iso 17691 |
| [Lang] p. 57 | Definition | df-inito 17926 df-termo 17927 |
| [Lang] p. 58 | Example | irinitoringc 21421 |
| [Lang] p. 58 | Statement | initoeu1 17953 termoeu1 17960 |
| [Lang] p. 62 | Definition | df-func 17800 |
| [Lang] p. 65 | Definition | df-nat 17888 |
| [Lang] p. 91 | Note | df-ringc 20566 |
| [Lang] p. 92 | Statement | mxidlprm 33434 |
| [Lang] p. 92 | Definition | isprmidlc 33411 |
| [Lang] p. 128 | Remark | dsmmlmod 21687 |
| [Lang] p. 129 | Proof | lincscm 48412 lincscmcl 48414 lincsum 48411 lincsumcl 48413 |
| [Lang] p. 129 | Statement | lincolss 48416 |
| [Lang] p. 129 | Observation | dsmmfi 21680 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33616 qusdimsum 33617 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33596 |
| [Lang] p. 147 | Definition | snlindsntor 48453 |
| [Lang] p. 504 | Statement | mat1 22367 matring 22363 |
| [Lang] p. 504 | Definition | df-mamu 22311 |
| [Lang] p. 505 | Statement | mamuass 22322 mamutpos 22378 matassa 22364 mattposvs 22375 tposmap 22377 |
| [Lang] p. 513 | Definition | mdet1 22521 mdetf 22515 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22611 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22507 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22531 |
| [Lang] p. 515 | Definition | df-minmar1 22555 smadiadetr 22595 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22530 mdetralt 22528 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22543 |
| [Lang] p. 518 | Definition | df-madu 22554 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22565 madurid 22564 matinv 22597 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22810 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33652 fedgmul 33620 |
| [Lang], p. 561 | Remark | chpmatply1 22752 |
| [Lang], p. 561 | Definition | df-chpmat 22747 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44316 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44311 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44317 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5255 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2708 |
| [Levy] p. 59 | Definition | df-ttrcl 9637 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9680 |
| [Levy] p. 338 | Axiom | df-clel 2803 df-cleq 2721 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2803 df-cleq 2721 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2708 |
| [Levy] p. 358 | Axiom | df-clab 2708 |
| [Levy58] p. 2 | Definition I | isfin1-3 10315 |
| [Levy58] p. 2 | Definition II | df-fin2 10215 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10214 |
| [Levy58] p. 2 | Definition III | df-fin3 10217 |
| [Levy58] p. 3 | Definition V | df-fin5 10218 |
| [Levy58] p. 3 | Definition IV | df-fin4 10216 |
| [Levy58] p. 4 | Definition VI | df-fin6 10219 |
| [Levy58] p. 4 | Definition VII | df-fin7 10220 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10344 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27631 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27642 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27674 nosupbnd1 27659 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27676 nosupbnd2 27661 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27680 noetasuplem4 27681 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27677 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1768 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1769 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1771 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32387 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32391 mdsymi 32390 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32385 mdsymlem6 32387 mdsymlem7 32388 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32389 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32292 ssdmd2 32293 ssmd1 32290 ssmd2 32291 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32288 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32260 df-md 32259 mdbr 32273 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32310 mdslj1i 32298 mdslj2i 32299 mdslle1i 32296 mdslle2i 32297 mdslmd1i 32308 mdslmd2i 32309 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32300 mdsl2bi 32302 mdsl2i 32301 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32314 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32311 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32312 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32289 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32294 mdsl3 32295 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32313 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32408 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39307 hlrelat1 39387 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39025 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32315 cvmdi 32303 cvnbtwn4 32268 cvrnbtwn4 39265 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32316 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39326 cvp 32354 cvrp 39403 lcvp 39026 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32378 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32377 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39319 hlexch4N 39379 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32380 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39430 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39736 atpsubN 39740 df-pointsN 39489 pointpsubN 39738 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39491 pmap11 39749 pmaple 39748 pmapsub 39755 pmapval 39744 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39752 pmap1N 39754 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39757 pmapglb2N 39758 pmapglb2xN 39759 pmapglbx 39756 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39839 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39464 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39783 paddclN 39829 paddidm 39828 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39465 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39825 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39464 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39465 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19589 lsmmod2 19590 lssats 38998 shatomici 32337 shatomistici 32340 shmodi 31369 shmodsi 31368 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32279 mdsymlem7 32388 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31568 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31472 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32394 |
| [Margaris] p. 40 | Rule C | exlimiv 1930 |
| [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 1780 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30379 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44897 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44898 |
| [Margaris] p. 79 | Rule C | exinst01 44608 exinst11 44609 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1976 19.2g 2189 r19.2z 4454 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2203 rr19.3v 3630 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2160 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1826 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1781 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2182 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2206 19.9h 2286 exlimd 2219 exlimdh 2290 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2163 excomim 2164 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2326 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30380 conventions-labels 30380 conventions-labels 30380 conventions-labels 30380 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1827 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44360 albi 1818 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2226 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2227 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44362 exbi 1847 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2230 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44359 2alimdv 1918 alimd 2213 alimdh 1817 alimdv 1916 ax-4 1809 ralimdaa 3236 ralimdv 3147 ralimdva 3145 ralimdvva 3182 sbcimdv 3819 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2208 19.21h 2287 19.21t 2207 19.21vv 44358 alrimd 2216 alrimdd 2215 alrimdh 1863 alrimdv 1929 alrimi 2214 alrimih 1824 alrimiv 1927 alrimivv 1928 hbralrimi 3123 r19.21be 3228 r19.21bi 3227 ralrimd 3240 ralrimdv 3131 ralrimdva 3133 ralrimdvv 3179 ralrimdvva 3190 ralrimi 3233 ralrimia 3234 ralrimiv 3124 ralrimiva 3125 ralrimivv 3176 ralrimivva 3178 ralrimivvva 3181 ralrimivw 3129 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44361 2eximdv 1919 exim 1834 eximd 2217 eximdh 1864 eximdv 1917 rexim 3070 reximd2a 3245 reximdai 3237 reximdd 45135 reximddv 3149 reximddv2 3194 reximddv3 3150 reximdv 3148 reximdv2 3143 reximdva 3146 reximdvai 3144 reximdvva 3183 reximi2 3062 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2212 19.23bi 2192 19.23h 2288 19.23t 2211 exlimdv 1933 exlimdvv 1934 exlimexi 44507 exlimiv 1930 exlimivv 1932 rexlimd3 45131 rexlimdv 3132 rexlimdv3a 3138 rexlimdva 3134 rexlimdva2 3136 rexlimdvaa 3135 rexlimdvv 3191 rexlimdvva 3192 rexlimdvvva 3193 rexlimdvw 3139 rexlimiv 3127 rexlimiva 3126 rexlimivv 3177 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1991 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1880 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1870 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2228 r19.27z 4464 r19.27zv 4465 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2229 19.28vv 44368 r19.28z 4457 r19.28zf 45146 r19.28zv 4460 rr19.28v 3631 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1873 r19.29d2r 3120 r19.29imd 3098 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1881 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2235 19.31vv 44366 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2234 r19.32 47092 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44364 19.33 1884 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1992 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1877 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2231 19.36vv 44365 r19.36zv 4466 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2233 19.37vv 44367 r19.37zv 4461 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1839 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1990 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1887 19.40 1886 r19.40 3099 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2236 19.41rg 44533 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2237 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1882 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2238 r19.44zv 4463 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2239 r19.45zv 4462 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2603 |
| [Mayet] p. 370 | Remark | jpi 32249 largei 32246 stri 32236 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32191 ishst 32193 |
| [Mayet3] p. 10 | Theorem | hstrbi 32245 hstri 32244 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31707 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31708 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32257 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31311 chsupcl 31319 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32339 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32333 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32360 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39970 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18428 latj32 18426 latjass 18424 |
| [Megill] p. 444 | Axiom C5 | ax-5 1910 ax5ALT 38893 |
| [Megill] p. 444 | Section 7 | conventions 30379 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38887 ax-c11n 38874 axc11n 2424 |
| [Megill] p. 446 | Lemma L17 | equtrr 2022 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38882 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38914 hbnae 2430 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2479 sbid 2256 sbidd-misc 49701 sbidd 49700 |
| [Megill] p. 448 | Remark 9.6 | axc14 2461 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38870 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38869 sp 2184 |
| [Megill] p. 448 | Scheme C6' | ax-11 2158 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38871 |
| [Megill] p. 448 | Scheme C8' | ax-7 2008 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38876 |
| [Megill] p. 448 | Scheme C10' | ax-6 1967 ax-c10 38872 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38873 |
| [Megill] p. 448 | Scheme C12' | ax-8 2111 |
| [Megill] p. 448 | Scheme C13' | ax-9 2119 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38877 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38875 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38878 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38890 dral1 2437 dral2-o 38916 dral2 2436 drex1 2439 drex2 2440 drsb1 2493 drsb2 2267 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2174 sbequ 2084 sbid2v 2507 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38883 hba1 2293 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46886 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3839 rspsbca 3840 stdpc4 2069 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38870 ra4 3846 stdpc5 2209 |
| [Mendelson] p. 81 | Rule C | exlimiv 1930 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2028 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2251 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3748 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5469 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4357 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4358 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4236 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4293 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4237 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4100 |
| [Mendelson] p. 231 | Definition of union | dfun3 4235 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5406 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4864 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5522 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4577 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5523 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4891 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5780 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6229 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7731 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6326 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8536 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9081 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9002 xpsneng 9003 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9009 xpcomeng 9010 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9012 |
| [Mendelson] p. 255 | Definition | brsdom 8923 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9005 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8780 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8985 mapsnend 8984 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9087 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9086 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8832 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8988 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9006 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10108 djucomen 10107 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10112 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10106 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8472 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8499 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10488 |
| [Mendelson] p. 281 | Definition | df-r1 9693 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9742 |
| [Mendelson] p. 287 | Axiom system MK | ru 3748 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30238 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30273 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30275 vdgn1frgrv3 30276 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30277 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30270 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30263 2pthfrgrrn 30261 2pthfrgrrn2 30262 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31231 |
| [Monk1] p. 22 | Remark | conventions 30379 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30379 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4198 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5737 ssrelf 32593 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5738 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5165 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6223 coi2 6224 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5874 rn0 5879 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6102 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5649 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5882 rnxp 6131 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5729 xp0 6119 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6037 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6034 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7870 imaexg 7869 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6031 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7029 funfvop 7004 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6897 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6908 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6546 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7211 dff13f 7212 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7175 funrnex 7912 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7203 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6188 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4924 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7964 df-1st 7947 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7965 df-2nd 7948 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9783 ranksnb 9756 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9784 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9785 rankunb 9779 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9767 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9693 r1val2 9766 |
| [Monk1] p. 117 | Lemma | zorn2 10435 zorn2g 10432 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9915 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10490 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9910 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1809 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2008 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2178 ax-c15 38875 ax12v2 2180 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38870 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2158 |
| [Monk2] p. 109 | Lemma 15 | equvini 2453 equvinv 2029 eqvinop 5442 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1910 ax5ALT 38893 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2142 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2158 |
| [Monk2] p. 114 | Lemma 21 | sp 2184 |
| [Monk2] p. 114 | Lemma 22 | axc4 2320 hba1-o 38883 hba1 2293 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2154 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2177 nfra2 3347 nfra2w 3272 |
| [Moore] p. 53 | Part I | df-mre 17523 |
| [Munkres] p. 77 | Example 2 | distop 22915 indistop 22922 indistopon 22921 |
| [Munkres] p. 77 | Example 3 | fctop 22924 fctop2 22925 |
| [Munkres] p. 77 | Example 4 | cctop 22926 |
| [Munkres] p. 78 | Definition of basis | df-bases 22866 isbasis3g 22869 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17382 tgval2 22876 |
| [Munkres] p. 79 | Remark | tgcl 22889 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22883 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22907 tgss3 22906 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22908 basgen2 22909 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37330 topdifinfeq 37331 topdifinffin 37329 topdifinfindis 37327 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23080 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22958 topcld 22955 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22959 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22961 |
| [Munkres] p. 94 | Definition of closure | clsval 22957 |
| [Munkres] p. 94 | Definition of interior | ntrval 22956 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22995 elcls 22993 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23003 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23068 neindisj 23037 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23070 |
| [Munkres] p. 97 | Definition of limit point | islp2 23065 lpval 23059 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23235 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23147 iscn 23155 iscn2 23158 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23200 cncnp2 23201 cncnpi 23198 df-cnp 23148 iscnp 23157 iscnp2 23159 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24464 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25244 |
| [Nathanson] p. 123 | Remark | reprgt 34605 reprinfz1 34606 reprlt 34603 |
| [Nathanson] p. 123 | Definition | df-repr 34593 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34625 |
| [Nathanson] p. 123 | Proposition | breprexp 34617 breprexpnat 34618 itgexpif 34590 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32083 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47804 |
| [Pfenning] p. 17 | Definition XM | natded 30382 |
| [Pfenning] p. 17 | Definition NNC | natded 30382 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30382 |
| [Pfenning] p. 18 | Rule" | natded 30382 |
| [Pfenning] p. 18 | Definition /\I | natded 30382 |
| [Pfenning] p. 18 | Definition ` `E | natded 30382 natded 30382 natded 30382 natded 30382 natded 30382 |
| [Pfenning] p. 18 | Definition ` `I | natded 30382 natded 30382 natded 30382 natded 30382 natded 30382 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30382 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30382 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30382 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30382 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30382 |
| [Pfenning] p. 127 | Definition =E | natded 30382 |
| [Pfenning] p. 127 | Definition =I | natded 30382 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25135 df-dip 30680 dip0l 30697 ip0l 21578 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25176 ipval 30682 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30693 ipcj 21576 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25138 dipdir 30821 ipdir 21581 ipdiri 30809 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30689 nmsq 25127 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30804 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30806 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30807 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25144 dipass 30824 ipass 21587 ipassi 30820 |
| [Prugovecki] p. 186 | Definition of bra | braval 31923 df-bra 31829 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31830 kbval 31933 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32361 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39875 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32375 atcvat4i 32376 cvrat3 39429 cvrat4 39430 lsatcvat3 39038 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32261 cvrval 39255 df-cv 32258 df-lcv 39005 lspsncv0 21088 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39887 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39888 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2708 rabid 3424 rabidd 45142 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2279 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2721 |
| [Quine] p. 19 | Definition 2.9 | conventions 30379 df-v 3446 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2867 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2864 abid2f 2922 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2276 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2086 sbalex 2243 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2803 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2729 eqid1 30446 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2736 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3751 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3752 dfsbcq2 3753 |
| [Quine] p. 43 | Theorem 6.8 | vex 3448 |
| [Quine] p. 43 | Theorem 6.9 | isset 3458 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3554 spcgv 3559 spcimgf 3513 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3763 spsbcd 3764 |
| [Quine] p. 44 | Theorem 6.12 | elex 3465 |
| [Quine] p. 44 | Theorem 6.13 | elab 3643 elabg 3640 elabgf 3638 |
| [Quine] p. 44 | Theorem 6.14 | noel 4297 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4677 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4588 df-sn 4586 |
| [Quine] p. 49 | Theorem 7.4 | snss 4745 snssg 4743 |
| [Quine] p. 49 | Theorem 7.5 | prss 4780 prssg 4779 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4722 prid1g 4720 prid2 4723 prid2g 4721 snid 4622 snidg 4620 |
| [Quine] p. 51 | Theorem 7.12 | snex 5386 |
| [Quine] p. 51 | Theorem 7.13 | prex 5387 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4886 unisnALT 44908 unisng 4885 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4890 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4897 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4895 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6466 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47080 dfiota2 6453 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47089 iotaval 6470 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6477 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6472 |
| [Quine] p. 58 | Definition 9.1 | df-op 4592 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5480 opabidw 5479 opelopab 5497 opelopaba 5491 opelopabaf 5499 opelopabf 5500 opelopabg 5493 opelopabga 5488 opelopabgf 5495 oprabid 7401 oprabidw 7400 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5637 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5639 |
| [Quine] p. 64 | Definition 9.15 | df-id 5526 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6565 |
| [Quine] p. 65 | Theorem 10.4 | funi 6532 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6553 funsng 6551 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6501 |
| [Quine] p. 65 | Definition 10.2 | args 6052 dffv4 6837 |
| [Quine] p. 68 | Definition 10.11 | conventions 30379 df-fv 6507 fv2 6835 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14213 nn0opth2i 14212 nn0opthi 14211 omopthi 8602 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8355 |
| [Quine] p. 232 | Equation i | carddom 10483 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6588 funimaexg 6587 |
| [Quine] p. 331 | Axiom system NF | ru 3748 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31063 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30680 polid 31138 polid2i 31136 polidi 31137 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30792 |
| [ReedSimon] p. 195 | Remark | lnophm 31998 lnophmi 31997 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32111 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32113 leopmuli 32112 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32116 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31831 leoppos 32105 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32115 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32104 |
| [Roman] p. 4 | Definition | df-dmat 22410 df-dmatalt 48380 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20073 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20155 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48467 |
| [Roman] p. 112 | Note | isldepslvec2 48467 ldepsnlinc 48490 zlmodzxznm 48479 |
| [Roman] p. 112 | Example | zlmodzxzequa 48478 zlmodzxzequap 48481 zlmodzxzldep 48486 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22810 |
| [Rosenlicht] p. 80 | Theorem | heicant 37642 |
| [Rosser] p. 281 | Definition | df-op 4592 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34629 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34630 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48347 pmtr3ncom 19389 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19385 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19328 cayleyth 19329 |
| [Rudin] p. 164 | Equation 27 | efcan 16038 |
| [Rudin] p. 164 | Equation 30 | efzval 16046 |
| [Rudin] p. 167 | Equation 48 | absefi 16140 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1771 |
| [Sanford] p. 39 | Rule 4 | mptxor 1769 |
| [Sanford] p. 40 | Rule 1 | mptnan 1768 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6076 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6079 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6073 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6071 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17523 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17524 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17524 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17526 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10066 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43044 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10375 axdc3 10383 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20157 isrngo 37884 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31521 |
| [Schechter] p. 276 | Definition of span | df-span 31288 spanval 31312 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22913 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6345 onelord 43233 ordelon 6344 ordelord 6342 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43234 sucidg 6403 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6375 onsuc 7767 ord0 6374 ordsuci 7764 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43235 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5213 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43010 elon2 6331 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6326 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5534 epelg 5532 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9526 epirron 43236 ordirr 6338 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43238 oneptr 43237 ontr1 6367 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6363 oneptri 43239 ordtri3or 6352 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8442 ord0eln0 6376 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6389 onsucss 43248 trsucss 6410 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7773 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6416 ordnbtwn 6415 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43250 ordnexbtwnsuc 43249 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10330 onsucf1lem 43251 onsucf1o 43254 onsucf1olem 43252 onsucrn 43253 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43255 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7801 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43244 ordne0gt0 43243 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43246 limnsuc 43247 onsucelab 43245 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9572 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7816 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9575 ordom 7832 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9576 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8581 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7736 ssorduni 7735 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8472 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9579 limom 7838 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8411 df1o2 8418 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8457 oa0suclim 43257 oalim 8473 oasuc 8465 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8458 om0suclim 43258 omlim 8474 omsuc 8467 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8463 oe0m1 8462 oe0suclim 43259 oelim 8475 oesuc 8468 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43211 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43261 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43262 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43263 limexissupab 43265 limiun 43264 limuni 6382 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8479 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8483 om1om1r 43266 om1r 8484 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8476 oaomoecl 43260 oecl 8478 omcl 8477 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43213 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8485 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8486 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43267 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43268 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8552 nnamecl 43269 nnecl 8554 nnmcl 8553 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43270 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8493 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8494 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8501 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43272 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43273 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43275 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8500 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43279 omword1 8514 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43278 oaordnrex 43277 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43274 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43280 omword2 8515 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43281 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43282 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43283 omordi 8507 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8509 omord2com 43284 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43285 df-2o 8412 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43288 oewordi 8532 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43289 oeworde 8534 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43290 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43291 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43287 omnord1ex 43286 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43292 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43294 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43298 oenord1ex 43297 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43299 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8502 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43293 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8520 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8521 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43301 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8538 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43302 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43303 cantnfub2 43304 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43307 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28894 axtgcgrrflx 28442 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28895 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28896 axtgcgrid 28443 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28428 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28907 axtgsegcon 28444 df-trkgcb 28430 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28918 axtg5seg 28445 df-trkgcb 28430 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28919 axtgbtwnid 28446 df-trkgb 28429 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28921 axtgpasch 28447 df-trkgb 28429 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28940 df-trkg2d 34649 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28450 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28451 df-trkg2d 34649 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28943 axtgeucl 28452 df-trkge 28431 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28956 axtgcont 28449 axtgcont1 28448 df-trkgb 28429 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35968 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35970 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35973 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35977 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35978 tgcgrcomimp 28457 tgcgrcoml 28459 tgcgrcomr 28458 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35983 tgcgrtriv 28464 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35987 tg5segofs 34657 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34654 df-ofs 35964 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35989 tgcgrextend 28465 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35991 tgsegconeq 28466 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36003 btwntriv2 35993 tgbtwntriv2 28467 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 35994 tgbtwncom 28468 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 35997 tgbtwntriv1 28471 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 35998 tgbtwnswapid 28472 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36004 btwnintr 36000 tgbtwnexch2 28476 tgbtwnintr 28473 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36006 btwnexch3 36001 tgbtwnexch 28478 tgbtwnexch3 28474 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36005 tgbtwnouttr 28477 tgbtwnouttr2 28475 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28939 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36008 tgbtwndiff 28486 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28479 trisegint 36009 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36025 tgifscgr 28488 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28538 colrot1 28539 colrot2 28540 lncom 28602 lnrot1 28603 lnrot2 28604 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36021 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36026 tgcgrsub 28489 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36036 tgcgrxfr 28498 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28497 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36022 df-cgrg 28491 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28491 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36037 tgbtwnxfr 28510 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36043 colinearperm2 36045 colinearperm3 36044 colinearperm4 36046 colinearperm5 36047 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28513 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36020 tgellng 28533 tglng 28526 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36048 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36056 lnxfr 28546 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36057 lnext 28547 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36061 tgfscgr 28548 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36062 lncgr 28549 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36023 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36064 lnid 28550 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36065 tgidinside 28551 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36082 tgbtwnconn1 28555 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36083 tgbtwnconn2 28556 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36084 tgbtwnconn3 28557 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36090 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36088 legov 28565 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28566 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28579 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36091 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36093 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36095 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36096 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36097 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36094 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36099 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28567 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28569 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28570 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28571 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28572 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36106 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36107 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36102 df-outsideof 36101 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36103 ishlg 28582 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28587 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28589 outsideofrflx 36108 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28583 hlcomd 28584 outsideofcom 36109 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28590 outsideoftr 36110 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28598 outsideofeu 36112 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36119 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36120 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36113 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36128 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36129 tglineelsb2 28612 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36131 linerflx1 36130 linerflx2 36132 tglinecom 28615 tglinerflx1 28613 tglinerflx2 28614 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36134 tglinethru 28616 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36118 tglng 28526 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28574 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36137 tglinethrueu 28619 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36138 tglineineq 28623 tglineinteq 28625 tglineintmo 28622 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28629 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28630 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28631 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28646 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28642 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28634 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28633 ismir 28639 mirbtwn 28638 mircgr 28637 mirfv 28636 mirval 28635 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28644 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28645 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28646 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28649 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28650 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28655 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28652 mirbtwni 28651 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28653 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28665 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28669 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28666 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28667 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28668 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28671 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28672 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28678 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28674 israg 28677 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28679 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28680 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28682 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28683 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28684 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28685 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28686 ragncol 28689 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28687 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28693 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28697 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28694 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28676 isperp 28692 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28695 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28702 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28710 colperpexlem2 28711 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28713 colperpexlem3 28712 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28718 midex 28717 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28715 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28724 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28719 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28728 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28731 opphllem6 28732 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28734 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28447 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28735 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28743 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28738 hpgbr 28740 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28745 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28744 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28746 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28747 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28748 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28749 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28750 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28764 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28754 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28768 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28769 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28770 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28771 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28772 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28775 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28777 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28755 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28778 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28781 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28782 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28783 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28784 trgcopyeu 28786 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28810 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28789 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28798 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28796 cgrahl2 28797 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28799 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28800 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28802 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28803 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28806 cgrahl 28807 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28811 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28812 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28813 acopyeu 28814 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28821 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28825 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28818 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28833 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28826 isleag 28827 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28835 tgsas1 28834 tgsas2 28836 tgsas3 28837 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28839 tgasa1 28838 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28840 tgsss2 28841 tgsss3 28842 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27215 dchrsum 27213 dchrsum2 27212 sumdchr 27216 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27217 sum2dchr 27218 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19982 ablfacrp2 19983 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27160 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27161 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27168 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27426 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27429 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27483 vmalogdivsum2 27482 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27473 dirith2 27472 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27471 rpvmasum 27470 rpvmasum2 27456 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27431 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27469 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27436 dchrisumlem1 27433 dchrisumlem2 27434 dchrisumlem3 27435 dchrisumlema 27432 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27439 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27468 dchrmusumlem 27466 dchrvmasumlem 27467 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27438 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27440 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27464 dchrisum0re 27457 dchrisumn0 27465 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27450 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27454 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27455 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27510 pntrsumbnd2 27511 pntrsumo1 27509 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27474 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27476 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27478 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27481 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27486 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27487 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27492 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27494 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27495 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27503 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27504 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27501 selberg3lem2 27502 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27505 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27499 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27512 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27513 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27514 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27528 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27540 pntlemb 27541 pntlemc 27539 pntlemd 27538 pntlemg 27542 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27540 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27532 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27537 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27540 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27553 pntleml 27555 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33726 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33713 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33745 constrinvcl 33756 constrmulcl 33754 constrnegcl 33746 constrsqrtcl 33762 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33732 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33742 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33764 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33774 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4265 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4364 dif0 4337 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4451 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4434 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4256 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4257 |
| [Stoll] p. 20 | Remark | invdif 4238 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4594 |
| [Stoll] p. 43 | Definition | uniiun 5017 |
| [Stoll] p. 44 | Definition | intiin 5018 |
| [Stoll] p. 45 | Definition | df-iin 4954 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4953 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4265 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44317 |
| [Suppes] p. 22 | Theorem 2 | eq0 4309 eq0f 4306 |
| [Suppes] p. 22 | Theorem 4 | eqss 3959 eqssd 3961 eqssi 3960 |
| [Suppes] p. 23 | Theorem 5 | ss0 4361 ss0b 4360 |
| [Suppes] p. 23 | Theorem 6 | sstr 3952 sstrALT2 44817 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4062 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4063 |
| [Suppes] p. 23 | Theorem 9 | psstr 4066 |
| [Suppes] p. 23 | Theorem 10 | pssss 4057 |
| [Suppes] p. 25 | Theorem 12 | elin 3927 elun 4112 |
| [Suppes] p. 26 | Theorem 15 | inidm 4186 |
| [Suppes] p. 26 | Theorem 16 | in0 4354 |
| [Suppes] p. 27 | Theorem 23 | unidm 4116 |
| [Suppes] p. 27 | Theorem 24 | un0 4353 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4137 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4145 |
| [Suppes] p. 27 | Theorem 27 | unss 4149 |
| [Suppes] p. 27 | Theorem 28 | indir 4245 |
| [Suppes] p. 27 | Theorem 29 | undir 4246 |
| [Suppes] p. 28 | Theorem 32 | difid 4335 |
| [Suppes] p. 29 | Theorem 33 | difin 4231 |
| [Suppes] p. 29 | Theorem 34 | indif 4239 |
| [Suppes] p. 29 | Theorem 35 | undif1 4435 |
| [Suppes] p. 29 | Theorem 36 | difun2 4440 |
| [Suppes] p. 29 | Theorem 37 | difin0 4433 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4431 |
| [Suppes] p. 29 | Theorem 39 | difundi 4249 |
| [Suppes] p. 29 | Theorem 40 | difindi 4251 |
| [Suppes] p. 30 | Theorem 41 | nalset 5263 |
| [Suppes] p. 39 | Theorem 61 | uniss 4875 |
| [Suppes] p. 39 | Theorem 65 | uniop 5470 |
| [Suppes] p. 41 | Theorem 70 | intsn 4944 |
| [Suppes] p. 42 | Theorem 71 | intpr 4942 intprg 4941 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5426 |
| [Suppes] p. 42 | Theorem 78 | intun 4940 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4992 dfiun2g 4990 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4993 |
| [Suppes] p. 47 | Theorem 86 | elpw 4563 elpw2 5284 elpw2g 5283 elpwg 4562 elpwgdedVD 44899 |
| [Suppes] p. 47 | Theorem 87 | pwid 4581 |
| [Suppes] p. 47 | Theorem 89 | pw0 4772 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4773 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5646 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5787 xpindir 5788 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5700 xpundir 5701 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9525 |
| [Suppes] p. 58 | Theorem 2 | relss 5736 |
| [Suppes] p. 59 | Theorem 4 | eldm 5854 eldm2 5855 eldm2g 5853 eldmg 5852 |
| [Suppes] p. 59 | Definition 3 | df-dm 5641 |
| [Suppes] p. 60 | Theorem 6 | dmin 5865 |
| [Suppes] p. 60 | Theorem 8 | rnun 6106 |
| [Suppes] p. 60 | Theorem 9 | rnin 6107 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5842 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5836 brcnvg 5833 |
| [Suppes] p. 62 | Equation 5 | elcnv 5830 elcnv2 5831 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6064 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6105 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6103 |
| [Suppes] p. 63 | Definition | dftrrels2 38559 |
| [Suppes] p. 63 | Theorem 20 | co02 6221 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5927 |
| [Suppes] p. 63 | Definition 7 | df-co 5640 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5839 |
| [Suppes] p. 64 | Theorem 27 | coass 6226 |
| [Suppes] p. 65 | Theorem 31 | resundi 5953 |
| [Suppes] p. 65 | Theorem 34 | elima 6025 elima2 6026 elima3 6027 elimag 6024 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6110 |
| [Suppes] p. 66 | Theorem 40 | dminss 6114 |
| [Suppes] p. 66 | Theorem 41 | imainss 6115 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6118 |
| [Suppes] p. 81 | Definition 34 | dfec2 8651 |
| [Suppes] p. 82 | Theorem 72 | elec 8694 elecALTV 38248 elecg 8692 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38595 erth 8702 erth2 8703 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38598 erdisj 8705 |
| [Suppes] p. 83 | Definition 35, | df-parts 38750 dfmembpart2 38755 |
| [Suppes] p. 89 | Theorem 96 | map0b 8833 |
| [Suppes] p. 89 | Theorem 97 | map0 8837 map0g 8834 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8838 mapsnd 8836 |
| [Suppes] p. 89 | Theorem 99 | mapss 8839 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9997 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9996 |
| [Suppes] p. 92 | Theorem 1 | enref 8933 enrefg 8932 |
| [Suppes] p. 92 | Theorem 2 | ensym 8951 ensymb 8950 ensymi 8952 |
| [Suppes] p. 92 | Theorem 3 | entr 8954 |
| [Suppes] p. 92 | Theorem 4 | unen 8994 |
| [Suppes] p. 94 | Theorem 15 | endom 8927 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8948 |
| [Suppes] p. 94 | Theorem 17 | domtr 8955 |
| [Suppes] p. 95 | Theorem 18 | sbth 9038 |
| [Suppes] p. 97 | Theorem 23 | canth2 9071 canth2g 9072 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9042 df-sdom 8898 dfsdom2 9041 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9055 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9044 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9043 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9053 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8930 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9056 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9051 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8979 fundmeng 8980 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9016 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9052 |
| [Suppes] p. 104 | Theorem 37 | fofi 9238 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9244 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9244 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10480 |
| [Suppes] p. 130 | Definition 3 | df-tr 5210 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7736 |
| [Suppes] p. 134 | Definition 6 | df-suc 6326 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7856 finds 7852 finds1 7855 finds2 7854 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9581 isfinite2 9221 isfiniteg 9224 unbnn 9219 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10847 df-ltpq 10839 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7819 tfinds 7816 tfinds2 7820 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8492 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8494 |
| [Suppes] p. 211 | Theorem 25 | oaass 8502 |
| [Suppes] p. 225 | Definition 8 | iscard2 9905 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10492 |
| [Suppes] p. 228 | Theorem 59 | harcard 9907 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9995 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6372 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7749 onminsb 7750 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10501 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9999 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10006 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10000 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9869 |
| [Suppes] p. 242 | Theorem 6 | weth 10424 |
| [Suppes] p. 242 | Theorem 8 | entric 10486 |
| [Suppes] p. 242 | Theorem 9 | carden 10480 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35676 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35680 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2701 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2721 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2803 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2723 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2749 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7373 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3748 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5371 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4610 elpr2 4612 elpr2g 4611 elprg 4608 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4600 elsn2 4625 elsn2g 4624 elsng 4599 velsn 4601 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5422 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4595 sneqr 4800 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4606 dfsn2 4598 dfsn2ALT 4607 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7697 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5431 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5419 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5403 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7700 unexg 7699 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4651 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4868 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3918 df-un 3916 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4884 uniprg 4883 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5327 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4649 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6392 elsucg 6390 sstr2 3950 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4117 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4168 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4131 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4187 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4243 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4244 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3931 df-ss 3928 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4561 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4146 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3929 sseqin2 4182 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3966 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4196 inss2 4197 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4008 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4878 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5404 sspwimp 44900 sspwimpALT 44907 sspwimpALT2 44910 sspwimpcf 44902 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5411 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5229 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3403 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5257 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3914 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4295 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4335 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4312 n0f 4308 neq0 4311 neq0f 4307 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9524 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9661 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9663 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3446 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5265 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4359 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5271 ssexg 5273 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5267 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9531 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9526 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4325 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4094 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4259 undif3VD 44864 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4095 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4102 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3045 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3054 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7709 xpexg 7706 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5638 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6571 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6747 fun11 6574 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6513 svrelfun 6572 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5841 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5843 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5643 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5644 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5640 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6155 dfrel2 6150 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5647 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5765 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5772 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5785 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5965 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5945 opelresi 5947 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5972 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5961 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5966 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6542 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6068 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6540 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6749 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2602 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30379 df-fv 6507 fv3 6858 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7881 cnvexg 7880 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7865 dmexg 7857 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7866 rnexg 7858 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44436 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7876 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6853 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47168 tz6.12-1-afv2 47235 tz6.12-1 6863 tz6.12-afv 47167 tz6.12-afv2 47234 tz6.12 6865 tz6.12c-afv2 47236 tz6.12c 6862 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47231 tz6.12-2 6828 tz6.12i-afv2 47237 tz6.12i 6868 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6502 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6503 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6505 wfo 6497 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6504 wf1 6496 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6506 wf1o 6498 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6985 eqfnfv2 6986 eqfnfv2f 6989 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6941 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7173 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7171 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6588 funimaexg 6587 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5103 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5540 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5592 dffr3 6059 eliniseg 6054 iniseg 6057 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5531 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5608 fr3nr 7728 frirr 5607 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5584 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7730 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5595 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5617 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6308 tz6.26i 6309 wefrc 5625 wereu2 5628 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6310 wfii 6311 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6508 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7286 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7287 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7293 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7294 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7295 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7299 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7306 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7308 |
| [TakeutiZaring] p. 35 | Notation | wtr 5209 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44437 tz7.2 5614 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5215 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6333 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6341 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6342 ordelordALT 44520 ordelordALTVD 44849 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6348 ordelssne 6347 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6346 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6350 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7738 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7739 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6324 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6352 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44532 ordon 7733 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7734 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7809 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6368 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5211 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7748 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7786 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6426 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6425 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7735 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4897 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6326 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6402 sucidg 6403 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7767 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6416 ordnbtwn 6415 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7783 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6325 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7837 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7842 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7797 ordelsuc 7775 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7777 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7807 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7824 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7845 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7846 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7847 |
| [TakeutiZaring] p. 43 | Remark | omon 7834 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9564 omex 9572 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7832 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7851 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7848 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7849 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7827 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4922 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5228 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4923 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5294 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7751 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6371 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4907 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9589 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7746 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8321 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8342 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8343 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8344 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8351 tz7.44-2 8352 tz7.44-3 8353 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8313 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8308 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8292 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8390 tz7.49c 8391 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8388 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8387 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8389 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2649 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9940 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9941 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8473 oasuc 8465 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7817 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8476 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8457 oa0r 8479 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8477 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8489 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8560 nnaordi 8559 oaord 8488 oaordi 8487 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5008 uniss2 4901 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8491 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8496 oawordex 8498 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8552 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8589 |
| [TakeutiZaring] p. 60 | Remark | oancom 9580 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8501 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8557 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8493 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8460 omlim 8474 omsuc 8467 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8458 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8554 nnmcl 8553 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8573 nnmordi 8572 omord 8509 omordi 8507 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8510 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8577 omwordri 8513 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8480 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8483 om1r 8484 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8516 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8518 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8519 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8520 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8521 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8549 oe0 8463 oelim 8475 oesuc 8468 onesuc 8471 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8461 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8527 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8528 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8462 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8486 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8529 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8535 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8533 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8534 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8538 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8540 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9657 tz9.1 9658 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9693 r10 9697 r1lim 9701 r1limg 9700 r1suc 9699 r1sucg 9698 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9709 r1ord2 9710 r1ordg 9707 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9719 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9744 tz9.13 9720 tz9.13g 9721 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9694 rankval 9745 rankvalb 9726 rankvalg 9746 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9768 rankelb 9753 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9782 rankval3 9769 rankval3b 9755 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9758 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9724 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9763 rankr1c 9750 rankr1g 9761 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9764 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9778 rankssb 9777 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9771 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9770 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10404 dfac3 10050 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9959 numth 10401 numth2 10400 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10475 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10476 cardid2 9882 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9889 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10480 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9888 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9873 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9894 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9886 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9091 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8966 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9096 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9020 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9892 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10027 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9147 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9155 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10028 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9152 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10017 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9995 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9901 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10145 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9249 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8899 isfi 8924 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9156 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10463 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9013 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10455 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10115 unxpdom 9176 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9903 cardsdomelir 9902 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9178 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9943 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8778 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10491 infxpidm2 9946 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10136 infxp 10143 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9025 pw2f1o 9023 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9084 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10416 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10411 ac6s5 10420 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10472 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10473 uniimadomf 10474 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10203 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10198 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10183 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10180 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10186 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10193 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10202 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10511 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10181 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10205 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10026 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10025 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10037 alephfp2 10038 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10628 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10041 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10498 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10512 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10513 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38869 |
| [Tarski] p. 67 | Scheme B5 | sp 2184 |
| [Tarski] p. 68 | Lemma 6 | avril1 30442 equid 2012 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2017 |
| [Tarski] p. 70 | Lemma 14 | spim 2385 spime 2387 spimew 1971 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2178 ax-c15 38875 ax12i 1966 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2086 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1968 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1910 ax5ALT 38893 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2008 ax-8 2111 ax-9 2119 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28444 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28445 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28447 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28447 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28448 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16187 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37646 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37648 |
| [Weierstrass] p. 272 | Definition | df-mdet 22505 mdetuni 22542 |
| [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 37426 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43782 imim2 58 wl-luk-imim2 37421 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47013 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2656 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37424 |
| [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 44909 wl-luk-notnotr 37425 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43812 axfrege28 43811 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 37418 |
| [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 30380 pm2.27 42 wl-luk-pm2.27 37416 |
| [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 38338 |
| [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 44340 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44341 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1870 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44342 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44343 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44344 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1893 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44345 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44346 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44347 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44348 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44349 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44351 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44352 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44353 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44350 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2091 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44356 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44357 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2071 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2161 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1829 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1830 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44358 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44359 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44360 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44361 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44363 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44362 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1887 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44365 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44366 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44364 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1828 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44367 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44368 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1846 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44369 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2344 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1860 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44374 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44370 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44371 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44372 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44373 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44378 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44375 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44376 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44377 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44379 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2562 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44389 pm13.13b 44390 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44391 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3006 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3007 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3629 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44397 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44398 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44392 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44535 pm13.193 44393 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44394 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44395 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44396 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44403 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44402 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44401 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3813 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44404 pm14.122b 44405 pm14.122c 44406 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44407 pm14.123b 44408 pm14.123c 44409 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44411 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44410 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44412 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6480 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44413 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6481 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44414 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44416 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2626 eupickbi 2629 sbaniota 44417 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44415 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2577 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44419 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30379 df-fv 6507 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9930 pm54.43lem 9929 |
| [Young] p. 141 | Definition of operator ordering | leop2 32103 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32109 idleop 32110 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42809 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42816 pellexlem1 42810 |