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 17623 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17623 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18032 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17644 0funcg 49557 df-termc 49945 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50022 prsthinc 49936 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50050 df-mndtc 50050 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50046 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17667 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50038 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50063 oppgoppchom 50062 oppgoppcid 50064 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17737 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17725 invisoinvl 17746 |
| [Adamek] p. 28 | Example 3.13 | idinv 17745 idiso 17744 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17730 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17704 df-iso 17705 dfiso2 17728 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17711 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17762 cicerALT 49518 |
| [Adamek] p. 29 | Definition 3.15 | cic 17755 df-cic 17752 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17814 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17726 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17727 isoco 17733 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17814 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17837 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49776 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17830 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50046 discthing 49933 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49890 prsthinc 49936 thincciso 49925 thincciso2 49927 thincciso3 49928 thinccisod 49926 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50050 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17844 cofucla 49568 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49634 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18067 catcisoi 49872 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18122 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17863 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17862 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18122 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17887 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17893 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17892 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18107 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18107 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49604 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49595 funcoppc 17831 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18055 elcatchom 49869 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17881 fthoppf 49636 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17880 fulloppf 49635 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18064 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49557 df-catc 18055 |
| [Adamek] p. 45 | Exercise 3G | incat 50073 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50076 nelsubc3 49543 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49623 imasubc2 49624 imasubc3 49628 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17794 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17795 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49543 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17806 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17768 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49632 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49631 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49633 ressffth 17896 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50074 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17902 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17923 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17927 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17903 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17929 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49557 df-inito 17940 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49557 df-termc 49945 initc 49563 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21467 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17941 oppctermo 49708 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17968 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17972 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49709 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17942 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21468 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17975 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17703 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49941 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49940 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49905 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17738 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17740 |
| [Adamek] p. 185 | Section 10.67 | updjud 9847 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50117 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50117 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50117 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50118 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50118 |
| [Adamek] p. 478 | Item Rng | df-ringc 20612 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49021 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49043 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14522 df-pfx 14623 df-substr 14593 df-word 14465 lencl 14484 wrd0 14490 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24682 df-nmoo 30836 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32244 hmopidmchi 32242 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32292 pjcmul2i 32293 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32009 unoplin 32011 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32010 unopadj2 32029 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32104 lnopunii 32103 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32177 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27938 |
| [Alling] p. 184 | Axiom B | bdayfo 27660 |
| [Alling] p. 184 | Axiom O | ltsso 27659 |
| [Alling] p. 184 | Axiom SD | nodense 27675 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27766 |
| [Alling] p. 185 | Theorem | conway 27790 |
| [Alling] p. 185 | Axiom FE | noeta 27726 |
| [Alling] p. 186 | Theorem 4 | lesrec 27810 lesrecd 27811 |
| [Alling], p. 2 | Definition | rp-brsslt 43865 |
| [Alling], p. 3 | Note | nla0001 43868 nla0002 43866 nla0003 43867 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11319 addcan2d 11339 addcan2i 11329 addcand 11338 addcani 11328 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11372 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11431 negsubd 11500 negsubi 11461 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11433 negnegd 11485 negnegi 11453 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11572 subdid 11595 subdii 11588 subdir 11573 subdird 11596 subdiri 11589 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11314 mul01d 11334 mul01i 11325 mul02 11313 mul02d 11333 mul02i 11324 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11776 mulcan2d 11773 mulcand 11772 mulcani 11778 |
| [Apostol] p. 18 | Theorem I.8 | receu 11784 xreceu 33001 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11814 divrecd 11923 divreci 11889 divreczi 11882 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11841 recreci 11876 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11779 mul0ord 11787 mul0ori 11786 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11578 mul2negd 11594 mul2negi 11587 mulneg1 11575 mulneg1d 11592 mulneg1i 11585 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11859 divadddivd 11964 divadddivi 11906 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11844 divmuldivd 11961 divmuldivi 11904 rdivmuldivd 20382 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11845 divdivdivd 11967 divdivdivi 11907 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12955 rpaddcld 12990 rpmulcl 12956 rpmulcld 12991 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12965 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12968 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11261 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11732 ltadd1dd 11750 ltadd1i 11693 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 11994 ltmul1a 11993 ltmul1i 12063 ltmul1ii 12073 ltmul2 11995 ltmul2d 13017 ltmul2dd 13031 ltmul2i 12066 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11659 msqgt0d 11706 msqgt0i 11676 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11661 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11645 lt0neg1d 11708 ltneg 11639 ltnegd 11717 ltnegi 11683 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11624 lt2addd 11762 lt2addi 11701 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12932 |
| [Apostol] p. 21 | Exercise 4 | recgt0 11990 recgt0d 12079 recgt0i 12050 recgt0ii 12051 |
| [Apostol] p. 22 | Definition of integers | df-z 12514 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12177 |
| [Apostol] p. 22 | Definition of rationals | df-q 12888 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9358 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12422 |
| [Apostol] p. 26 | Theorem I.29 | arch 12423 archd 45607 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12621 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12424 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12886 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12885 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13140 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16297 zneo 12601 zneoALTV 48142 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26710 msqsqrtd 15394 resqrtth 15206 sqrtth 15316 sqrtthi 15322 sqsqrtd 15393 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12166 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12852 |
| [Apostol] p. 361 | Remark | crreczi 14179 |
| [Apostol] p. 363 | Remark | absgt0i 15351 |
| [Apostol] p. 363 | Example | abssubd 15407 abssubi 15355 |
| [ApostolNT] p. 7 | Remark | fmtno0 48000 fmtno1 48001 fmtno2 48010 fmtno3 48011 fmtno4 48012 fmtno5fac 48042 fmtnofz04prm 48037 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47988 |
| [ApostolNT] p. 8 | Definition | df-ppi 27081 |
| [ApostolNT] p. 14 | Definition | df-dvds 16211 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16227 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16252 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16247 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16240 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16242 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16228 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16229 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16234 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16269 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16271 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16273 |
| [ApostolNT] p. 15 | Definition | df-gcd 16453 dfgcd2 16504 |
| [ApostolNT] p. 16 | Definition | isprm2 16640 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16611 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16875 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16471 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16505 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16507 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16486 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16478 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16670 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16672 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16888 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16882 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16361 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16545 |
| [ApostolNT] p. 24 | Definition | df-mu 27082 |
| [ApostolNT] p. 25 | Definition | df-phi 16725 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27172 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16750 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16735 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16739 |
| [ApostolNT] p. 32 | Definition | df-vma 27079 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27174 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27198 |
| [ApostolNT] p. 38 | Remark | df-sgm 27083 |
| [ApostolNT] p. 38 | Definition | df-sgm 27083 |
| [ApostolNT] p. 75 | Definition | df-chp 27080 df-cht 27078 |
| [ApostolNT] p. 104 | Definition | congr 16622 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16214 |
| [ApostolNT] p. 106 | Definition | moddvds 16221 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16304 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16305 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13836 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13876 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14189 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16246 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16625 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17034 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16627 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16742 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16761 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16743 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27053 |
| [ApostolNT] p. 179 | Definition | df-lgs 27277 lgsprme0 27321 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27322 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27298 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27313 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27370 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27389 2lgsoddprm 27398 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27356 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27365 |
| [ApostolNT] p. 188 | Definition | df-lgs 27277 lgs1 27323 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27314 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27316 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27324 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27325 |
| [Baer] p. 40 | Property (b) | mapdord 42095 |
| [Baer] p. 40 | Property (c) | mapd11 42096 |
| [Baer] p. 40 | Property (e) | mapdin 42119 mapdlsm 42121 |
| [Baer] p. 40 | Property (f) | mapd0 42122 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42082 mapd1o 42105 |
| [Baer] p. 41 | Property (g) | mapdat 42124 |
| [Baer] p. 44 | Part (1) | mapdpg 42163 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42258 mapdheq 42185 mapdheq2 42186 mapdheq2biN 42187 |
| [Baer] p. 45 | Part (3) | baerlem3 42170 |
| [Baer] p. 46 | Part (4) | mapdheq4 42189 mapdheq4lem 42188 |
| [Baer] p. 46 | Part (5) | baerlem5a 42171 baerlem5abmN 42175 baerlem5amN 42173 baerlem5b 42172 baerlem5bmN 42174 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42278 hdmap1l6a 42266 hdmap1l6e 42271 hdmap1l6f 42272 hdmap1l6g 42273 hdmap1l6lem1 42264 hdmap1l6lem2 42265 mapdh6N 42204 mapdh6aN 42192 mapdh6eN 42197 mapdh6fN 42198 mapdh6gN 42199 mapdh6lem1N 42190 mapdh6lem2N 42191 |
| [Baer] p. 48 | Part 9 | hdmapval 42285 |
| [Baer] p. 48 | Part 10 | hdmap10 42297 |
| [Baer] p. 48 | Part 11 | hdmapadd 42300 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42274 mapdh6hN 42200 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42210 mapdh75d 42211 mapdh75e 42209 mapdh75fN 42212 mapdh7cN 42206 mapdh7dN 42207 mapdh7eN 42205 mapdh7fN 42208 |
| [Baer] p. 48 | Part (8) | mapdh8 42245 mapdh8a 42232 mapdh8aa 42233 mapdh8ab 42234 mapdh8ac 42235 mapdh8ad 42236 mapdh8b 42237 mapdh8c 42238 mapdh8d 42240 mapdh8d0N 42239 mapdh8e 42241 mapdh8g 42242 mapdh8i 42243 mapdh8j 42244 |
| [Baer] p. 48 | Part (9) | mapdh9a 42246 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42226 |
| [Baer] p. 49 | Part 12 | hdmap11 42305 hdmapeq0 42301 hdmapf1oN 42322 hdmapneg 42303 hdmaprnN 42321 hdmaprnlem1N 42306 hdmaprnlem3N 42307 hdmaprnlem3uN 42308 hdmaprnlem4N 42310 hdmaprnlem6N 42311 hdmaprnlem7N 42312 hdmaprnlem8N 42313 hdmaprnlem9N 42314 hdmapsub 42304 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42325 hdmap14lem10 42334 hdmap14lem1a 42323 hdmap14lem2N 42326 hdmap14lem2a 42324 hdmap14lem3 42327 hdmap14lem8 42332 hdmap14lem9 42333 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42335 hdmap14lem12 42336 hdmap14lem13 42337 hdmap14lem14 42338 hdmap14lem15 42339 hgmapval 42344 |
| [Baer] p. 50 | Part 15 | hgmapadd 42351 hgmapmul 42352 hgmaprnlem2N 42354 hgmapvs 42348 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42358 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42374 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42375 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42376 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42377 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42379 hgmapvv 42383 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42378 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42380 |
| [Baer] p. 111 | Line 15 | hdmapg 42387 hdmapglem7 42386 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26711 2irrexpqALT 26781 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2570 |
| [BellMachover] p. 460 | Notation | df-mo 2540 |
| [BellMachover] p. 460 | Definition | mo3 2565 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2709 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2713 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5220 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5231 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37384 sepex 5235 |
| [BellMachover] p. 466 | Problem | axpow2 5302 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5303 |
| [BellMachover] p. 466 | Axiom Union | axun2 7682 |
| [BellMachover] p. 468 | Definition | df-ord 6318 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6333 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6340 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6335 |
| [BellMachover] p. 471 | Definition of N | df-om 7809 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7746 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6320 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9552 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7824 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9677 |
| [BellMachover] p. 478 | Definition | rankval2 9731 rankval2b 35263 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9695 r1ord3g 9692 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9502 |
| [BellMachover] p. 488 | Axiom AC | ac5 10388 dfac4 10033 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10021 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39776 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32444 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32486 chirredi 32485 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32474 |
| [Beran] p. 3 | Definition of join | sshjval3 31445 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31707 cmcm2i 31684 cmcm2ii 31689 cmt2N 39707 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31708 lecmi 31693 lecmii 31694 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31682 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31711 cm2ji 31716 cm2mi 31717 |
| [Beran] p. 95 | Definition | df-sh 31298 issh2 31300 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31177 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31190 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31181 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31919 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31921 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31920 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31922 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31173 his1i 31191 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31174 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31175 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31176 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31059 dfhnorm2 31213 normval 31215 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31275 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31064 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31332 |
| [Beran] p. 96 | Definition of converge | df-hlim 31063 hlimi 31279 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31224 norm-i 31220 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31228 norm-ii 31229 normlem0 31200 normlem1 31201 normlem2 31202 normlem3 31203 normlem4 31204 normlem5 31205 normlem6 31206 normlem7 31207 normlem7tALT 31210 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31230 norm-iii 31231 |
| [Beran] p. 98 | Remark 3.4 | bcs 31272 bcsiALT 31270 bcsiHIL 31271 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31212 normpar 31246 normpari 31245 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31237 normpyth 31236 normpythi 31233 |
| [Beran] p. 99 | Remark | lnfn0 32138 lnfn0i 32133 lnop0 32057 lnop0i 32061 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32117 nmcfnex 32144 nmcfnexi 32142 nmcopex 32120 nmcopexi 32118 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32145 nmcfnlbi 32143 nmcoplb 32121 nmcoplbi 32119 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32147 lnfnconi 32146 lnopcon 32126 lnopconi 32125 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31247 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31244 norm3adifii 31239 norm3dif 31241 norm3difi 31238 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31392 pjhth 31484 pjhtheu 31485 pjpjhth 31516 pjpjhthi 31517 pjth 25415 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31497 ococi 31496 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32152 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32153 riesz4 32155 riesz4i 32154 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32170 cnlnadjeu 32169 cnlnadjeui 32168 cnlnadji 32167 cnlnadjlem1 32158 nmopadjlei 32179 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32182 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32181 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32183 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32027 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32193 nmopcoadji 32192 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32184 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32194 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32191 pjadj2coi 32295 pjadjcoi 32252 |
| [Beran] p. 107 | Definition | df-ch 31312 isch2 31314 |
| [Beran] p. 107 | Remark 3.12 | choccl 31397 isch3 31332 occl 31395 ocsh 31374 shoccl 31396 shocsh 31375 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31499 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31423 |
| [Beran] p. 109 | Property (i) | pjadj2 32278 pjadj3 32279 pjadji 31776 pjadjii 31765 |
| [Beran] p. 109 | Property (ii) | pjidmco 32272 pjidmcoi 32268 pjidmi 31764 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32264 |
| [Beran] p. 111 | Remark | ho0val 31841 pjch1 31761 |
| [Beran] p. 111 | Definition | df-hfmul 31825 df-hfsum 31824 df-hodif 31823 df-homul 31822 df-hosum 31821 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31762 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31785 pjchi 31523 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31530 pjoc2i 31529 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31771 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32256 pjssmii 31772 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32255 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32254 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32259 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32257 pjssge0ii 31773 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32258 pjdifnormii 31774 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1778 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1776 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1779 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1774 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34457 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34465 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34463 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34467 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34487 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34518 df-sitm 34496 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34518 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34495 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29136 isuhgrop 29158 isusgrop 29250 isuspgrop 29249 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48334 df-subgr 29356 uhgrspan1 29391 uhgrspansubgr 29379 |
| [Bollobas] p. 3 | Definition | df-gric 48354 gricuspgr 48391 isuspgrim 48369 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29543 df-clnbgr 48292 df-cusgr 29500 df-nbgr 29421 fusgrmaxsize 29553 |
| [Bollobas] p. 4 | Definition | df-upwlks 48607 df-wlks 29688 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29639 finsumvtxdgeven 29641 fusgr1th 29640 fusgrvtxdgonume 29643 vtxdgoddnumeven 29642 |
| [Bollobas] p. 5 | Notation | df-pths 29802 |
| [Bollobas] p. 5 | Definition | df-crcts 29874 df-cycls 29875 df-trls 29779 df-wlkson 29689 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29147 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48673 df-cllaw 48659 df-mgm 18597 df-mgm2 48692 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48674 df-asslaw 48661 df-sgrp 18676 df-sgrp2 48694 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48693 df-comlaw 48660 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18692 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33106 mndlactf1o 33110 mndractf1 33108 mndractf1o 33111 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20205 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20123 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33798 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33802 assarrginv 33801 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33843 fldextrspunfld 33841 fldextrspunlem1 33840 fldextrspunlem2 33842 fldextrspunlsp 33839 fldextrspunlsplem 33838 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33617 dfufd2 33630 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7233 fcofo 7234 |
| [BourbakiTop1] p. | Remark | xnegmnf 13151 xnegpnf 13150 |
| [BourbakiTop1] p. | Remark | rexneg 13152 |
| [BourbakiTop1] p. | Remark 3 | ust0 24194 ustfilxp 24187 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24064 |
| [BourbakiTop1] p. | Criterion | ishmeo 23733 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24257 iducn 24256 snfil 23838 |
| [BourbakiTop1] p. | Example 2 | neifil 23854 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24041 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24277 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34122 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23837 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24249 df-ust 24175 filintn0 23835 filn0 23836 istgp 24051 ucnprima 24255 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24260 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24271 df-usp 24231 df-utop 24205 trust 24203 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34021 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23090 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23243 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24180 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24183 |
| [BourbakiTop1] p. | Property V_ii | innei 23099 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23107 neissex 23101 |
| [BourbakiTop1] p. | Proposition 1 | neips 23087 neiss 23083 ucncn 24258 ustund 24196 ustuqtop 24220 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23241 neiptopreu 23107 utop2nei 24224 utop3cls 24225 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24265 uspreg 24247 utopreg 24226 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23665 imasncls 23666 imasnopn 23664 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23974 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24182 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24184 |
| [BourbakiTop1] p. | Property V_iii | elnei 23085 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24276 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24181 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24185 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23361 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23820 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22868 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34018 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46505 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46507 stoweid 46506 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46444 stoweidlem10 46453 stoweidlem14 46457 stoweidlem15 46458 stoweidlem35 46478 stoweidlem36 46479 stoweidlem37 46480 stoweidlem38 46481 stoweidlem40 46483 stoweidlem41 46484 stoweidlem43 46486 stoweidlem44 46487 stoweidlem46 46489 stoweidlem5 46448 stoweidlem50 46493 stoweidlem52 46495 stoweidlem53 46496 stoweidlem55 46498 stoweidlem56 46499 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46466 stoweidlem24 46467 stoweidlem27 46470 stoweidlem28 46471 stoweidlem30 46473 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46477 stoweidlem59 46502 stoweidlem60 46503 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46488 stoweidlem49 46492 stoweidlem7 46450 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46474 stoweidlem39 46482 stoweidlem42 46485 stoweidlem48 46491 stoweidlem51 46494 stoweidlem54 46497 stoweidlem57 46500 stoweidlem58 46501 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46468 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46460 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46454 stoweidlem13 46456 stoweidlem26 46469 stoweidlem61 46504 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46461 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48673 df-mgm 18597 df-mgm2 48692 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18676 df-sgrp2 48694 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19004 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5168 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30493 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30493 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30493 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30493 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30493 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30493 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30493 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30493 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30493 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30493 |
| [Clemente] p. 14 | Proof 5.11 | natded 30493 |
| [Clemente] p. 14 | Definition E` `n | natded 30493 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30495 ex-natded5.2 30494 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30498 ex-natded5.3 30497 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30500 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30502 ex-natded5.7 30501 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30504 ex-natded5.8 30503 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30506 ex-natded5.13 30505 |
| [Clemente] p. 32 | Definition I` `n | natded 30493 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30493 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30493 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30493 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30507 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30508 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30510 ex-natded9.26 30509 |
| [Cohen] p. 301 | Remark | relogoprlem 26571 |
| [Cohen] p. 301 | Property 2 | relogmul 26572 relogmuld 26605 |
| [Cohen] p. 301 | Property 3 | relogdiv 26573 relogdivd 26606 |
| [Cohen] p. 301 | Property 4 | relogexp 26576 |
| [Cohen] p. 301 | Property 1a | log1 26565 |
| [Cohen] p. 301 | Property 1b | loge 26566 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26768 |
| [Cohen4] p. 349 | Property | relogbf 26772 |
| [Cohen4] p. 352 | Definition | elogb 26751 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26758 |
| [Cohen4] p. 361 | Property 3 | logbrec 26763 relogbdiv 26760 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26756 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26761 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26749 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26750 |
| [Cohen4] p. 367 | Property | logbchbase 26752 |
| [Cohen4] p. 377 | Property 2 | logblt 26765 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34450 sxbrsigalem4 34452 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18512 acsinfd 18511 acsinfdimd 18513 acsmap2d 18510 acsmapd 18509 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34455 |
| [Connell] p. 57 | Definition | df-scmat 22465 df-scmatalt 48872 |
| [Conway] p. 4 | Definition | lesrec 27810 lesrecd 27811 |
| [Conway] p. 5 | Definition | addsval 27973 addsval2 27974 df-adds 27971 df-muls 28118 df-negs 28032 |
| [Conway] p. 7 | Theorem | 0lt1s 27823 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28473 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 27872 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 27871 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27750 |
| [Conway] p. 17 | Theorem 3 | addsass 28016 addsassd 28017 addscom 27977 addscomd 27978 addsrid 27975 addsridd 27976 |
| [Conway] p. 17 | Definition | df-0s 27818 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28055 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28052 negsidd 28053 |
| [Conway] p. 18 | Theorem 5 | leadds1 28000 leadds1d 28006 |
| [Conway] p. 18 | Definition | df-1s 27819 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28047 negscld 28048 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27991 |
| [Conway] p. 19 | Note | mulsunif2 28181 |
| [Conway] p. 19 | Theorem 7 | addsdi 28166 addsdid 28167 addsdird 28168 mulnegs1d 28171 mulnegs2d 28172 mulsass 28177 mulsassd 28178 mulscom 28150 mulscomd 28151 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28145 mulscld 28146 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28149 ltmuls 28147 ltmulsd 28148 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28155 mulsgt0d 28156 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28229 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27815 |
| [Conway] p. 24 | Definition | df-reno 28501 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28510 remulscl 28513 renegscl 28509 |
| [Conway] p. 27 | Definition | df-ons 28263 elons2 28269 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28273 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28275 onswe 28283 |
| [Conway] p. 29 | Remark | madebday 27911 newbday 27913 oldbday 27912 |
| [Conway] p. 29 | Definition | df-made 27838 df-new 27840 df-old 27839 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13809 |
| [Crawley] p. 1 | Definition of poset | df-poset 18268 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39843 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40647 dalaw 40343 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42418 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40447 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40563 df-ldil 40561 isldil 40567 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40562 df-trnN 40564 isltrn 40576 ltrnu 40578 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40248 cdlema2N 40249 exatleN 39861 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39933 cdlemb 40251 cdlemb2 40498 cdlemb3 41063 idltrn 40607 l1cvat 39512 lhpat 40500 lhpat2 40502 lshpat 39513 ltrnel 40596 ltrnmw 40608 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40648 cdlemc2 40649 ltrnnidn 40631 trlat 40626 trljat1 40623 trljat2 40624 trljat3 40625 trlne 40642 trlnidat 40630 trlnle 40643 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40448 |
| [Crawley] p. 113 | Lemma C | cdlemc 40654 cdlemc3 40650 cdlemc4 40651 |
| [Crawley] p. 113 | Lemma D | cdlemd 40664 cdlemd1 40655 cdlemd2 40656 cdlemd3 40657 cdlemd4 40658 cdlemd5 40659 cdlemd6 40660 cdlemd7 40661 cdlemd8 40662 cdlemd9 40663 cdleme31sde 40842 cdleme31se 40839 cdleme31se2 40840 cdleme31snd 40843 cdleme32a 40898 cdleme32b 40899 cdleme32c 40900 cdleme32d 40901 cdleme32e 40902 cdleme32f 40903 cdleme32fva 40894 cdleme32fva1 40895 cdleme32fvcl 40897 cdleme32le 40904 cdleme48fv 40956 cdleme4gfv 40964 cdleme50eq 40998 cdleme50f 40999 cdleme50f1 41000 cdleme50f1o 41003 cdleme50laut 41004 cdleme50ldil 41005 cdleme50lebi 40997 cdleme50rn 41002 cdleme50rnlem 41001 cdlemeg49le 40968 cdlemeg49lebilem 40996 |
| [Crawley] p. 113 | Lemma E | cdleme 41017 cdleme00a 40666 cdleme01N 40678 cdleme02N 40679 cdleme0a 40668 cdleme0aa 40667 cdleme0b 40669 cdleme0c 40670 cdleme0cp 40671 cdleme0cq 40672 cdleme0dN 40673 cdleme0e 40674 cdleme0ex1N 40680 cdleme0ex2N 40681 cdleme0fN 40675 cdleme0gN 40676 cdleme0moN 40682 cdleme1 40684 cdleme10 40711 cdleme10tN 40715 cdleme11 40727 cdleme11a 40717 cdleme11c 40718 cdleme11dN 40719 cdleme11e 40720 cdleme11fN 40721 cdleme11g 40722 cdleme11h 40723 cdleme11j 40724 cdleme11k 40725 cdleme11l 40726 cdleme12 40728 cdleme13 40729 cdleme14 40730 cdleme15 40735 cdleme15a 40731 cdleme15b 40732 cdleme15c 40733 cdleme15d 40734 cdleme16 40742 cdleme16aN 40716 cdleme16b 40736 cdleme16c 40737 cdleme16d 40738 cdleme16e 40739 cdleme16f 40740 cdleme16g 40741 cdleme19a 40760 cdleme19b 40761 cdleme19c 40762 cdleme19d 40763 cdleme19e 40764 cdleme19f 40765 cdleme1b 40683 cdleme2 40685 cdleme20aN 40766 cdleme20bN 40767 cdleme20c 40768 cdleme20d 40769 cdleme20e 40770 cdleme20f 40771 cdleme20g 40772 cdleme20h 40773 cdleme20i 40774 cdleme20j 40775 cdleme20k 40776 cdleme20l 40779 cdleme20l1 40777 cdleme20l2 40778 cdleme20m 40780 cdleme20y 40759 cdleme20zN 40758 cdleme21 40794 cdleme21d 40787 cdleme21e 40788 cdleme22a 40797 cdleme22aa 40796 cdleme22b 40798 cdleme22cN 40799 cdleme22d 40800 cdleme22e 40801 cdleme22eALTN 40802 cdleme22f 40803 cdleme22f2 40804 cdleme22g 40805 cdleme23a 40806 cdleme23b 40807 cdleme23c 40808 cdleme26e 40816 cdleme26eALTN 40818 cdleme26ee 40817 cdleme26f 40820 cdleme26f2 40822 cdleme26f2ALTN 40821 cdleme26fALTN 40819 cdleme27N 40826 cdleme27a 40824 cdleme27cl 40823 cdleme28c 40829 cdleme3 40694 cdleme30a 40835 cdleme31fv 40847 cdleme31fv1 40848 cdleme31fv1s 40849 cdleme31fv2 40850 cdleme31id 40851 cdleme31sc 40841 cdleme31sdnN 40844 cdleme31sn 40837 cdleme31sn1 40838 cdleme31sn1c 40845 cdleme31sn2 40846 cdleme31so 40836 cdleme35a 40905 cdleme35b 40907 cdleme35c 40908 cdleme35d 40909 cdleme35e 40910 cdleme35f 40911 cdleme35fnpq 40906 cdleme35g 40912 cdleme35h 40913 cdleme35h2 40914 cdleme35sn2aw 40915 cdleme35sn3a 40916 cdleme36a 40917 cdleme36m 40918 cdleme37m 40919 cdleme38m 40920 cdleme38n 40921 cdleme39a 40922 cdleme39n 40923 cdleme3b 40686 cdleme3c 40687 cdleme3d 40688 cdleme3e 40689 cdleme3fN 40690 cdleme3fa 40693 cdleme3g 40691 cdleme3h 40692 cdleme4 40695 cdleme40m 40924 cdleme40n 40925 cdleme40v 40926 cdleme40w 40927 cdleme41fva11 40934 cdleme41sn3aw 40931 cdleme41sn4aw 40932 cdleme41snaw 40933 cdleme42a 40928 cdleme42b 40935 cdleme42c 40929 cdleme42d 40930 cdleme42e 40936 cdleme42f 40937 cdleme42g 40938 cdleme42h 40939 cdleme42i 40940 cdleme42k 40941 cdleme42ke 40942 cdleme42keg 40943 cdleme42mN 40944 cdleme42mgN 40945 cdleme43aN 40946 cdleme43bN 40947 cdleme43cN 40948 cdleme43dN 40949 cdleme5 40697 cdleme50ex 41016 cdleme50ltrn 41014 cdleme51finvN 41013 cdleme51finvfvN 41012 cdleme51finvtrN 41015 cdleme6 40698 cdleme7 40706 cdleme7a 40700 cdleme7aa 40699 cdleme7b 40701 cdleme7c 40702 cdleme7d 40703 cdleme7e 40704 cdleme7ga 40705 cdleme8 40707 cdleme8tN 40712 cdleme9 40710 cdleme9a 40708 cdleme9b 40709 cdleme9tN 40714 cdleme9taN 40713 cdlemeda 40755 cdlemedb 40754 cdlemednpq 40756 cdlemednuN 40757 cdlemefr27cl 40860 cdlemefr32fva1 40867 cdlemefr32fvaN 40866 cdlemefrs32fva 40857 cdlemefrs32fva1 40858 cdlemefs27cl 40870 cdlemefs32fva1 40880 cdlemefs32fvaN 40879 cdlemesner 40753 cdlemeulpq 40677 |
| [Crawley] p. 114 | Lemma E | 4atex 40533 4atexlem7 40532 cdleme0nex 40747 cdleme17a 40743 cdleme17c 40745 cdleme17d 40955 cdleme17d1 40746 cdleme17d2 40952 cdleme18a 40748 cdleme18b 40749 cdleme18c 40750 cdleme18d 40752 cdleme4a 40696 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40782 cdleme21at 40785 cdleme21b 40783 cdleme21c 40784 cdleme21ct 40786 cdleme21f 40789 cdleme21g 40790 cdleme21h 40791 cdleme21i 40792 cdleme22gb 40751 |
| [Crawley] p. 116 | Lemma F | cdlemf 41020 cdlemf1 41018 cdlemf2 41019 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41024 cdlemg16 41114 cdlemg28 41161 cdlemg28a 41150 cdlemg28b 41160 cdlemg3a 41054 cdlemg42 41186 cdlemg43 41187 cdlemg44 41190 cdlemg44a 41188 cdlemg46 41192 cdlemg47 41193 cdlemg9 41091 ltrnco 41176 ltrncom 41195 tgrpabl 41208 trlco 41184 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41200 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41134 cdlemg17b 41119 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41213 df-edring 41214 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41217 |
| [Crawley] p. 118 | Remark | tendopltp 41237 |
| [Crawley] p. 118 | Lemma H | cdlemh 41274 cdlemh1 41272 cdlemh2 41273 |
| [Crawley] p. 118 | Lemma I | cdlemi 41277 cdlemi1 41275 cdlemi2 41276 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41278 cdlemj2 41279 cdlemj3 41280 tendocan 41281 |
| [Crawley] p. 118 | Lemma K | cdlemk 41431 cdlemk1 41288 cdlemk10 41300 cdlemk11 41306 cdlemk11t 41403 cdlemk11ta 41386 cdlemk11tb 41388 cdlemk11tc 41402 cdlemk11u-2N 41346 cdlemk11u 41328 cdlemk12 41307 cdlemk12u-2N 41347 cdlemk12u 41329 cdlemk13-2N 41333 cdlemk13 41309 cdlemk14-2N 41335 cdlemk14 41311 cdlemk15-2N 41336 cdlemk15 41312 cdlemk16-2N 41337 cdlemk16 41314 cdlemk16a 41313 cdlemk17-2N 41338 cdlemk17 41315 cdlemk18-2N 41343 cdlemk18-3N 41357 cdlemk18 41325 cdlemk19-2N 41344 cdlemk19 41326 cdlemk19u 41427 cdlemk1u 41316 cdlemk2 41289 cdlemk20-2N 41349 cdlemk20 41331 cdlemk21-2N 41348 cdlemk21N 41330 cdlemk22-3 41358 cdlemk22 41350 cdlemk23-3 41359 cdlemk24-3 41360 cdlemk25-3 41361 cdlemk26-3 41363 cdlemk26b-3 41362 cdlemk27-3 41364 cdlemk28-3 41365 cdlemk29-3 41368 cdlemk3 41290 cdlemk30 41351 cdlemk31 41353 cdlemk32 41354 cdlemk33N 41366 cdlemk34 41367 cdlemk35 41369 cdlemk36 41370 cdlemk37 41371 cdlemk38 41372 cdlemk39 41373 cdlemk39u 41425 cdlemk4 41291 cdlemk41 41377 cdlemk42 41398 cdlemk42yN 41401 cdlemk43N 41420 cdlemk45 41404 cdlemk46 41405 cdlemk47 41406 cdlemk48 41407 cdlemk49 41408 cdlemk5 41293 cdlemk50 41409 cdlemk51 41410 cdlemk52 41411 cdlemk53 41414 cdlemk54 41415 cdlemk55 41418 cdlemk55u 41423 cdlemk56 41428 cdlemk5a 41292 cdlemk5auN 41317 cdlemk5u 41318 cdlemk6 41294 cdlemk6u 41319 cdlemk7 41305 cdlemk7u-2N 41345 cdlemk7u 41327 cdlemk8 41295 cdlemk9 41296 cdlemk9bN 41297 cdlemki 41298 cdlemkid 41393 cdlemkj-2N 41339 cdlemkj 41320 cdlemksat 41303 cdlemksel 41302 cdlemksv 41301 cdlemksv2 41304 cdlemkuat 41323 cdlemkuel-2N 41341 cdlemkuel-3 41355 cdlemkuel 41322 cdlemkuv-2N 41340 cdlemkuv2-2 41342 cdlemkuv2-3N 41356 cdlemkuv2 41324 cdlemkuvN 41321 cdlemkvcl 41299 cdlemky 41383 cdlemkyyN 41419 tendoex 41432 |
| [Crawley] p. 120 | Remark | dva1dim 41442 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41433 cdleml2N 41434 cdleml3N 41435 cdleml4N 41436 cdleml5N 41437 cdleml6 41438 cdleml7 41439 cdleml8 41440 cdleml9 41441 dia1dim 41518 |
| [Crawley] p. 120 | Lemma M | dia11N 41505 diaf11N 41506 dialss 41503 diaord 41504 dibf11N 41618 djajN 41594 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41489 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41575 dia2dimlem1 41521 dia2dimlem2 41522 dia2dimlem3 41523 dia2dimlem4 41524 dia2dimlem5 41525 diaf1oN 41587 diarnN 41586 dvheveccl 41569 dvhopN 41573 |
| [Crawley] p. 121 | Lemma N | cdlemn 41669 cdlemn10 41663 cdlemn11 41668 cdlemn11a 41664 cdlemn11b 41665 cdlemn11c 41666 cdlemn11pre 41667 cdlemn2 41652 cdlemn2a 41653 cdlemn3 41654 cdlemn4 41655 cdlemn4a 41656 cdlemn5 41658 cdlemn5pre 41657 cdlemn6 41659 cdlemn7 41660 cdlemn8 41661 cdlemn9 41662 diclspsn 41651 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41630 |
| [Crawley] p. 122 | Lemma N | dih11 41722 dihf11 41724 dihjust 41674 dihjustlem 41673 dihord 41721 dihord1 41675 dihord10 41680 dihord11b 41679 dihord11c 41681 dihord2 41684 dihord2a 41676 dihord2b 41677 dihord2cN 41678 dihord2pre 41682 dihord2pre2 41683 dihordlem6 41670 dihordlem7 41671 dihordlem7b 41672 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41687 dihfval 41688 dihval 41689 |
| [Diestel] p. 3 | Definition | df-gric 48354 df-grim 48351 isuspgrim 48369 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29500 df-nbgr 29421 |
| [Diestel] p. 3 | Definition by | df-grisom 48350 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48334 df-subgr 29356 uhgrspan1 29391 uhgrspansubgr 29379 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29643 vtxdgoddnumeven 29642 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29147 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34029 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34041 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34033 zarcls1 34034 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34044 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34047 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34050 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3893 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9557 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8766 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9565 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9893 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10466 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5240 |
| [Enderton] p. 19 | Definition | df-tp 4573 |
| [Enderton] p. 26 | Exercise 5 | unissb 4884 |
| [Enderton] p. 26 | Exercise 10 | pwel 5316 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5515 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5022 iinin2 5021 iinun2 5016 iunin1 5015 iunin1f 32647 iunin2 5014 uniin1 32641 uniin2 32642 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5020 iundif2 5017 |
| [Enderton] p. 32 | Exercise 20 | unineq 4229 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5041 |
| [Enderton] p. 33 | Exercise 25 | iununi 5042 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5049 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7716 iunpwss 5050 |
| [Enderton] p. 36 | Definition | opthwiener 5460 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5395 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4889 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5416 rnex 7852 rnexg 7844 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5861 rnuni 6104 |
| [Enderton] p. 42 | Definition of a function | dffun7 6517 dffun8 6518 |
| [Enderton] p. 43 | Definition of function value | funfv2 6920 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6559 |
| [Enderton] p. 44 | Definition (d) | dfima2 6019 dfima3 6020 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6929 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10384 ac7g 10385 df-ac 10027 dfac2 10043 dfac2a 10041 dfac2b 10042 dfac3 10032 dfac7 10044 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7192 |
| [Enderton] p. 52 | Definition | df-map 8766 |
| [Enderton] p. 53 | Exercise 21 | coass 6222 |
| [Enderton] p. 53 | Exercise 27 | dmco 6211 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6566 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6059 |
| [Enderton] p. 54 | Remark | ixpf 8859 ixpssmap 8871 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8837 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10394 ac9s 10404 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39026 erref 8655 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39029 erthi 8691 |
| [Enderton] p. 57 | Definition | df-ec 8636 |
| [Enderton] p. 58 | Definition | df-qs 8640 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8636 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5857 |
| [Enderton] p. 68 | Definition of successor | df-suc 6321 |
| [Enderton] p. 71 | Definition | df-tr 5194 dftr4 5199 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6396 unisucg 6395 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6396 unisucg 6395 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5208 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5210 trintALT 45322 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8531 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8533 onasuc 8454 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7361 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8532 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8534 onmsuc 8455 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8549 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8536 nnacom 8544 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8550 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8551 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8553 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8537 nnmsucr 8552 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8565 |
| [Enderton] p. 129 | Definition | df-en 8885 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7312 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9926 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16169 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9132 |
| [Enderton] p. 135 | Corollary 6C | php3 9134 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9131 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9163 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9165 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9094 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9098 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9070 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10091 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10092 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10087 dju1en 10083 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9244 unifi 9245 unifi2 9246 |
| [Enderton] p. 144 | Corollary 6K | undif2 4418 unfi 9096 unfi2 9211 |
| [Enderton] p. 145 | Figure 38 | ffoss 7890 |
| [Enderton] p. 145 | Definition | df-dom 8886 |
| [Enderton] p. 146 | Example 1 | domen 8899 domeng 8900 |
| [Enderton] p. 146 | Example 3 | nndomo 9143 nnsdom 9564 nnsdomg 9200 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10095 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9071 xpdom1 9005 xpdom1g 9003 xpdom2g 9002 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9077 |
| [Enderton] p. 151 | Theorem 6M | zorn 10418 zorng 10415 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10403 dfac5 10040 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10487 |
| [Enderton] p. 164 | Example | infdif 10119 |
| [Enderton] p. 168 | Definition | df-po 5530 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6430 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6362 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6429 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6370 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7781 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7726 |
| [Enderton] p. 194 | Remark | onprc 7723 |
| [Enderton] p. 194 | Exercise 16 | suc11 6424 |
| [Enderton] p. 197 | Definition | df-card 9852 |
| [Enderton] p. 197 | Theorem 7P | carden 10462 |
| [Enderton] p. 200 | Exercise 25 | tfis 7797 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9689 |
| [Enderton] p. 202 | Definition | df-r1 9677 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9699 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9780 rankval4b 35264 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9516 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9770 rankprb 9764 rankpw 9756 rankpwi 9736 rankuniss 9779 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9528 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9529 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10021 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9987 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10001 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8272 |
| [Enderton] p. 222 | Definition of kard | karden 9808 kardex 9807 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8524 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8526 |
| [Enderton] p. 240 | Exercise 25 | oarec 8488 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10161 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17597 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17539 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18508 mrieqv2d 17594 mrieqvd 17593 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17598 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17603 mreexexlem2d 17600 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18514 mreexfidimd 17605 |
| [Frege1879] p. 11 | Statement | df3or2 44210 |
| [Frege1879] p. 12 | Statement | df3an2 44211 dfxor4 44208 dfxor5 44209 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44232 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44233 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44237 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44241 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44242 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44248 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44250 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44251 axfrege8 44249 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37772 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44254 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44262 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44256 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44255 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44264 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44265 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44268 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44258 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44263 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44260 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44266 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44270 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44269 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44261 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44267 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44257 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44259 rp-frege25 44247 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44252 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44272 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44253 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44273 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44276 axfrege31 44275 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44274 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44277 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44278 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44279 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44280 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44281 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44282 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44283 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44284 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44285 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44287 axfrege41 44286 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44288 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44289 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44290 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44291 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44292 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44293 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44294 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44295 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44296 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44299 ax-frege52c 44330 frege52aid 44300 frege52b 44331 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44304 ax-frege54c 44334 frege54b 44335 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44297 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3731 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44302 frege53aid 44301 frege53b 44332 frege53c 44356 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2737 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44310 frege55aid 44307 frege55b 44339 frege55c 44360 frege55cor1a 44311 frege55lem2a 44309 frege55lem2b 44338 frege55lem2c 44359 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44313 frege56aid 44312 frege56b 44340 frege56c 44361 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44317 ax-frege58b 44343 frege58bid 44344 frege58c 44363 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44315 frege57aid 44314 frege57b 44341 frege57c 44362 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3742 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44319 frege59b 44346 frege59c 44364 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44320 frege60b 44347 frege60c 44365 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44321 frege61b 44348 frege61c 44366 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44322 frege62b 44349 frege62c 44367 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44323 frege63b 44350 frege63c 44368 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44324 frege64b 44351 frege64c 44369 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44325 frege65b 44352 frege65c 44370 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44326 frege66b 44353 frege66c 44371 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44327 frege67b 44354 frege67c 44372 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44328 frege68b 44355 frege68c 44373 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44374 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44375 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44376 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44377 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44378 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44381 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44379 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44380 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44382 frege77d 44188 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44383 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44384 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44385 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44386 frege81d 44189 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44387 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44388 frege83d 44190 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44389 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44390 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44391 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44392 frege87d 44192 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44393 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44394 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44395 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44396 frege91d 44193 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44397 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44398 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44399 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44400 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44404 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44401 frege96d 44191 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44402 frege97d 44194 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44403 frege98d 44195 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44405 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44406 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44407 frege102d 44196 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44408 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44409 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44410 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44411 frege106d 44197 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44412 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44413 frege108d 44198 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44414 frege109d 44199 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44415 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44416 frege111d 44201 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44417 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44418 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44419 frege114d 44200 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44420 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44421 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44422 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44423 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44424 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44425 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44426 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44427 frege122d 44202 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44428 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44429 frege124d 44203 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44430 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44431 frege126d 44204 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44432 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44433 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44434 frege129d 44205 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44435 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44436 frege131d 44206 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44437 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44438 frege133d 44207 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46756 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47079 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46779 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46894 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46914 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46905 meadjunre 46919 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46906 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46907 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46903 meaiunle 46912 meaiunlelem 46911 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46924 meaiuninc2 46925 meaiuninc3 46928 meaiuninc3v 46927 meaiunincf 46926 meaiuninclem 46923 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46930 meaiininc2 46931 meaiininclem 46929 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46949 caragendifcl 46957 caratheodory 46971 omelesplit 46961 |
| [Fremlin1] p. 19 | Definition 113A | isome 46937 isomennd 46974 isomenndlem 46973 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46959 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46978 voncmpl 47064 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46941 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46966 carageniuncllem1 46964 carageniuncllem2 46965 caragenuncl 46956 caragenuncllem 46955 caragenunicl 46967 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46975 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46969 caratheodorylem2 46970 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46978 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47037 hoidmv1lelem1 47034 hoidmv1lelem2 47035 hoidmv1lelem3 47036 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47081 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47037 hoidmvle 47043 hoidmvlelem1 47038 hoidmvlelem2 47039 hoidmvlelem3 47040 hoidmvlelem4 47041 hoidmvlelem5 47042 hsphoidmvle2 47028 hsphoif 47019 hsphoival 47022 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46991 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46999 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47026 hoidmvn0val 47027 hoidmvval 47020 hoidmvval0 47030 hoidmvval0b 47033 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47031 hsphoidmvle 47029 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46980 df-voln 46982 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47047 ovn0 47009 ovn0lem 47008 ovnf 47006 ovnome 47016 ovnssle 47004 ovnsslelem 47003 ovnsupge0 47000 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47046 ovnhoilem1 47044 ovnhoilem2 47045 vonhoi 47110 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47063 hoidifhspf 47061 hoidifhspval 47051 hoidifhspval2 47058 hoidifhspval3 47062 hspmbl 47072 hspmbllem1 47069 hspmbllem2 47070 hspmbllem3 47071 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47064 vonmea 47017 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47015 ovnsubadd2 47089 ovnsubadd2lem 47088 ovnsubaddlem1 47013 ovnsubaddlem2 47014 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47074 hoimbl2 47108 hoimbllem 47073 hspdifhsp 47059 opnvonmbl 47077 opnvonmbllem2 47076 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47079 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47122 iccvonmbllem 47121 ioovonmbl 47120 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47128 vonicclem2 47127 vonioo 47125 vonioolem2 47124 vonn0icc 47131 vonn0icc2 47135 vonn0ioo 47130 vonn0ioo2 47133 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47132 snvonmbl 47129 vonct 47136 vonsn 47134 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46802 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46801 subsaliuncllem 46800 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47168 salpreimalegt 47152 salpreimaltle 47169 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47171 issmff 47177 issmflem 47170 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47188 issmflelem 47187 smfpreimale 47197 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47199 issmfgtlem 47198 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47139 issmf 47171 issmff 47177 issmfge 47213 issmfgelem 47212 issmfgt 47199 issmfgtlem 47198 issmfle 47188 issmflelem 47187 issmflem 47170 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47150 salpreimagtlt 47173 salpreimalelt 47172 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47213 issmfgelem 47212 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47196 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47194 cnfsmf 47183 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47210 decsmflem 47209 incsmf 47185 incsmflem 47184 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47144 pimconstlt1 47145 smfconst 47192 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47208 smfaddlem1 47206 smfaddlem2 47207 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47239 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47238 smfmullem1 47234 smfmullem2 47235 smfmullem3 47236 smfmullem4 47237 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47240 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47243 smfpimbor1lem2 47242 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47245 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47233 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47232 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47241 smfresal 47231 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47220 smflim2 47249 smflimlem1 47214 smflimlem2 47215 smflimlem3 47216 smflimlem4 47217 smflimlem5 47218 smflimlem6 47219 smflimmpt 47253 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47257 smfsuplem1 47254 smfsuplem2 47255 smfsuplem3 47256 smfsupmpt 47258 smfsupxr 47259 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47261 smfinflem 47260 smfinfmpt 47262 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47220 smflim2 47249 smflimmpt 47253 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47251 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47281 smfdivdmmbl2 47284 smfinfdmmbl 47292 smfinfdmmbllem 47291 smfsupdmmbl 47288 smfsupdmmbllem 47287 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47271 smflimsuplem2 47264 smflimsuplem6 47268 smflimsuplem7 47269 smflimsuplem8 47270 smflimsupmpt 47272 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47274 smfliminflem 47273 smfliminfmpt 47275 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47139 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47285 fsupdm2 47286 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47276 adddmmbl2 47277 finfdm 47289 finfdm2 47290 fsupdm 47285 fsupdm2 47286 muldmmbl 47278 muldmmbl2 47279 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47289 finfdm2 47290 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25512 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25555 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25565 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38030 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38033 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9548 inf1 9532 inf2 9533 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10823 enqer 10833 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10828 df-nq 10824 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10820 df-plq 10826 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7595 df-mpq 10821 df-mq 10827 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10829 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10887 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10888 ltbtwnnq 10890 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10883 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10884 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10891 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10893 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10905 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10907 |
| [Gleason] p. 122 | Definition | df-1p 10894 |
| [Gleason] p. 122 | Remark (1) | prub 10906 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10945 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10897 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10944 psslinpr 10943 supexpr 10966 suplem1pr 10964 suplem2pr 10965 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10930 addclprlem1 10928 addclprlem2 10929 df-plp 10895 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10934 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10933 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10946 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10955 ltexprlem1 10948 ltexprlem2 10949 ltexprlem3 10950 ltexprlem4 10951 ltexprlem5 10952 ltexprlem6 10953 ltexprlem7 10954 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10957 ltaprlem 10956 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10958 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10959 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10896 mulclpr 10932 mulclprlem 10931 reclem2pr 10960 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10941 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10936 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10935 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10940 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10963 reclem3pr 10961 reclem4pr 10962 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10967 enrer 10975 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10972 df-1r 10973 df-nr 10968 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10970 df-plr 10969 negexsr 11014 recexsr 11019 recexsrlem 11015 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10971 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12143 creur 12142 cru 12140 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11100 axcnre 11076 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15066 crimd 15183 crimi 15144 crre 15065 crred 15182 crrei 15143 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15068 remimd 15149 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15235 absval2d 15399 absval2i 15349 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15092 cjaddd 15171 cjaddi 15139 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15093 cjmuld 15172 cjmuli 15140 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15091 cjcjd 15150 cjcji 15122 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15090 cjreb 15074 cjrebd 15153 cjrebi 15125 cjred 15177 rere 15073 rereb 15071 rerebd 15152 rerebi 15124 rered 15175 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15099 addcjd 15163 addcji 15134 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15189 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15230 abscjd 15404 abscji 15353 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15240 abs00d 15400 abs00i 15350 absne0d 15401 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15273 releabsd 15405 releabsi 15354 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15245 absmuld 15408 absmuli 15356 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15233 sqabsaddi 15357 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15282 abstrid 15410 abstrii 15360 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14013 exp0 14016 expp1 14019 expp1d 14098 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26659 cxpaddd 26697 expadd 14055 expaddd 14099 expaddz 14057 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26668 cxpmuld 26717 expmul 14058 expmuld 14100 expmulz 14059 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26665 mulcxpd 26708 mulexp 14052 mulexpd 14112 mulexpz 14053 |
| [Gleason] p. 140 | Exercise 1 | znnen 16168 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13452 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15583 rlimadd 15594 rlimdiv 15597 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15585 rlimsub 15595 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15584 rlimmul 15596 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15588 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15534 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15555 climcj 15556 climim 15558 climre 15557 rlimabs 15560 rlimcj 15561 rlimim 15563 rlimre 15562 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11173 df-xr 11172 ltxr 13055 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15422 limsupval 15425 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15621 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15630 caucvgb 15631 caucvgbf 45932 caucvgr 15627 climcau 15622 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15768 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15837 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15287 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13776 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21336 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24317 xmet0 24316 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24333 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24324 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24326 mstri 24443 xmettri 24325 xmstri 24442 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24356 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23622 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25286 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24514 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24840 addcn2 15545 mulcn 24842 mulcn2 15547 subcn 24841 subcn2 15546 |
| [Gleason] p. 295 | Remark | bcval3 14257 bcval4 14258 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14272 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14255 df-bc 14254 |
| [Gleason] p. 296 | Remark | bcn0 14261 bcnn 14263 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15784 |
| [Gleason] p. 308 | Equation 2 | ef0 16045 |
| [Gleason] p. 308 | Equation 3 | efcj 16046 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16052 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16057 |
| [Gleason] p. 310 | Equation 14 | sinadd 16120 |
| [Gleason] p. 310 | Equation 15 | cosadd 16121 |
| [Gleason] p. 311 | Equation 17 | sincossq 16132 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16137 sinbnd 16136 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14167 sqeqori 14165 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16026 |
| [Godowski] p. 730 | Equation SF | goeqi 32364 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31759 |
| [Golan] p. 1 | Remark | srgisid 20179 |
| [Golan] p. 1 | Definition | df-srg 20157 |
| [Golan] p. 149 | Definition | df-slmd 33282 |
| [Gonshor] p. 7 | Definition | df-cuts 27771 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27810 lesrecd 27811 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27931 cofcut1d 27932 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27933 cofcut2d 27934 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27935 cofcutr1d 27936 cofcutr2d 27937 |
| [Gonshor] p. 13 | Definition | df-adds 27971 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27987 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28013 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28141 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28161 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28469 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28471 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28470 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28506 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28029 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36362 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17537 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17539 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48661 df-cllaw 48659 df-comlaw 48660 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48673 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48694 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39200 dfmembpart2 39205 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32156 riesz2 32157 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32032 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32264 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32276 elpjidm 32275 pjnmopi 32239 |
| [Halmos] p. 44 | Remark | pjinormi 31778 pjinormii 31767 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32280 pjrn 31798 pjrni 31793 pjvec 31787 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31818 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32245 hmopidmpji 32243 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32282 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32271 pjocvec 31788 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32260 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32263 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32266 pjssdif2i 32265 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31946 |
| [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 1797 |
| [Hatcher] p. 25 | Definition | df-phtpc 24968 df-phtpy 24947 |
| [Hatcher] p. 26 | Definition | df-pco 24981 df-pi1 24984 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24971 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25026 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22464 df-dmatalt 48871 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48290 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48275 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48287 bgoldbtbnd 48282 bgoldbtbnd 48282 tgblthelfgott 48288 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34807 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34808 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34822 hgt750lemb 34821 hgt750leme 34823 hgt750lemf 34818 hgt750lemg 34819 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48284 tgoldbachgt 34828 tgoldbachgtALTV 48285 tgoldbachgtd 34827 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34809 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30584 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18909 grpoideu 30600 mndideu 18702 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18939 grpoinveu 30610 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18970 grpo2inv 30622 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18983 grpoinvop 30624 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19005 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1770 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1771 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1773 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32511 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32524 cdj3i 32532 cdj3lem1 32525 cdjreui 32523 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32522 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42418 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42348 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42370 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42371 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42368 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42374 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42293 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42388 |
| [Holland95] p. 204 | Definition of involution | df-srng 20806 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39960 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41985 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41938 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40390 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41834 poml4N 40410 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41925 pexmidALTN 40435 pexmidN 40426 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41990 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39581 ldualset 39582 |
| [Holland95] p. 222 | Item 1 | df-lines 39958 df-pointsN 39959 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40360 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40404 omllaw4 39703 pol1N 40367 polcon3N 40374 |
| [Holland95] p. 223 | Definition | df-psubclN 40392 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40363 |
| [Holmes] p. 40 | Definition | df-xrn 38712 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31175 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32273 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32054 eigre 31926 eigrei 31925 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32055 eigorth 31929 eigorthi 31928 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31927 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30399 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30395 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30396 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30397 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30415 frgrregorufr0 30414 frgrregorufrg 30416 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30422 frrusgrord 30431 frrusgrord0 30430 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30178 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30405 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30408 frgrwopreg2 30409 frgrwopregasn 30406 frgrwopregbsn 30407 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30411 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30425 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30428 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30176 numclwlk1 30461 numclwlk1lem1 30459 numclwlk1lem2 30460 numclwwlk1 30451 numclwwlk8 30482 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30402 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29859 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30437 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30463 numclwwlkovh0 30462 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30471 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30068 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30475 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30478 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30481 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30493 natded 30493 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30493 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30493 natded 30493 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30493 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2731 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10491 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10489 alephmul 10490 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10488 infmap2 10128 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9727 |
| [Jech] p. 72 | Equation 9.3 | scott0 9799 scottex 9798 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9780 rankval4b 35264 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9804 |
| [Jech] p. 78 | Note | opthprc 5686 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43358 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43446 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43447 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43370 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43374 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43375 rmyp1 43376 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43377 rmym1 43378 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43368 rmx1 43369 rmxluc 43379 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43372 rmy1 43373 rmyluc 43380 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43382 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43383 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43403 jm2.17b 43404 jm2.17c 43405 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43436 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43440 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43431 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43406 jm2.24nn 43402 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43445 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43451 rmygeid 43407 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43463 |
| [Juillerat] p. 11 | Section *5 | etransc 46726 etransclem47 46724 etransclem48 46725 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46721 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46723 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46709 |
| [Juillerat] p. 13 | Proof | etransclem35 46712 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46715 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46701 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46718 |
| [Juillerat] p. 14 | Proof | etransclem23 46700 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1969 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2014 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2019 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2009 cbvaliw 2008 wl-cbvmotv 37849 wl-motae 37851 wl-moteq 37850 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1988 spimw 1972 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2035 spw 2036 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31607 chabs1i 31609 chabs2 31608 chabs2i 31610 chjass 31624 chjassi 31577 latabs1 18430 latabs2 18431 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32429 ela 32430 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32374 cvrval2 39731 |
| [Kalmbach] p. 16 | Definition | df-ol 39635 df-oml 39636 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31675 cmbri 31681 cmtvalN 39668 df-cm 31674 df-cmtN 39634 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39704 pjoml5 31704 pjoml5i 31679 |
| [Kalmbach] p. 22 | Definition | pjoml2 31702 pjoml2i 31676 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31705 cmcmi 31683 cmcmii 31688 cmtcomN 39706 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39702 omlsi 31495 pjoml 31527 pjomli 31526 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39701 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31687 cmcm3 31706 cmcm3i 31685 cmcm3ii 31690 cmcm4i 31686 cmt3N 39708 cmt4N 39709 cmtbr2N 39710 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31699 cmbr3i 31691 cmtbr3N 39711 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31709 fh1i 31712 fh2 31710 fh2i 31713 omlfh1N 39715 |
| [Kalmbach] p. 65 | Remark | chjatom 32448 chslej 31589 chsleji 31549 shslej 31471 shsleji 31461 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31586 chocini 31545 chsupcl 31431 chsupval2 31501 h0elch 31346 helch 31334 hsupval2 31500 ocin 31387 ococss 31384 shococss 31385 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31403 |
| [Kalmbach] p. 66 | Remark | df-pjh 31486 pjssmi 32256 pjssmii 31772 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31736 osumi 31733 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32291 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32491 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32401 |
| [Kalmbach] p. 140 | Remark | hatomic 32451 hatomici 32450 hatomistici 32453 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39776 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32472 lsatexch 39500 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32446 cvlcvr1 39796 cvr1 39867 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32465 cvexchi 32460 cvrexch 39877 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32455 hlrelat 39859 hlrelat5N 39858 lrelat 39471 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21129 lsmsatcv 39467 spansncv 31744 spansncvi 31743 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39486 spansncv2 32384 |
| [Kalmbach] p. 266 | Definition | df-st 32302 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31940 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10558 fpwwe2 10555 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10559 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10566 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10561 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10563 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10576 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10580 gchxpidm 10581 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10592 gchhar 10591 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10126 unxpwdom 9495 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10582 |
| [Kreyszig] p. 3 | Property M1 | metcl 24306 xmetcl 24305 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24313 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24546 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11861 muleqadd 11783 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24412 |
| [Kreyszig] p. 19 | Remark | mopntopon 24413 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24472 mopnm 24418 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24470 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24475 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24516 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23232 lmmbr 25234 lmmbr2 25235 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23354 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25289 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25252 iscmet2 25270 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25292 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23435 metelcls 25281 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25282 metcld2 25283 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25075 lmodvneg1 20889 nvinv 30730 vcm 30667 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25071 lmod0vs 20879 slmd0vs 33305 vc0 30665 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20880 slmdvs0 33306 vcz 30666 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30782 ngpmet 24577 nrmmetd 24548 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30777 imsdval2 30778 ncvspds 25137 ngpds 24578 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24563 nvnd 30779 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24592 nmge0 24591 nvge0 30764 nvz 30760 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24598 nvabs 30763 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30892 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30836 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30898 blocni 30896 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30897 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25180 ipeq0 21626 ipz 30810 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25192 pythi 30941 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30945 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25214 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15810 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25412 minveco 30975 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30841 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25305 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30964 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32214 leopg 32213 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32232 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31009 |
| [Kulpa] p. 547 | Theorem | poimir 37985 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37984 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37983 |
| [Kulpa] p. 548 | Theorem | broucube 37986 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37978 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37979 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2388 axnul 5240 |
| [Kunen] p. 11 | Axiom 3 | axnul 5240 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5224 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8776 mapvalg 8774 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10433 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7883 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9677 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9719 r1elssi 9718 |
| [Kunen] p. 107 | Exercise 4 | rankop 9771 rankopb 9765 rankuni 9776 rankxplim 9792 rankxpsuc 9795 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45396 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45404 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45403 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45405 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45410 rexabso 45411 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45417 n0abso 45418 ssabso 45416 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45419 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45429 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45424 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45427 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45428 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45423 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45435 wfaxpr 45440 wfaxreg 45442 wfaxrep 45436 wfaxsep 45437 wfaxun 45441 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45426 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45439 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45435 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45434 omelaxinf2 45431 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45444 wfaxinf2 45443 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45457 permaxext 45447 permaxinf2 45455 permaxnul 45450 permaxpow 45451 permaxpr 45452 permaxrep 45448 permaxsep 45449 permaxun 45453 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45445 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45456 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4947 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33830 |
| [Lang] p. | Definition | df-rn 5633 |
| [Lang] p. 3 | Statement | lidrideqd 18626 mndbn0 18707 |
| [Lang] p. 3 | Definition | df-mnd 18692 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18644 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18798 |
| [Lang] p. 5 | Equation | gsumreidx 19881 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48655 |
| [Lang] p. 6 | Example | nn0mnd 48652 |
| [Lang] p. 6 | Equation | gsumxp2 19944 |
| [Lang] p. 6 | Statement | cycsubm 19166 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19045 |
| [Lang] p. 6 | Observation | mndlsmidm 19634 |
| [Lang] p. 7 | Definition | dfgrp2e 18928 |
| [Lang] p. 30 | Definition | df-tocyc 33188 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33233 |
| [Lang] p. 32 | Property (b) | cyc3conja 33238 cycpmconjv 33223 |
| [Lang] p. 53 | Definition | df-cat 17623 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18053 cat1lem 18052 |
| [Lang] p. 54 | Definition | df-iso 17705 |
| [Lang] p. 57 | Definition | df-inito 17940 df-termo 17941 |
| [Lang] p. 58 | Example | irinitoringc 21467 |
| [Lang] p. 58 | Statement | initoeu1 17967 termoeu1 17974 |
| [Lang] p. 62 | Definition | df-func 17814 |
| [Lang] p. 65 | Definition | df-nat 17902 |
| [Lang] p. 91 | Note | df-ringc 20612 |
| [Lang] p. 92 | Statement | mxidlprm 33550 |
| [Lang] p. 92 | Definition | isprmidlc 33527 |
| [Lang] p. 128 | Remark | dsmmlmod 21733 |
| [Lang] p. 129 | Proof | lincscm 48903 lincscmcl 48905 lincsum 48902 lincsumcl 48904 |
| [Lang] p. 129 | Statement | lincolss 48907 |
| [Lang] p. 129 | Observation | dsmmfi 21726 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33792 qusdimsum 33793 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33772 |
| [Lang] p. 147 | Definition | snlindsntor 48944 |
| [Lang] p. 504 | Statement | mat1 22421 matring 22417 |
| [Lang] p. 504 | Definition | df-mamu 22365 |
| [Lang] p. 505 | Statement | mamuass 22376 mamutpos 22432 matassa 22418 mattposvs 22429 tposmap 22431 |
| [Lang] p. 513 | Definition | mdet1 22575 mdetf 22569 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22665 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22561 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22585 |
| [Lang] p. 515 | Definition | df-minmar1 22609 smadiadetr 22649 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22584 mdetralt 22582 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22597 |
| [Lang] p. 518 | Definition | df-madu 22608 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22619 madurid 22618 matinv 22651 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22864 |
| [Lang], p. 190 | Chapter 6 | vieta 33744 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33859 finextalg 33863 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33828 fedgmul 33796 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33890 |
| [Lang], p. 561 | Remark | chpmatply1 22806 |
| [Lang], p. 561 | Definition | df-chpmat 22801 |
| [Lang2] p. 3 | Notations | df-ind 12149 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44776 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44771 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44777 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5240 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2716 wl-df.clab 37834 |
| [Levy] p. 59 | Definition | df-ttrcl 9618 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9664 |
| [Levy] p. 338 | Axiom | df-clel 2812 df-cleq 2729 wl-df.clel 37838 wl-df.cleq 37835 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2812 df-cleq 2729 wl-df.clel 37838 wl-df.cleq 37835 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2716 wl-df.clab 37834 |
| [Levy] p. 358 | Axiom | df-clab 2716 wl-df.clab 37834 |
| [Levy58] p. 2 | Definition I | isfin1-3 10297 |
| [Levy58] p. 2 | Definition II | df-fin2 10197 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10196 |
| [Levy58] p. 2 | Definition III | df-fin3 10199 |
| [Levy58] p. 3 | Definition V | df-fin5 10200 |
| [Levy58] p. 3 | Definition IV | df-fin4 10198 |
| [Levy58] p. 4 | Definition VI | df-fin6 10201 |
| [Levy58] p. 4 | Definition VII | df-fin7 10202 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10326 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27669 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27680 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27712 nosupbnd1 27697 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27714 nosupbnd2 27699 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27718 noetasuplem4 27719 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27715 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1770 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1771 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1773 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32499 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32503 mdsymi 32502 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32497 mdsymlem6 32499 mdsymlem7 32500 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32501 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32404 ssdmd2 32405 ssmd1 32402 ssmd2 32403 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32400 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32372 df-md 32371 mdbr 32385 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32422 mdslj1i 32410 mdslj2i 32411 mdslle1i 32408 mdslle2i 32409 mdslmd1i 32420 mdslmd2i 32421 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32412 mdsl2bi 32414 mdsl2i 32413 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32426 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32423 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32424 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32401 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32406 mdsl3 32407 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32425 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32520 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39778 hlrelat1 39857 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39496 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32427 cvmdi 32415 cvnbtwn4 32380 cvrnbtwn4 39736 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32428 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39797 cvp 32466 cvrp 39873 lcvp 39497 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32490 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32489 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39790 hlexch4N 39849 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32492 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39900 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40206 atpsubN 40210 df-pointsN 39959 pointpsubN 40208 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39961 pmap11 40219 pmaple 40218 pmapsub 40225 pmapval 40214 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40222 pmap1N 40224 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40227 pmapglb2N 40228 pmapglb2xN 40229 pmapglbx 40226 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40309 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39934 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40253 paddclN 40299 paddidm 40298 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39935 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40295 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39934 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39935 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19639 lsmmod2 19640 lssats 39469 shatomici 32449 shatomistici 32452 shmodi 31481 shmodsi 31480 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32391 mdsymlem7 32500 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31680 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31584 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32506 |
| [Margaris] p. 40 | Rule C | exlimiv 1932 |
| [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 1782 df-or 849 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30490 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45356 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45357 |
| [Margaris] p. 79 | Rule C | exinst01 45067 exinst11 45068 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1978 19.2g 2196 r19.2z 4440 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2210 rr19.3v 3610 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2165 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1828 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1783 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2189 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2213 19.9h 2293 exlimd 2226 exlimdh 2297 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2168 excomim 2169 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2333 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30491 conventions-labels 30491 conventions-labels 30491 conventions-labels 30491 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1829 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44820 albi 1820 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2233 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2234 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44822 exbi 1849 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2237 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44819 2alimdv 1920 alimd 2220 alimdh 1819 alimdv 1918 ax-4 1811 ralimdaa 3239 ralimdv 3152 ralimdva 3150 ralimdvva 3185 sbcimdv 3798 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2215 19.21h 2294 19.21t 2214 19.21vv 44818 alrimd 2223 alrimdd 2222 alrimdh 1865 alrimdv 1931 alrimi 2221 alrimih 1826 alrimiv 1929 alrimivv 1930 bj-alrimdh 36902 hbralrimi 3128 r19.21be 3231 r19.21bi 3230 ralrimd 3243 ralrimdv 3136 ralrimdva 3138 ralrimdvv 3182 ralrimdvva 3193 ralrimi 3236 ralrimia 3237 ralrimiv 3129 ralrimiva 3130 ralrimivv 3179 ralrimivva 3181 ralrimivvva 3184 ralrimivw 3134 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44821 2eximdv 1921 bj-exim 36917 exim 1836 eximd 2224 eximdh 1866 eximdv 1919 rexim 3079 reximd2a 3248 reximdai 3240 reximdd 45593 reximddv 3154 reximddv2 3197 reximddv3 3155 reximdv 3153 reximdv2 3148 reximdva 3151 reximdvai 3149 reximdvva 3186 reximi2 3071 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2219 19.23bi 2199 19.23h 2295 19.23t 2218 exlimdv 1935 exlimdvv 1936 exlimexi 44966 exlimiv 1932 exlimivv 1934 rexlimd3 45589 rexlimdv 3137 rexlimdv3a 3143 rexlimdva 3139 rexlimdva2 3141 rexlimdvaa 3140 rexlimdvv 3194 rexlimdvva 3195 rexlimdvvva 3196 rexlimdvw 3144 rexlimiv 3132 rexlimiva 3131 rexlimivv 3180 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1993 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1882 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1872 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2235 r19.27z 4451 r19.27zv 4452 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2236 19.28vv 44828 r19.28z 4443 r19.28zf 45604 r19.28zv 4447 rr19.28v 3611 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1875 r19.29d2r 3125 r19.29imd 3103 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1883 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2242 19.31vv 44826 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2241 r19.32 47543 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44824 19.33 1886 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1994 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1879 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2238 19.36vv 44825 r19.36zv 4453 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2240 19.37vv 44827 r19.37zv 4448 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1841 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1992 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1889 19.40 1888 r19.40 3104 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2243 19.41rg 44992 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2244 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1884 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2245 r19.44zv 4450 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2246 r19.45zv 4449 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2611 |
| [Mayet] p. 370 | Remark | jpi 32361 largei 32358 stri 32348 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32303 ishst 32305 |
| [Mayet3] p. 10 | Theorem | hstrbi 32357 hstri 32356 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31819 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31820 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32369 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31423 chsupcl 31431 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32451 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32445 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32472 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40440 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18442 latj32 18440 latjass 18438 |
| [Megill] p. 444 | Axiom C5 | ax-5 1912 ax5ALT 39364 |
| [Megill] p. 444 | Section 7 | conventions 30490 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39358 ax-c11n 39345 axc11n 2431 |
| [Megill] p. 446 | Lemma L17 | equtrr 2024 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39353 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39385 hbnae 2437 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2486 sbid 2263 sbidd-misc 50191 sbidd 50190 |
| [Megill] p. 448 | Remark 9.6 | axc14 2468 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39341 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39340 sp 2191 |
| [Megill] p. 448 | Scheme C6' | ax-11 2163 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39342 |
| [Megill] p. 448 | Scheme C8' | ax-7 2010 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39347 |
| [Megill] p. 448 | Scheme C10' | ax-6 1969 ax-c10 39343 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39344 |
| [Megill] p. 448 | Scheme C12' | ax-8 2116 |
| [Megill] p. 448 | Scheme C13' | ax-9 2124 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39348 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39346 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39349 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39361 dral1 2444 dral2-o 39387 dral2 2443 drex1 2446 drex2 2447 drsb1 2500 drsb2 2274 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2179 sbequ 2089 sbid2v 2514 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39354 hba1 2300 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47337 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3818 rspsbca 3819 stdpc4 2074 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39341 ra4 3825 stdpc5 2216 |
| [Mendelson] p. 81 | Rule C | exlimiv 1932 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2030 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2258 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3727 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5460 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4339 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4340 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4218 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4275 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4219 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4082 |
| [Mendelson] p. 231 | Definition of union | dfun3 4217 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5396 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4848 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5513 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4560 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5514 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4875 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5773 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6225 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7720 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6321 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8522 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9069 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8990 xpsneng 8991 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 8997 xpcomeng 8998 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9000 |
| [Mendelson] p. 255 | Definition | brsdom 8912 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 8993 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8768 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8975 mapsnend 8974 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9075 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9074 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8821 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8978 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 8994 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10090 djucomen 10089 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10094 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10088 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8457 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8484 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10470 |
| [Mendelson] p. 281 | Definition | df-r1 9677 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9726 |
| [Mendelson] p. 287 | Axiom system MK | ru 3727 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30349 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30384 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30386 vdgn1frgrv3 30387 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30388 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30381 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30374 2pthfrgrrn 30372 2pthfrgrrn2 30373 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31343 |
| [Monk1] p. 22 | Remark | conventions 30490 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30490 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4180 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5730 ssrelf 32708 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5731 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5149 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6219 coi2 6220 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5867 rn0 5873 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6097 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5640 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5876 rnxp 6126 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5721 xp0 5722 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6034 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6031 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7856 imaexg 7855 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6028 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7019 funfvop 6994 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6886 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6897 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6536 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7200 dff13f 7201 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7165 funrnex 7898 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7193 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6183 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4907 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7950 df-1st 7933 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7951 df-2nd 7934 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9767 ranksnb 9740 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9768 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9769 rankunb 9763 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9751 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9677 r1val2 9750 |
| [Monk1] p. 117 | Lemma | zorn2 10417 zorn2g 10414 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9899 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10472 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9894 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1811 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2010 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2185 ax-c15 39346 ax12v2 2187 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39341 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2163 |
| [Monk2] p. 109 | Lemma 15 | equvini 2460 equvinv 2031 eqvinop 5433 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1912 ax5ALT 39364 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2147 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2163 |
| [Monk2] p. 114 | Lemma 21 | sp 2191 |
| [Monk2] p. 114 | Lemma 22 | axc4 2327 hba1-o 39354 hba1 2300 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2159 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2182 nfra2 3339 nfra2w 3274 |
| [Moore] p. 53 | Part I | df-mre 17537 |
| [Munkres] p. 77 | Example 2 | distop 22969 indistop 22976 indistopon 22975 |
| [Munkres] p. 77 | Example 3 | fctop 22978 fctop2 22979 |
| [Munkres] p. 77 | Example 4 | cctop 22980 |
| [Munkres] p. 78 | Definition of basis | df-bases 22920 isbasis3g 22923 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17395 tgval2 22930 |
| [Munkres] p. 79 | Remark | tgcl 22943 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22937 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22961 tgss3 22960 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22962 basgen2 22963 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37676 topdifinfeq 37677 topdifinffin 37675 topdifinfindis 37673 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23134 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23012 topcld 23009 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23013 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23015 |
| [Munkres] p. 94 | Definition of closure | clsval 23011 |
| [Munkres] p. 94 | Definition of interior | ntrval 23010 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23049 elcls 23047 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23057 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23122 neindisj 23091 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23124 |
| [Munkres] p. 97 | Definition of limit point | islp2 23119 lpval 23113 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23289 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23201 iscn 23209 iscn2 23212 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23254 cncnp2 23255 cncnpi 23252 df-cnp 23202 iscnp 23211 iscnp2 23213 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24517 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25287 |
| [Nathanson] p. 123 | Remark | reprgt 34786 reprinfz1 34787 reprlt 34784 |
| [Nathanson] p. 123 | Definition | df-repr 34774 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34806 |
| [Nathanson] p. 123 | Proposition | breprexp 34798 breprexpnat 34799 itgexpif 34771 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32195 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48283 |
| [Pfenning] p. 17 | Definition XM | natded 30493 |
| [Pfenning] p. 17 | Definition NNC | natded 30493 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30493 |
| [Pfenning] p. 18 | Rule" | natded 30493 |
| [Pfenning] p. 18 | Definition /\I | natded 30493 |
| [Pfenning] p. 18 | Definition ` `E | natded 30493 natded 30493 natded 30493 natded 30493 natded 30493 |
| [Pfenning] p. 18 | Definition ` `I | natded 30493 natded 30493 natded 30493 natded 30493 natded 30493 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30493 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30493 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30493 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30493 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30493 |
| [Pfenning] p. 127 | Definition =E | natded 30493 |
| [Pfenning] p. 127 | Definition =I | natded 30493 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25178 df-dip 30792 dip0l 30809 ip0l 21624 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25219 ipval 30794 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30805 ipcj 21622 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25181 dipdir 30933 ipdir 21627 ipdiri 30921 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30801 nmsq 25170 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30916 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30918 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30919 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25187 dipass 30936 ipass 21633 ipassi 30932 |
| [Prugovecki] p. 186 | Definition of bra | braval 32035 df-bra 31941 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31942 kbval 32045 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32473 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40345 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32487 atcvat4i 32488 cvrat3 39899 cvrat4 39900 lsatcvat3 39509 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32373 cvrval 39726 df-cv 32370 df-lcv 39476 lspsncv0 21134 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40357 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40358 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2716 rabid 3411 rabidd 45600 wl-df.clab 37834 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2286 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2729 wl-df.cleq 37835 |
| [Quine] p. 19 | Definition 2.9 | conventions 30490 df-v 3432 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2876 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2873 abid2f 2930 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2283 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2091 sbalex 2250 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2812 wl-df.clel 37838 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2737 eqid1 30557 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2744 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3730 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3731 dfsbcq2 3732 |
| [Quine] p. 43 | Theorem 6.8 | vex 3434 |
| [Quine] p. 43 | Theorem 6.9 | isset 3444 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3534 spcgv 3539 spcimgf 3496 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3742 spsbcd 3743 |
| [Quine] p. 44 | Theorem 6.12 | elex 3451 |
| [Quine] p. 44 | Theorem 6.13 | elab 3623 elabg 3620 elabgf 3618 |
| [Quine] p. 44 | Theorem 6.14 | noel 4279 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4662 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4571 df-sn 4569 |
| [Quine] p. 49 | Theorem 7.4 | snss 4729 snssg 4728 |
| [Quine] p. 49 | Theorem 7.5 | prss 4764 prssg 4763 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4707 prid1g 4705 prid2 4708 prid2g 4706 snid 4607 snidg 4605 |
| [Quine] p. 51 | Theorem 7.12 | snex 5374 |
| [Quine] p. 51 | Theorem 7.13 | prex 5373 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4870 unisnALT 45367 unisng 4869 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4874 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4882 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4879 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6460 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47531 dfiota2 6447 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47540 iotaval 6464 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6470 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6466 |
| [Quine] p. 58 | Definition 9.1 | df-op 4575 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5471 opabidw 5470 opelopab 5488 opelopaba 5482 opelopabaf 5490 opelopabf 5491 opelopabg 5484 opelopabga 5479 opelopabgf 5486 oprabid 7390 oprabidw 7389 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5628 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5630 |
| [Quine] p. 64 | Definition 9.15 | df-id 5517 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6555 |
| [Quine] p. 65 | Theorem 10.4 | funi 6522 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6543 funsng 6541 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6492 |
| [Quine] p. 65 | Definition 10.2 | args 6049 dffv4 6829 |
| [Quine] p. 68 | Definition 10.11 | conventions 30490 df-fv 6498 fv2 6827 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14223 nn0opth2i 14222 nn0opthi 14221 omopthi 8588 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8340 |
| [Quine] p. 232 | Equation i | carddom 10465 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6578 funimaexg 6577 |
| [Quine] p. 331 | Axiom system NF | ru 3727 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31175 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30792 polid 31250 polid2i 31248 polidi 31249 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30904 |
| [ReedSimon] p. 195 | Remark | lnophm 32110 lnophmi 32109 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32223 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32225 leopmuli 32224 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32228 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31943 leoppos 32217 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32227 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32216 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48084 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48092 |
| [Roman] p. 4 | Definition | df-dmat 22464 df-dmatalt 48871 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20123 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20205 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48958 |
| [Roman] p. 112 | Note | isldepslvec2 48958 ldepsnlinc 48981 zlmodzxznm 48970 |
| [Roman] p. 112 | Example | zlmodzxzequa 48969 zlmodzxzequap 48972 zlmodzxzldep 48977 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22864 |
| [Rosenlicht] p. 80 | Theorem | heicant 37987 |
| [Rosser] p. 281 | Definition | df-op 4575 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34810 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34811 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48839 pmtr3ncom 19439 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19435 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19378 cayleyth 19379 |
| [Rudin] p. 164 | Equation 27 | efcan 16050 |
| [Rudin] p. 164 | Equation 30 | efzval 16058 |
| [Rudin] p. 167 | Equation 48 | absefi 16152 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1773 |
| [Sanford] p. 39 | Rule 4 | mptxor 1771 |
| [Sanford] p. 40 | Rule 1 | mptnan 1770 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6070 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6073 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6069 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6067 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17537 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17538 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17538 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17540 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10048 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43505 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10357 axdc3 10365 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20207 isrngo 38229 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31633 |
| [Schechter] p. 276 | Definition of span | df-span 31400 spanval 31424 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22967 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6340 onelord 43694 ordelon 6339 ordelord 6337 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43695 sucidg 6398 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6370 onsuc 7755 ord0 6369 ordsuci 7753 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43696 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5197 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43471 elon2 6326 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6321 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5525 epelg 5523 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9505 epirron 43697 ordirr 6333 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43699 oneptr 43698 ontr1 6362 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6358 oneptri 43700 ordtri3or 6347 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8427 ord0eln0 6371 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6384 onsucss 43709 trsucss 6405 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7760 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6411 ordnbtwn 6410 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43711 ordnexbtwnsuc 43710 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10312 onsucf1lem 43712 onsucf1o 43715 onsucf1olem 43713 onsucrn 43714 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43716 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7787 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43705 ordne0gt0 43704 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43707 limnsuc 43708 onsucelab 43706 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9553 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7802 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9556 ordom 7818 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9557 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8567 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7725 ssorduni 7724 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8457 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9560 limom 7824 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8396 df1o2 8403 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8442 oa0suclim 43718 oalim 8458 oasuc 8450 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8443 om0suclim 43719 omlim 8459 omsuc 8452 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8448 oe0m1 8447 oe0suclim 43720 oelim 8460 oesuc 8453 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43672 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43722 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43723 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43724 limexissupab 43726 limiun 43725 limuni 6377 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8464 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8468 om1om1r 43727 om1r 8469 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8461 oaomoecl 43721 oecl 8463 omcl 8462 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43674 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8470 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8471 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43728 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43729 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8538 nnamecl 43730 nnecl 8540 nnmcl 8539 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43731 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8478 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8479 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8486 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43733 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43734 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43736 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8485 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43740 omword1 8499 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43739 oaordnrex 43738 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43735 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43741 omword2 8500 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43742 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43743 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43744 omordi 8492 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8494 omord2com 43745 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43746 df-2o 8397 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43749 oewordi 8518 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43750 oeworde 8520 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43751 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43752 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43748 omnord1ex 43747 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43753 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43755 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43759 oenord1ex 43758 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43760 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8487 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43754 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8505 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8506 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43762 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8524 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43763 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43764 cantnfub2 43765 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43768 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29002 axtgcgrrflx 28549 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29003 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29004 axtgcgrid 28550 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28535 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29015 axtgsegcon 28551 df-trkgcb 28537 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29026 axtg5seg 28552 df-trkgcb 28537 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29027 axtgbtwnid 28553 df-trkgb 28536 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29029 axtgpasch 28554 df-trkgb 28536 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29048 df-trkg2d 34830 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28557 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28558 df-trkg2d 34830 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29051 axtgeucl 28559 df-trkge 28538 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29064 axtgcont 28556 axtgcont1 28555 df-trkgb 28536 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36190 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36192 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36195 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36199 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36200 tgcgrcomimp 28564 tgcgrcoml 28566 tgcgrcomr 28565 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36205 tgcgrtriv 28571 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36209 tg5segofs 34838 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34835 df-ofs 36186 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36211 tgcgrextend 28572 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36213 tgsegconeq 28573 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36225 btwntriv2 36215 tgbtwntriv2 28574 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36216 tgbtwncom 28575 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36219 tgbtwntriv1 28578 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36220 tgbtwnswapid 28579 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36226 btwnintr 36222 tgbtwnexch2 28583 tgbtwnintr 28580 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36228 btwnexch3 36223 tgbtwnexch 28585 tgbtwnexch3 28581 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36227 tgbtwnouttr 28584 tgbtwnouttr2 28582 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29047 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36230 tgbtwndiff 28593 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28586 trisegint 36231 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36247 tgifscgr 28595 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28645 colrot1 28646 colrot2 28647 lncom 28709 lnrot1 28710 lnrot2 28711 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36243 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36248 tgcgrsub 28596 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36258 tgcgrxfr 28605 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28604 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36244 df-cgrg 28598 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28598 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36259 tgbtwnxfr 28617 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36265 colinearperm2 36267 colinearperm3 36266 colinearperm4 36268 colinearperm5 36269 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28620 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36242 tgellng 28640 tglng 28633 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36270 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36278 lnxfr 28653 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36279 lnext 28654 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36283 tgfscgr 28655 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36284 lncgr 28656 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36245 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36286 lnid 28657 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36287 tgidinside 28658 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36304 tgbtwnconn1 28662 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36305 tgbtwnconn2 28663 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36306 tgbtwnconn3 28664 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36312 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36310 legov 28672 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28673 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28686 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36313 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36315 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36317 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36318 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36319 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36316 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36321 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28674 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28676 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28677 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28678 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28679 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36328 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36329 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36324 df-outsideof 36323 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36325 ishlg 28689 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28694 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28696 outsideofrflx 36330 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28690 hlcomd 28691 outsideofcom 36331 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28697 outsideoftr 36332 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28705 outsideofeu 36334 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36341 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36342 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36335 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36350 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36351 tglineelsb2 28719 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36353 linerflx1 36352 linerflx2 36354 tglinecom 28722 tglinerflx1 28720 tglinerflx2 28721 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36356 tglinethru 28723 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36340 tglng 28633 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28681 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36359 tglinethrueu 28726 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36360 tglineineq 28730 tglineinteq 28732 tglineintmo 28729 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28736 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28737 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28738 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28753 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28749 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28741 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28740 ismir 28746 mirbtwn 28745 mircgr 28744 mirfv 28743 mirval 28742 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28751 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28752 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28753 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28756 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28757 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28762 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28759 mirbtwni 28758 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28760 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28772 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28776 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28773 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28774 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28775 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28778 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28779 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28785 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28781 israg 28784 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28786 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28787 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28789 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28790 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28791 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28792 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28793 ragncol 28796 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28794 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28800 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28804 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28801 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28783 isperp 28799 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28802 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28809 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28817 colperpexlem2 28818 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28820 colperpexlem3 28819 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28825 midex 28824 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28822 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28831 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28826 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28835 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28838 opphllem6 28839 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28841 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28554 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28842 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28850 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28845 hpgbr 28847 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28852 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28851 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28853 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28854 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28855 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28856 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28857 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28871 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28861 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28875 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28876 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28877 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28878 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28879 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28882 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28884 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28862 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28885 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28888 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28889 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28890 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28891 trgcopyeu 28893 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28917 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28896 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28905 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28903 cgrahl2 28904 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28906 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28907 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28909 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28910 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28913 cgrahl 28914 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28918 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28919 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28920 acopyeu 28921 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28928 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28932 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28925 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28940 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28933 isleag 28934 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28942 tgsas1 28941 tgsas2 28943 tgsas3 28944 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28946 tgasa1 28945 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28947 tgsss2 28948 tgsss3 28949 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27253 dchrsum 27251 dchrsum2 27250 sumdchr 27254 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27255 sum2dchr 27256 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20032 ablfacrp2 20033 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27198 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27199 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27206 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27464 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27467 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27521 vmalogdivsum2 27520 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27511 dirith2 27510 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27509 rpvmasum 27508 rpvmasum2 27494 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27469 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27507 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27474 dchrisumlem1 27471 dchrisumlem2 27472 dchrisumlem3 27473 dchrisumlema 27470 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27477 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27506 dchrmusumlem 27504 dchrvmasumlem 27505 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27476 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27478 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27502 dchrisum0re 27495 dchrisumn0 27503 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27488 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27492 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27493 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27548 pntrsumbnd2 27549 pntrsumo1 27547 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27512 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27514 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27516 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27519 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27524 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27525 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27530 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27532 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27533 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27541 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27542 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27539 selberg3lem2 27540 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27543 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27537 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27550 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27551 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27552 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27566 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27578 pntlemb 27579 pntlemc 27577 pntlemd 27576 pntlemg 27580 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27578 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27570 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27575 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27578 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27591 pntleml 27593 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33908 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33895 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33927 constrinvcl 33938 constrmulcl 33936 constrnegcl 33928 constrsqrtcl 33944 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33914 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33924 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33946 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33956 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4247 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4346 dif0 4319 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4432 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4416 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4238 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4239 |
| [Stoll] p. 20 | Remark | invdif 4220 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4577 |
| [Stoll] p. 43 | Definition | uniiun 5002 |
| [Stoll] p. 44 | Definition | intiin 5003 |
| [Stoll] p. 45 | Definition | df-iin 4937 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4936 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4247 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44777 |
| [Suppes] p. 22 | Theorem 2 | eq0 4291 eq0f 4288 |
| [Suppes] p. 22 | Theorem 4 | eqss 3938 eqssd 3940 eqssi 3939 |
| [Suppes] p. 23 | Theorem 5 | ss0 4343 ss0b 4342 |
| [Suppes] p. 23 | Theorem 6 | sstr 3931 sstrALT2 45276 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4044 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4045 |
| [Suppes] p. 23 | Theorem 9 | psstr 4048 |
| [Suppes] p. 23 | Theorem 10 | pssss 4039 |
| [Suppes] p. 25 | Theorem 12 | elin 3906 elun 4094 |
| [Suppes] p. 26 | Theorem 15 | inidm 4168 |
| [Suppes] p. 26 | Theorem 16 | in0 4336 |
| [Suppes] p. 27 | Theorem 23 | unidm 4098 |
| [Suppes] p. 27 | Theorem 24 | un0 4335 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4119 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4127 |
| [Suppes] p. 27 | Theorem 27 | unss 4131 |
| [Suppes] p. 27 | Theorem 28 | indir 4227 |
| [Suppes] p. 27 | Theorem 29 | undir 4228 |
| [Suppes] p. 28 | Theorem 32 | difid 4317 |
| [Suppes] p. 29 | Theorem 33 | difin 4213 |
| [Suppes] p. 29 | Theorem 34 | indif 4221 |
| [Suppes] p. 29 | Theorem 35 | undif1 4417 |
| [Suppes] p. 29 | Theorem 36 | difun2 4422 |
| [Suppes] p. 29 | Theorem 37 | difin0 4415 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4413 |
| [Suppes] p. 29 | Theorem 39 | difundi 4231 |
| [Suppes] p. 29 | Theorem 40 | difindi 4233 |
| [Suppes] p. 30 | Theorem 41 | nalset 5248 |
| [Suppes] p. 39 | Theorem 61 | uniss 4859 |
| [Suppes] p. 39 | Theorem 65 | uniop 5461 |
| [Suppes] p. 41 | Theorem 70 | intsn 4927 |
| [Suppes] p. 42 | Theorem 71 | intpr 4925 intprg 4924 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5417 |
| [Suppes] p. 42 | Theorem 78 | intun 4923 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4975 dfiun2g 4973 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4976 |
| [Suppes] p. 47 | Theorem 86 | elpw 4546 elpw2 5269 elpw2g 5268 elpwg 4545 elpwgdedVD 45358 |
| [Suppes] p. 47 | Theorem 87 | pwid 4564 |
| [Suppes] p. 47 | Theorem 89 | pw0 4756 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4757 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5637 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5780 xpindir 5781 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5691 xpundir 5692 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9503 |
| [Suppes] p. 58 | Theorem 2 | relss 5729 |
| [Suppes] p. 59 | Theorem 4 | eldm 5847 eldm2 5848 eldm2g 5846 eldmg 5845 |
| [Suppes] p. 59 | Definition 3 | df-dm 5632 |
| [Suppes] p. 60 | Theorem 6 | dmin 5858 |
| [Suppes] p. 60 | Theorem 8 | rnun 6101 |
| [Suppes] p. 60 | Theorem 9 | rnin 6102 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5835 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5829 brcnvg 5826 |
| [Suppes] p. 62 | Equation 5 | elcnv 5823 elcnv2 5824 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6061 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6100 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6098 |
| [Suppes] p. 63 | Definition | dftrrels2 38991 |
| [Suppes] p. 63 | Theorem 20 | co02 6217 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5922 |
| [Suppes] p. 63 | Definition 7 | df-co 5631 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5832 |
| [Suppes] p. 64 | Theorem 27 | coass 6222 |
| [Suppes] p. 65 | Theorem 31 | resundi 5950 |
| [Suppes] p. 65 | Theorem 34 | elima 6022 elima2 6023 elima3 6024 elimag 6021 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6105 |
| [Suppes] p. 66 | Theorem 40 | dminss 6109 |
| [Suppes] p. 66 | Theorem 41 | imainss 6110 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6113 |
| [Suppes] p. 81 | Definition 34 | dfec2 8637 |
| [Suppes] p. 82 | Theorem 72 | elec 8681 elecALTV 38603 elecg 8679 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39027 erth 8689 erth2 8690 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39030 erdisj 8692 |
| [Suppes] p. 83 | Definition 35, | df-parts 39200 dfmembpart2 39205 |
| [Suppes] p. 89 | Theorem 96 | map0b 8822 |
| [Suppes] p. 89 | Theorem 97 | map0 8826 map0g 8823 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8827 mapsnd 8825 |
| [Suppes] p. 89 | Theorem 99 | mapss 8828 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9979 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9978 |
| [Suppes] p. 92 | Theorem 1 | enref 8923 enrefg 8922 |
| [Suppes] p. 92 | Theorem 2 | ensym 8941 ensymb 8940 ensymi 8942 |
| [Suppes] p. 92 | Theorem 3 | entr 8944 |
| [Suppes] p. 92 | Theorem 4 | unen 8983 |
| [Suppes] p. 94 | Theorem 15 | endom 8917 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8938 |
| [Suppes] p. 94 | Theorem 17 | domtr 8945 |
| [Suppes] p. 95 | Theorem 18 | sbth 9026 |
| [Suppes] p. 97 | Theorem 23 | canth2 9059 canth2g 9060 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9030 df-sdom 8887 dfsdom2 9029 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9043 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9032 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9031 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9041 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8920 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9044 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9039 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8969 fundmeng 8970 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9004 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9040 |
| [Suppes] p. 104 | Theorem 37 | fofi 9214 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9220 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9220 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10462 |
| [Suppes] p. 130 | Definition 3 | df-tr 5194 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7725 |
| [Suppes] p. 134 | Definition 6 | df-suc 6321 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7842 finds 7838 finds1 7841 finds2 7840 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9562 isfinite2 9199 isfiniteg 9201 unbnn 9197 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10830 df-ltpq 10822 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7805 tfinds 7802 tfinds2 7806 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8477 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8479 |
| [Suppes] p. 211 | Theorem 25 | oaass 8487 |
| [Suppes] p. 225 | Definition 8 | iscard2 9889 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10474 |
| [Suppes] p. 228 | Theorem 59 | harcard 9891 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9977 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6367 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7738 onminsb 7739 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10484 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9981 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9988 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9982 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9853 |
| [Suppes] p. 242 | Theorem 6 | weth 10406 |
| [Suppes] p. 242 | Theorem 8 | entric 10468 |
| [Suppes] p. 242 | Theorem 9 | carden 10462 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35899 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35903 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2709 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2729 wl-df.cleq 37835 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2812 wl-df.clel 37838 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2731 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2757 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7362 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3727 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5356 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4593 elpr2 4595 elpr2g 4594 elprg 4591 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4583 elsn2 4610 elsn2g 4609 elsng 4582 velsn 4584 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5413 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4578 sneqr 4784 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4589 dfsn2 4581 dfsn2ALT 4590 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7686 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5422 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5409 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5393 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7689 unexg 7688 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4636 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4852 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3897 df-un 3895 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4868 uniprg 4867 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5312 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4634 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6387 elsucg 6385 sstr2 3929 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4099 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4150 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4113 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4169 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4225 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4226 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3910 df-ss 3907 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4544 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4128 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3908 sseqin2 4164 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3945 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4178 inss2 4179 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3987 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4862 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5394 sspwimp 45359 sspwimpALT 45366 sspwimpALT2 45369 sspwimpcf 45361 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5401 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5212 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3391 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5242 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3893 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 36848 dfnul2 4277 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4317 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4294 n0f 4290 neq0 4293 neq0f 4289 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9502 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9642 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9657 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3432 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5250 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4341 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5256 ssexg 5258 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5252 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9511 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9505 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4307 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4076 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4241 undif3VD 45323 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4077 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4084 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3053 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3063 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7698 xpexg 7695 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5629 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6561 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6737 fun11 6564 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6503 svrelfun 6562 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5834 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5836 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5634 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5635 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5631 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6150 dfrel2 6145 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5638 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5758 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5765 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5778 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5962 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5942 opelresi 5944 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5969 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5958 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5963 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6532 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6065 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6530 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6739 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2610 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30490 df-fv 6498 fv3 6850 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7867 cnvexg 7866 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7851 dmexg 7843 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7852 rnexg 7844 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44895 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7862 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6845 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47619 tz6.12-1-afv2 47686 tz6.12-1 6855 tz6.12-afv 47618 tz6.12-afv2 47685 tz6.12 6856 tz6.12c-afv2 47687 tz6.12c 6854 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47682 tz6.12-2 6819 tz6.12i-afv2 47688 tz6.12i 6858 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6493 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6494 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6496 wfo 6488 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6495 wf1 6487 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6497 wf1o 6489 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6975 eqfnfv2 6976 eqfnfv2f 6979 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6930 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7163 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7161 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6578 funimaexg 6577 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5087 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5531 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5583 dffr3 6056 eliniseg 6051 iniseg 6054 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5522 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5599 fr3nr 7717 frirr 5598 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5575 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7719 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5586 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5608 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6303 tz6.26i 6304 wefrc 5616 wereu2 5619 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6305 wfii 6306 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6499 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7275 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7276 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7282 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7283 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7284 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7288 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7295 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7297 |
| [TakeutiZaring] p. 35 | Notation | wtr 5193 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44896 tz7.2 5605 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5198 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6328 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6336 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6337 ordelordALT 44979 ordelordALTVD 45308 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6343 ordelssne 6342 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6341 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6345 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7727 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7728 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6319 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6347 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44991 ordon 7722 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7723 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7795 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6363 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5195 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7737 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7773 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6421 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6420 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7724 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4882 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6321 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6397 sucidg 6398 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7755 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6411 ordnbtwn 6410 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7770 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6320 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7823 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7828 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7783 ordelsuc 7762 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7764 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7793 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7810 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7831 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7832 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7833 |
| [TakeutiZaring] p. 43 | Remark | omon 7820 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9545 omex 9553 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7818 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7837 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7834 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7835 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7813 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4905 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5211 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4906 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5279 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7740 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6366 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4891 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9570 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7735 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8306 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8327 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8328 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8329 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8336 tz7.44-2 8337 tz7.44-3 8338 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8298 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8293 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8277 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8375 tz7.49c 8376 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8373 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8372 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8374 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2657 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9922 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9923 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8458 oasuc 8450 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7803 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8461 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8442 oa0r 8464 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8462 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8474 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8546 nnaordi 8545 oaord 8473 oaordi 8472 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4993 uniss2 4885 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8476 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8481 oawordex 8483 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8538 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8575 |
| [TakeutiZaring] p. 60 | Remark | oancom 9561 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8486 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8543 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8478 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8445 omlim 8459 omsuc 8452 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8443 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8540 nnmcl 8539 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8559 nnmordi 8558 omord 8494 omordi 8492 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8495 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8563 omwordri 8498 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8465 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8468 om1r 8469 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8501 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8503 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8504 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8505 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8506 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8535 oe0 8448 oelim 8460 oesuc 8453 onesuc 8456 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8446 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8513 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8514 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8447 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8471 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8515 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8521 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8519 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8520 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8524 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8526 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9638 tz9.1 9639 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9677 r10 9681 r1lim 9685 r1limg 9684 r1suc 9683 r1sucg 9682 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9693 r1ord2 9694 r1ordg 9691 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9703 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9728 tz9.13 9704 tz9.13g 9705 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9678 rankval 9729 rankvalb 9710 rankvalg 9730 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9752 rankelb 9737 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9766 rankval3 9753 rankval3b 9739 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9742 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9708 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9747 rankr1c 9734 rankr1g 9745 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9748 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9762 rankssb 9761 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9755 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9754 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10386 dfac3 10032 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9941 numth 10383 numth2 10382 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10457 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10458 cardid2 9866 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9873 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10462 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9872 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9857 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9878 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9870 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9079 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8956 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9084 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9008 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9876 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10009 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9131 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9139 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10010 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9136 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 9999 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9977 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9885 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10127 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9224 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8888 isfi 8913 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9140 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10445 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9001 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10437 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10097 unxpdom 9160 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9887 cardsdomelir 9886 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9162 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9925 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8766 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10473 infxpidm2 9928 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10118 infxp 10125 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9013 pw2f1o 9011 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9072 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10398 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10393 ac6s5 10402 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10454 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10455 uniimadomf 10456 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10185 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10180 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10165 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10162 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10168 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10175 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10184 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10494 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10163 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10187 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10008 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10007 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10019 alephfp2 10020 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10611 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10023 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10481 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10495 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10496 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39340 |
| [Tarski] p. 67 | Scheme B5 | sp 2191 |
| [Tarski] p. 68 | Lemma 6 | avril1 30553 equid 2014 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2019 |
| [Tarski] p. 70 | Lemma 14 | spim 2392 spime 2394 spimew 1973 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2185 ax-c15 39346 ax12i 1968 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2091 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1970 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1912 ax5ALT 39364 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2010 ax-8 2116 ax-9 2124 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28551 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28552 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28554 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28554 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28555 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16199 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37991 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37993 |
| [Weierstrass] p. 272 | Definition | df-mdet 22559 mdetuni 22596 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 904 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 870 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 920 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 970 |
| [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 37772 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44242 imim2 58 wl-luk-imim2 37767 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47464 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 897 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2664 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37770 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 898 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45368 wl-luk-notnotr 37771 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44272 axfrege28 44271 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 868 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 925 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37764 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 890 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 942 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30491 pm2.27 42 wl-luk-pm2.27 37762 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 923 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38703 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 924 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 973 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 971 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 908 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 945 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 882 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 883 |
| [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 | pm2.47 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 886 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 853 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 900 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 944 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 892 pm2.67 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 901 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 934 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 978 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 998 |
| [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 | pm3.35 803 |
| [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) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 623 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 810 |
| [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 963 pm3.44 962 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 966 |
| [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 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 905 pm4.25 906 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1010 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 871 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 922 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 634 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 638 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 979 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1008 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1025 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 999 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1001 pm4.45 1000 pm4.45im 828 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 986 pm4.56 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 992 pm4.57 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 857 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 851 |
| [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 | pm4.72 952 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 937 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 964 pm4.77 965 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1006 |
| [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 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1027 |
| [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 pm4.87 844 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 824 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 947 pm5.11g 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 950 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 949 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1014 |
| [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 | pm5.21 825 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1017 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 902 |
| [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 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [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 1007 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 951 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1030 |
| [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 1031 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 36899 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44800 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44801 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1872 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44802 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44803 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44804 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1895 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44805 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44806 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44807 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44808 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44809 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44811 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44812 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44813 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44810 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2096 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44816 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44817 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2076 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2166 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1831 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1832 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44818 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44819 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44820 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44821 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44823 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44822 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1889 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44825 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44826 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44824 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1830 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44827 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44828 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1848 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44829 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2351 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1862 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44834 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44830 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44831 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44832 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44833 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44838 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44835 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44836 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44837 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44839 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2570 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44849 pm13.13b 44850 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44851 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3014 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3015 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3609 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44857 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44858 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44852 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44994 pm13.193 44853 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44854 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44855 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44856 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44863 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44862 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44861 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3792 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44864 pm14.122b 44865 pm14.122c 44866 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44867 pm14.123b 44868 pm14.123c 44869 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44871 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44870 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44872 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6471 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44873 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6472 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44874 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44876 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2634 eupickbi 2637 sbaniota 44877 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44875 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2585 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44878 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30490 df-fv 6498 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9914 pm54.43lem 9913 |
| [Young] p. 141 | Definition of operator ordering | leop2 32215 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32221 idleop 32222 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43271 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43278 pellexlem1 43272 |