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 17714 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17714 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18123 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17735 0funcg 49714 df-termc 50102 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50179 prsthinc 50093 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50207 df-mndtc 50207 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50203 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17758 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50195 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50220 oppgoppchom 50219 oppgoppcid 50221 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17828 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17816 invisoinvl 17837 |
| [Adamek] p. 28 | Example 3.13 | idinv 17836 idiso 17835 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17821 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17795 df-iso 17796 dfiso2 17819 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17802 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17853 cicerALT 49675 |
| [Adamek] p. 29 | Definition 3.15 | cic 17846 df-cic 17843 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17905 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17817 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17818 isoco 17824 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17905 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17928 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49933 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17921 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50203 discthing 50090 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50047 prsthinc 50093 thincciso 50082 thincciso2 50084 thincciso3 50085 thinccisod 50083 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50207 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17935 cofucla 49725 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49791 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18158 catcisoi 50029 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18213 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17954 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17953 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18213 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17978 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17984 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17983 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18198 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18198 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49761 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49752 funcoppc 17922 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18146 elcatchom 50026 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17972 fthoppf 49793 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17971 fulloppf 49792 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18155 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49714 df-catc 18146 |
| [Adamek] p. 45 | Exercise 3G | incat 50230 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50233 nelsubc3 49700 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49780 imasubc2 49781 imasubc3 49785 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17885 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17886 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49700 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17897 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17859 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49789 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49788 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49790 ressffth 17987 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50231 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17993 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18014 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18018 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17994 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18020 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49714 df-inito 18031 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49714 df-termc 50102 initc 49720 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21589 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18032 oppctermo 49865 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18059 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18063 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49866 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18033 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21590 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18066 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17794 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50098 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50097 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50062 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17829 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17831 |
| [Adamek] p. 185 | Section 10.67 | updjud 9908 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50274 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50274 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50274 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50275 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50275 |
| [Adamek] p. 478 | Item Rng | df-ringc 20722 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49179 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49201 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14598 df-pfx 14699 df-substr 14669 df-word 14541 lencl 14560 wrd0 14566 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24826 df-nmoo 31006 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32414 hmopidmchi 32412 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32462 pjcmul2i 32463 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32179 unoplin 32181 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32180 unopadj2 32199 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32274 lnopunii 32273 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32347 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28078 |
| [Alling] p. 184 | Axiom B | bdayfo 27799 |
| [Alling] p. 184 | Axiom O | ltsso 27798 |
| [Alling] p. 184 | Axiom SD | nodense 27814 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27906 |
| [Alling] p. 185 | Theorem | conway 27930 |
| [Alling] p. 185 | Axiom FE | noeta 27865 |
| [Alling] p. 186 | Theorem 4 | lesrec 27950 lesrecd 27951 |
| [Alling], p. 2 | Definition | rp-brsslt 44011 |
| [Alling], p. 3 | Note | nla0001 44014 nla0002 44012 nla0003 44013 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11382 addcan2d 11402 addcan2i 11392 addcand 11401 addcani 11391 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11435 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11494 negsubd 11563 negsubi 11524 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11496 negnegd 11548 negnegi 11516 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11635 subdid 11658 subdii 11651 subdir 11636 subdird 11659 subdiri 11652 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11377 mul01d 11397 mul01i 11388 mul02 11376 mul02d 11396 mul02i 11387 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11839 mulcan2d 11836 mulcand 11835 mulcani 11841 |
| [Apostol] p. 18 | Theorem I.8 | receu 11847 xreceu 33154 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11876 divrecd 11985 divreci 11951 divreczi 11944 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11903 recreci 11938 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11842 mul0ord 11850 mul0ori 11849 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11641 mul2negd 11657 mul2negi 11650 mulneg1 11638 mulneg1d 11655 mulneg1i 11648 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11921 divadddivd 12026 divadddivi 11968 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11906 divmuldivd 12023 divmuldivi 11966 rdivmuldivd 20486 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11907 divdivdivd 12029 divdivdivi 11969 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13031 rpaddcld 13066 rpmulcl 13032 rpmulcld 13067 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13041 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13044 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11324 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11795 ltadd1dd 11813 ltadd1i 11756 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12056 ltmul1a 12055 ltmul1i 12124 ltmul1ii 12134 ltmul2 12057 ltmul2d 13093 ltmul2dd 13107 ltmul2i 12127 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11722 msqgt0d 11769 msqgt0i 11739 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11724 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11708 lt0neg1d 11771 ltneg 11702 ltnegd 11780 ltnegi 11746 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11687 lt2addd 11825 lt2addi 11764 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13008 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12052 recgt0d 12140 recgt0i 12111 recgt0ii 12112 |
| [Apostol] p. 22 | Definition of integers | df-z 12583 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12238 |
| [Apostol] p. 22 | Definition of rationals | df-q 12964 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9402 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12491 |
| [Apostol] p. 26 | Theorem I.29 | arch 12492 archd 45738 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12690 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12493 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12962 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12961 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13216 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16387 zneo 12670 zneoALTV 48289 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26853 msqsqrtd 15484 resqrtth 15296 sqrtth 15406 sqrtthi 15412 sqsqrtd 15483 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12227 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12928 |
| [Apostol] p. 361 | Remark | crreczi 14255 |
| [Apostol] p. 363 | Remark | absgt0i 15441 |
| [Apostol] p. 363 | Example | abssubd 15497 abssubi 15445 |
| [ApostolNT] p. 7 | Remark | fmtno0 48147 fmtno1 48148 fmtno2 48157 fmtno3 48158 fmtno4 48159 fmtno5fac 48189 fmtnofz04prm 48184 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48135 |
| [ApostolNT] p. 8 | Definition | df-ppi 27222 |
| [ApostolNT] p. 14 | Definition | df-dvds 16301 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16317 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16342 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16337 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16330 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16332 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16318 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16319 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16324 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16359 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16361 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16363 |
| [ApostolNT] p. 15 | Definition | df-gcd 16543 dfgcd2 16594 |
| [ApostolNT] p. 16 | Definition | isprm2 16730 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16701 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16965 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16561 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16595 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16597 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16576 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16568 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16760 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16762 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16978 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16972 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16451 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16635 |
| [ApostolNT] p. 24 | Definition | df-mu 27223 |
| [ApostolNT] p. 25 | Definition | df-phi 16815 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27313 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16840 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16825 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16829 |
| [ApostolNT] p. 32 | Definition | df-vma 27220 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27315 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27338 |
| [ApostolNT] p. 38 | Remark | df-sgm 27224 |
| [ApostolNT] p. 38 | Definition | df-sgm 27224 |
| [ApostolNT] p. 75 | Definition | df-chp 27221 df-cht 27219 |
| [ApostolNT] p. 104 | Definition | congr 16712 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16304 |
| [ApostolNT] p. 106 | Definition | moddvds 16311 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16394 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16395 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13912 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13952 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14265 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16336 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16715 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17124 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16717 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16832 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16851 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16833 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27194 |
| [ApostolNT] p. 179 | Definition | df-lgs 27417 lgsprme0 27461 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27462 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27438 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27453 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27510 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27529 2lgsoddprm 27538 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27496 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27505 |
| [ApostolNT] p. 188 | Definition | df-lgs 27417 lgs1 27463 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27454 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27456 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27464 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27465 |
| [Baer] p. 40 | Property (b) | mapdord 42274 |
| [Baer] p. 40 | Property (c) | mapd11 42275 |
| [Baer] p. 40 | Property (e) | mapdin 42298 mapdlsm 42300 |
| [Baer] p. 40 | Property (f) | mapd0 42301 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42261 mapd1o 42284 |
| [Baer] p. 41 | Property (g) | mapdat 42303 |
| [Baer] p. 44 | Part (1) | mapdpg 42342 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42437 mapdheq 42364 mapdheq2 42365 mapdheq2biN 42366 |
| [Baer] p. 45 | Part (3) | baerlem3 42349 |
| [Baer] p. 46 | Part (4) | mapdheq4 42368 mapdheq4lem 42367 |
| [Baer] p. 46 | Part (5) | baerlem5a 42350 baerlem5abmN 42354 baerlem5amN 42352 baerlem5b 42351 baerlem5bmN 42353 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42457 hdmap1l6a 42445 hdmap1l6e 42450 hdmap1l6f 42451 hdmap1l6g 42452 hdmap1l6lem1 42443 hdmap1l6lem2 42444 mapdh6N 42383 mapdh6aN 42371 mapdh6eN 42376 mapdh6fN 42377 mapdh6gN 42378 mapdh6lem1N 42369 mapdh6lem2N 42370 |
| [Baer] p. 48 | Part 9 | hdmapval 42464 |
| [Baer] p. 48 | Part 10 | hdmap10 42476 |
| [Baer] p. 48 | Part 11 | hdmapadd 42479 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42453 mapdh6hN 42379 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42389 mapdh75d 42390 mapdh75e 42388 mapdh75fN 42391 mapdh7cN 42385 mapdh7dN 42386 mapdh7eN 42384 mapdh7fN 42387 |
| [Baer] p. 48 | Part (8) | mapdh8 42424 mapdh8a 42411 mapdh8aa 42412 mapdh8ab 42413 mapdh8ac 42414 mapdh8ad 42415 mapdh8b 42416 mapdh8c 42417 mapdh8d 42419 mapdh8d0N 42418 mapdh8e 42420 mapdh8g 42421 mapdh8i 42422 mapdh8j 42423 |
| [Baer] p. 48 | Part (9) | mapdh9a 42425 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42405 |
| [Baer] p. 49 | Part 12 | hdmap11 42484 hdmapeq0 42480 hdmapf1oN 42501 hdmapneg 42482 hdmaprnN 42500 hdmaprnlem1N 42485 hdmaprnlem3N 42486 hdmaprnlem3uN 42487 hdmaprnlem4N 42489 hdmaprnlem6N 42490 hdmaprnlem7N 42491 hdmaprnlem8N 42492 hdmaprnlem9N 42493 hdmapsub 42483 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42504 hdmap14lem10 42513 hdmap14lem1a 42502 hdmap14lem2N 42505 hdmap14lem2a 42503 hdmap14lem3 42506 hdmap14lem8 42511 hdmap14lem9 42512 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42514 hdmap14lem12 42515 hdmap14lem13 42516 hdmap14lem14 42517 hdmap14lem15 42518 hgmapval 42523 |
| [Baer] p. 50 | Part 15 | hgmapadd 42530 hgmapmul 42531 hgmaprnlem2N 42533 hgmapvs 42527 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42537 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42553 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42554 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42555 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42556 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42558 hgmapvv 42562 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42557 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42559 |
| [Baer] p. 111 | Line 15 | hdmapg 42566 hdmapglem7 42565 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26854 2irrexpqALT 26923 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2599 |
| [BellMachover] p. 460 | Notation | df-mo 2569 |
| [BellMachover] p. 460 | Definition | mo3 2594 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2737 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2741 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5240 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5251 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37561 sepex 5255 |
| [BellMachover] p. 466 | Problem | axpow2 5329 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5330 |
| [BellMachover] p. 466 | Axiom Union | axun2 7724 |
| [BellMachover] p. 468 | Definition | df-ord 6353 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6368 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6375 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6370 |
| [BellMachover] p. 471 | Definition of N | df-om 7851 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7788 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6355 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9599 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7866 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9724 |
| [BellMachover] p. 478 | Definition | rankval2 9778 rankval2b 35407 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9742 r1ord3g 9739 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9546 |
| [BellMachover] p. 488 | Axiom AC | ac5 10449 dfac4 10094 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10082 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39955 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32614 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32656 chirredi 32655 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32644 |
| [Beran] p. 3 | Definition of join | sshjval3 31615 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31877 cmcm2i 31854 cmcm2ii 31859 cmt2N 39886 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31878 lecmi 31863 lecmii 31864 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31852 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31881 cm2ji 31886 cm2mi 31887 |
| [Beran] p. 95 | Definition | df-sh 31468 issh2 31470 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31347 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31360 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31351 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32089 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32091 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32090 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32092 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31343 his1i 31361 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31344 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31345 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31346 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31229 dfhnorm2 31383 normval 31385 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31445 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31234 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31502 |
| [Beran] p. 96 | Definition of converge | df-hlim 31233 hlimi 31449 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31394 norm-i 31390 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31398 norm-ii 31399 normlem0 31370 normlem1 31371 normlem2 31372 normlem3 31373 normlem4 31374 normlem5 31375 normlem6 31376 normlem7 31377 normlem7tALT 31380 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31400 norm-iii 31401 |
| [Beran] p. 98 | Remark 3.4 | bcs 31442 bcsiALT 31440 bcsiHIL 31441 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31382 normpar 31416 normpari 31415 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31407 normpyth 31406 normpythi 31403 |
| [Beran] p. 99 | Remark | lnfn0 32308 lnfn0i 32303 lnop0 32227 lnop0i 32231 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32287 nmcfnex 32314 nmcfnexi 32312 nmcopex 32290 nmcopexi 32288 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32315 nmcfnlbi 32313 nmcoplb 32291 nmcoplbi 32289 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32317 lnfnconi 32316 lnopcon 32296 lnopconi 32295 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31417 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31414 norm3adifii 31409 norm3dif 31411 norm3difi 31408 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31562 pjhth 31654 pjhtheu 31655 pjpjhth 31686 pjpjhthi 31687 pjth 25559 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31667 ococi 31666 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32322 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32323 riesz4 32325 riesz4i 32324 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32340 cnlnadjeu 32339 cnlnadjeui 32338 cnlnadji 32337 cnlnadjlem1 32328 nmopadjlei 32349 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32352 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32351 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32353 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32197 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32363 nmopcoadji 32362 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32354 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32364 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32361 pjadj2coi 32465 pjadjcoi 32422 |
| [Beran] p. 107 | Definition | df-ch 31482 isch2 31484 |
| [Beran] p. 107 | Remark 3.12 | choccl 31567 isch3 31502 occl 31565 ocsh 31544 shoccl 31566 shocsh 31545 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31669 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31593 |
| [Beran] p. 109 | Property (i) | pjadj2 32448 pjadj3 32449 pjadji 31946 pjadjii 31935 |
| [Beran] p. 109 | Property (ii) | pjidmco 32442 pjidmcoi 32438 pjidmi 31934 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32434 |
| [Beran] p. 111 | Remark | ho0val 32011 pjch1 31931 |
| [Beran] p. 111 | Definition | df-hfmul 31995 df-hfsum 31994 df-hodif 31993 df-homul 31992 df-hosum 31991 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31932 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31955 pjchi 31693 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31700 pjoc2i 31699 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31941 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32426 pjssmii 31942 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32425 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32424 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32429 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32427 pjssge0ii 31943 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32428 pjdifnormii 31944 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1799 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1797 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1800 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1795 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34599 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34607 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34605 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34609 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34629 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34660 df-sitm 34638 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34660 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34637 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29307 isuhgrop 29329 isusgrop 29421 isuspgrop 29420 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48481 df-subgr 29527 uhgrspan1 29562 uhgrspansubgr 29550 |
| [Bollobas] p. 3 | Definition | df-gric 48501 gricuspgr 48538 isuspgrim 48516 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29713 df-clnbgr 48439 df-cusgr 29671 df-nbgr 29592 fusgrmaxsize 29723 |
| [Bollobas] p. 4 | Definition | df-upwlks 48754 df-wlks 29858 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29809 finsumvtxdgeven 29811 fusgr1th 29810 fusgrvtxdgonume 29813 vtxdgoddnumeven 29812 |
| [Bollobas] p. 5 | Notation | df-pths 29972 |
| [Bollobas] p. 5 | Definition | df-crcts 30044 df-cycls 30045 df-trls 29949 df-wlkson 29859 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29318 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48820 df-cllaw 48806 df-mgm 18688 df-mgm2 48839 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48821 df-asslaw 48808 df-sgrp 18767 df-sgrp2 48841 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48840 df-comlaw 48807 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18783 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33259 mndlactf1o 33263 mndractf1 33261 mndractf1o 33264 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20308 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20222 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33940 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33944 assarrginv 33943 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33985 fldextrspunfld 33983 fldextrspunlem1 33982 fldextrspunlem2 33984 fldextrspunlsp 33981 fldextrspunlsplem 33980 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33744 dfufd2 33757 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7275 fcofo 7276 |
| [BourbakiTop1] p. | Remark | xnegmnf 13227 xnegpnf 13226 |
| [BourbakiTop1] p. | Remark | rexneg 13228 |
| [BourbakiTop1] p. | Remark 3 | ust0 24338 ustfilxp 24331 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24208 |
| [BourbakiTop1] p. | Criterion | ishmeo 23877 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24401 iducn 24400 snfil 23982 |
| [BourbakiTop1] p. | Example 2 | neifil 23998 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24185 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24421 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34264 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23981 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24393 df-ust 24319 filintn0 23979 filn0 23980 istgp 24195 ucnprima 24399 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24404 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24415 df-usp 24375 df-utop 24349 trust 24347 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34163 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23234 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23387 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24324 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24327 |
| [BourbakiTop1] p. | Property V_ii | innei 23243 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23251 neissex 23245 |
| [BourbakiTop1] p. | Proposition 1 | neips 23231 neiss 23227 ucncn 24402 ustund 24340 ustuqtop 24364 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23385 neiptopreu 23251 utop2nei 24368 utop3cls 24369 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24409 uspreg 24391 utopreg 24370 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23809 imasncls 23810 imasnopn 23808 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24118 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24326 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24328 |
| [BourbakiTop1] p. | Property V_iii | elnei 23229 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24420 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24325 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24329 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23505 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23964 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23012 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34160 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46634 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46636 stoweid 46635 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46573 stoweidlem10 46582 stoweidlem14 46586 stoweidlem15 46587 stoweidlem35 46607 stoweidlem36 46608 stoweidlem37 46609 stoweidlem38 46610 stoweidlem40 46612 stoweidlem41 46613 stoweidlem43 46615 stoweidlem44 46616 stoweidlem46 46618 stoweidlem5 46577 stoweidlem50 46622 stoweidlem52 46624 stoweidlem53 46625 stoweidlem55 46627 stoweidlem56 46628 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46595 stoweidlem24 46596 stoweidlem27 46599 stoweidlem28 46600 stoweidlem30 46602 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46606 stoweidlem59 46631 stoweidlem60 46632 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46617 stoweidlem49 46621 stoweidlem7 46579 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46603 stoweidlem39 46611 stoweidlem42 46614 stoweidlem48 46620 stoweidlem51 46623 stoweidlem54 46626 stoweidlem57 46629 stoweidlem58 46630 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46597 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46589 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46583 stoweidlem13 46585 stoweidlem26 46598 stoweidlem61 46633 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46590 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48820 df-mgm 18688 df-mgm2 48839 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18767 df-sgrp2 48841 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19096 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5187 |
| [Church] p. 129 | Section II.24 | df-ifp 1077 dfifp2 1078 |
| [Clemente] p. 10 | Definition IT | natded 30663 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30663 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30663 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30663 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30663 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30663 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30663 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30663 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30663 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30663 |
| [Clemente] p. 14 | Proof 5.11 | natded 30663 |
| [Clemente] p. 14 | Definition E` `n | natded 30663 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30665 ex-natded5.2 30664 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30668 ex-natded5.3 30667 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30670 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30672 ex-natded5.7 30671 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30674 ex-natded5.8 30673 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30676 ex-natded5.13 30675 |
| [Clemente] p. 32 | Definition I` `n | natded 30663 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30663 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30663 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30663 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30677 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30678 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30680 ex-natded9.26 30679 |
| [Cohen] p. 301 | Remark | relogoprlem 26714 |
| [Cohen] p. 301 | Property 2 | relogmul 26715 relogmuld 26748 |
| [Cohen] p. 301 | Property 3 | relogdiv 26716 relogdivd 26749 |
| [Cohen] p. 301 | Property 4 | relogexp 26719 |
| [Cohen] p. 301 | Property 1a | log1 26708 |
| [Cohen] p. 301 | Property 1b | loge 26709 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26910 |
| [Cohen4] p. 349 | Property | relogbf 26914 |
| [Cohen4] p. 352 | Definition | elogb 26893 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26900 |
| [Cohen4] p. 361 | Property 3 | logbrec 26905 relogbdiv 26902 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26898 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26903 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26891 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26892 |
| [Cohen4] p. 367 | Property | logbchbase 26894 |
| [Cohen4] p. 377 | Property 2 | logblt 26907 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34592 sxbrsigalem4 34594 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18603 acsinfd 18602 acsinfdimd 18604 acsmap2d 18601 acsmapd 18600 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34597 |
| [Connell] p. 57 | Definition | df-scmat 22609 df-scmatalt 49030 |
| [Conway] p. 4 | Definition | lesrec 27950 lesrecd 27951 |
| [Conway] p. 5 | Definition | addsval 28113 addsval2 28114 df-adds 28111 df-muls 28258 df-negs 28172 |
| [Conway] p. 7 | Theorem | 0lt1s 27963 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28613 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28012 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28011 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27889 |
| [Conway] p. 17 | Theorem 3 | addsass 28156 addsassd 28157 addscom 28117 addscomd 28118 addsrid 28115 addsridd 28116 |
| [Conway] p. 17 | Definition | df-0s 27958 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28195 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28192 negsidd 28193 |
| [Conway] p. 18 | Theorem 5 | leadds1 28140 leadds1d 28146 |
| [Conway] p. 18 | Definition | df-1s 27959 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28187 negscld 28188 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28131 |
| [Conway] p. 19 | Note | mulsunif2 28321 |
| [Conway] p. 19 | Theorem 7 | addsdi 28306 addsdid 28307 addsdird 28308 mulnegs1d 28311 mulnegs2d 28312 mulsass 28317 mulsassd 28318 mulscom 28290 mulscomd 28291 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28285 mulscld 28286 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28289 ltmuls 28287 ltmulsd 28288 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28295 mulsgt0d 28296 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28369 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27955 |
| [Conway] p. 24 | Definition | df-reno 28641 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28650 remulscl 28653 renegscl 28649 |
| [Conway] p. 27 | Definition | df-ons 28403 elons2 28409 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28413 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28415 onswe 28423 |
| [Conway] p. 29 | Remark | madebday 28051 newbday 28053 oldbday 28052 |
| [Conway] p. 29 | Definition | df-made 27978 df-new 27980 df-old 27979 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13885 |
| [Crawley] p. 1 | Definition of poset | df-poset 18359 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40022 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40826 dalaw 40522 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42597 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40626 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40742 df-ldil 40740 isldil 40746 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40741 df-trnN 40743 isltrn 40755 ltrnu 40757 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40427 cdlema2N 40428 exatleN 40040 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40112 cdlemb 40430 cdlemb2 40677 cdlemb3 41242 idltrn 40786 l1cvat 39691 lhpat 40679 lhpat2 40681 lshpat 39692 ltrnel 40775 ltrnmw 40787 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40827 cdlemc2 40828 ltrnnidn 40810 trlat 40805 trljat1 40802 trljat2 40803 trljat3 40804 trlne 40821 trlnidat 40809 trlnle 40822 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40627 |
| [Crawley] p. 113 | Lemma C | cdlemc 40833 cdlemc3 40829 cdlemc4 40830 |
| [Crawley] p. 113 | Lemma D | cdlemd 40843 cdlemd1 40834 cdlemd2 40835 cdlemd3 40836 cdlemd4 40837 cdlemd5 40838 cdlemd6 40839 cdlemd7 40840 cdlemd8 40841 cdlemd9 40842 cdleme31sde 41021 cdleme31se 41018 cdleme31se2 41019 cdleme31snd 41022 cdleme32a 41077 cdleme32b 41078 cdleme32c 41079 cdleme32d 41080 cdleme32e 41081 cdleme32f 41082 cdleme32fva 41073 cdleme32fva1 41074 cdleme32fvcl 41076 cdleme32le 41083 cdleme48fv 41135 cdleme4gfv 41143 cdleme50eq 41177 cdleme50f 41178 cdleme50f1 41179 cdleme50f1o 41182 cdleme50laut 41183 cdleme50ldil 41184 cdleme50lebi 41176 cdleme50rn 41181 cdleme50rnlem 41180 cdlemeg49le 41147 cdlemeg49lebilem 41175 |
| [Crawley] p. 113 | Lemma E | cdleme 41196 cdleme00a 40845 cdleme01N 40857 cdleme02N 40858 cdleme0a 40847 cdleme0aa 40846 cdleme0b 40848 cdleme0c 40849 cdleme0cp 40850 cdleme0cq 40851 cdleme0dN 40852 cdleme0e 40853 cdleme0ex1N 40859 cdleme0ex2N 40860 cdleme0fN 40854 cdleme0gN 40855 cdleme0moN 40861 cdleme1 40863 cdleme10 40890 cdleme10tN 40894 cdleme11 40906 cdleme11a 40896 cdleme11c 40897 cdleme11dN 40898 cdleme11e 40899 cdleme11fN 40900 cdleme11g 40901 cdleme11h 40902 cdleme11j 40903 cdleme11k 40904 cdleme11l 40905 cdleme12 40907 cdleme13 40908 cdleme14 40909 cdleme15 40914 cdleme15a 40910 cdleme15b 40911 cdleme15c 40912 cdleme15d 40913 cdleme16 40921 cdleme16aN 40895 cdleme16b 40915 cdleme16c 40916 cdleme16d 40917 cdleme16e 40918 cdleme16f 40919 cdleme16g 40920 cdleme19a 40939 cdleme19b 40940 cdleme19c 40941 cdleme19d 40942 cdleme19e 40943 cdleme19f 40944 cdleme1b 40862 cdleme2 40864 cdleme20aN 40945 cdleme20bN 40946 cdleme20c 40947 cdleme20d 40948 cdleme20e 40949 cdleme20f 40950 cdleme20g 40951 cdleme20h 40952 cdleme20i 40953 cdleme20j 40954 cdleme20k 40955 cdleme20l 40958 cdleme20l1 40956 cdleme20l2 40957 cdleme20m 40959 cdleme20y 40938 cdleme20zN 40937 cdleme21 40973 cdleme21d 40966 cdleme21e 40967 cdleme22a 40976 cdleme22aa 40975 cdleme22b 40977 cdleme22cN 40978 cdleme22d 40979 cdleme22e 40980 cdleme22eALTN 40981 cdleme22f 40982 cdleme22f2 40983 cdleme22g 40984 cdleme23a 40985 cdleme23b 40986 cdleme23c 40987 cdleme26e 40995 cdleme26eALTN 40997 cdleme26ee 40996 cdleme26f 40999 cdleme26f2 41001 cdleme26f2ALTN 41000 cdleme26fALTN 40998 cdleme27N 41005 cdleme27a 41003 cdleme27cl 41002 cdleme28c 41008 cdleme3 40873 cdleme30a 41014 cdleme31fv 41026 cdleme31fv1 41027 cdleme31fv1s 41028 cdleme31fv2 41029 cdleme31id 41030 cdleme31sc 41020 cdleme31sdnN 41023 cdleme31sn 41016 cdleme31sn1 41017 cdleme31sn1c 41024 cdleme31sn2 41025 cdleme31so 41015 cdleme35a 41084 cdleme35b 41086 cdleme35c 41087 cdleme35d 41088 cdleme35e 41089 cdleme35f 41090 cdleme35fnpq 41085 cdleme35g 41091 cdleme35h 41092 cdleme35h2 41093 cdleme35sn2aw 41094 cdleme35sn3a 41095 cdleme36a 41096 cdleme36m 41097 cdleme37m 41098 cdleme38m 41099 cdleme38n 41100 cdleme39a 41101 cdleme39n 41102 cdleme3b 40865 cdleme3c 40866 cdleme3d 40867 cdleme3e 40868 cdleme3fN 40869 cdleme3fa 40872 cdleme3g 40870 cdleme3h 40871 cdleme4 40874 cdleme40m 41103 cdleme40n 41104 cdleme40v 41105 cdleme40w 41106 cdleme41fva11 41113 cdleme41sn3aw 41110 cdleme41sn4aw 41111 cdleme41snaw 41112 cdleme42a 41107 cdleme42b 41114 cdleme42c 41108 cdleme42d 41109 cdleme42e 41115 cdleme42f 41116 cdleme42g 41117 cdleme42h 41118 cdleme42i 41119 cdleme42k 41120 cdleme42ke 41121 cdleme42keg 41122 cdleme42mN 41123 cdleme42mgN 41124 cdleme43aN 41125 cdleme43bN 41126 cdleme43cN 41127 cdleme43dN 41128 cdleme5 40876 cdleme50ex 41195 cdleme50ltrn 41193 cdleme51finvN 41192 cdleme51finvfvN 41191 cdleme51finvtrN 41194 cdleme6 40877 cdleme7 40885 cdleme7a 40879 cdleme7aa 40878 cdleme7b 40880 cdleme7c 40881 cdleme7d 40882 cdleme7e 40883 cdleme7ga 40884 cdleme8 40886 cdleme8tN 40891 cdleme9 40889 cdleme9a 40887 cdleme9b 40888 cdleme9tN 40893 cdleme9taN 40892 cdlemeda 40934 cdlemedb 40933 cdlemednpq 40935 cdlemednuN 40936 cdlemefr27cl 41039 cdlemefr32fva1 41046 cdlemefr32fvaN 41045 cdlemefrs32fva 41036 cdlemefrs32fva1 41037 cdlemefs27cl 41049 cdlemefs32fva1 41059 cdlemefs32fvaN 41058 cdlemesner 40932 cdlemeulpq 40856 |
| [Crawley] p. 114 | Lemma E | 4atex 40712 4atexlem7 40711 cdleme0nex 40926 cdleme17a 40922 cdleme17c 40924 cdleme17d 41134 cdleme17d1 40925 cdleme17d2 41131 cdleme18a 40927 cdleme18b 40928 cdleme18c 40929 cdleme18d 40931 cdleme4a 40875 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40961 cdleme21at 40964 cdleme21b 40962 cdleme21c 40963 cdleme21ct 40965 cdleme21f 40968 cdleme21g 40969 cdleme21h 40970 cdleme21i 40971 cdleme22gb 40930 |
| [Crawley] p. 116 | Lemma F | cdlemf 41199 cdlemf1 41197 cdlemf2 41198 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41203 cdlemg16 41293 cdlemg28 41340 cdlemg28a 41329 cdlemg28b 41339 cdlemg3a 41233 cdlemg42 41365 cdlemg43 41366 cdlemg44 41369 cdlemg44a 41367 cdlemg46 41371 cdlemg47 41372 cdlemg9 41270 ltrnco 41355 ltrncom 41374 tgrpabl 41387 trlco 41363 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41379 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41313 cdlemg17b 41298 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41392 df-edring 41393 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41396 |
| [Crawley] p. 118 | Remark | tendopltp 41416 |
| [Crawley] p. 118 | Lemma H | cdlemh 41453 cdlemh1 41451 cdlemh2 41452 |
| [Crawley] p. 118 | Lemma I | cdlemi 41456 cdlemi1 41454 cdlemi2 41455 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41457 cdlemj2 41458 cdlemj3 41459 tendocan 41460 |
| [Crawley] p. 118 | Lemma K | cdlemk 41610 cdlemk1 41467 cdlemk10 41479 cdlemk11 41485 cdlemk11t 41582 cdlemk11ta 41565 cdlemk11tb 41567 cdlemk11tc 41581 cdlemk11u-2N 41525 cdlemk11u 41507 cdlemk12 41486 cdlemk12u-2N 41526 cdlemk12u 41508 cdlemk13-2N 41512 cdlemk13 41488 cdlemk14-2N 41514 cdlemk14 41490 cdlemk15-2N 41515 cdlemk15 41491 cdlemk16-2N 41516 cdlemk16 41493 cdlemk16a 41492 cdlemk17-2N 41517 cdlemk17 41494 cdlemk18-2N 41522 cdlemk18-3N 41536 cdlemk18 41504 cdlemk19-2N 41523 cdlemk19 41505 cdlemk19u 41606 cdlemk1u 41495 cdlemk2 41468 cdlemk20-2N 41528 cdlemk20 41510 cdlemk21-2N 41527 cdlemk21N 41509 cdlemk22-3 41537 cdlemk22 41529 cdlemk23-3 41538 cdlemk24-3 41539 cdlemk25-3 41540 cdlemk26-3 41542 cdlemk26b-3 41541 cdlemk27-3 41543 cdlemk28-3 41544 cdlemk29-3 41547 cdlemk3 41469 cdlemk30 41530 cdlemk31 41532 cdlemk32 41533 cdlemk33N 41545 cdlemk34 41546 cdlemk35 41548 cdlemk36 41549 cdlemk37 41550 cdlemk38 41551 cdlemk39 41552 cdlemk39u 41604 cdlemk4 41470 cdlemk41 41556 cdlemk42 41577 cdlemk42yN 41580 cdlemk43N 41599 cdlemk45 41583 cdlemk46 41584 cdlemk47 41585 cdlemk48 41586 cdlemk49 41587 cdlemk5 41472 cdlemk50 41588 cdlemk51 41589 cdlemk52 41590 cdlemk53 41593 cdlemk54 41594 cdlemk55 41597 cdlemk55u 41602 cdlemk56 41607 cdlemk5a 41471 cdlemk5auN 41496 cdlemk5u 41497 cdlemk6 41473 cdlemk6u 41498 cdlemk7 41484 cdlemk7u-2N 41524 cdlemk7u 41506 cdlemk8 41474 cdlemk9 41475 cdlemk9bN 41476 cdlemki 41477 cdlemkid 41572 cdlemkj-2N 41518 cdlemkj 41499 cdlemksat 41482 cdlemksel 41481 cdlemksv 41480 cdlemksv2 41483 cdlemkuat 41502 cdlemkuel-2N 41520 cdlemkuel-3 41534 cdlemkuel 41501 cdlemkuv-2N 41519 cdlemkuv2-2 41521 cdlemkuv2-3N 41535 cdlemkuv2 41503 cdlemkuvN 41500 cdlemkvcl 41478 cdlemky 41562 cdlemkyyN 41598 tendoex 41611 |
| [Crawley] p. 120 | Remark | dva1dim 41621 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41612 cdleml2N 41613 cdleml3N 41614 cdleml4N 41615 cdleml5N 41616 cdleml6 41617 cdleml7 41618 cdleml8 41619 cdleml9 41620 dia1dim 41697 |
| [Crawley] p. 120 | Lemma M | dia11N 41684 diaf11N 41685 dialss 41682 diaord 41683 dibf11N 41797 djajN 41773 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41668 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41754 dia2dimlem1 41700 dia2dimlem2 41701 dia2dimlem3 41702 dia2dimlem4 41703 dia2dimlem5 41704 diaf1oN 41766 diarnN 41765 dvheveccl 41748 dvhopN 41752 |
| [Crawley] p. 121 | Lemma N | cdlemn 41848 cdlemn10 41842 cdlemn11 41847 cdlemn11a 41843 cdlemn11b 41844 cdlemn11c 41845 cdlemn11pre 41846 cdlemn2 41831 cdlemn2a 41832 cdlemn3 41833 cdlemn4 41834 cdlemn4a 41835 cdlemn5 41837 cdlemn5pre 41836 cdlemn6 41838 cdlemn7 41839 cdlemn8 41840 cdlemn9 41841 diclspsn 41830 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41809 |
| [Crawley] p. 122 | Lemma N | dih11 41901 dihf11 41903 dihjust 41853 dihjustlem 41852 dihord 41900 dihord1 41854 dihord10 41859 dihord11b 41858 dihord11c 41860 dihord2 41863 dihord2a 41855 dihord2b 41856 dihord2cN 41857 dihord2pre 41861 dihord2pre2 41862 dihordlem6 41849 dihordlem7 41850 dihordlem7b 41851 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41866 dihfval 41867 dihval 41868 |
| [Diestel] p. 3 | Definition | df-gric 48501 df-grim 48498 isuspgrim 48516 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29671 df-nbgr 29592 |
| [Diestel] p. 3 | Definition by | df-grisom 48497 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48481 df-subgr 29527 uhgrspan1 29562 uhgrspansubgr 29550 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29813 vtxdgoddnumeven 29812 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29318 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34171 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34183 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34175 zarcls1 34176 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34186 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34189 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34192 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3910 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9604 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8814 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9612 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9954 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10527 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5260 |
| [Enderton] p. 19 | Definition | df-tp 4590 |
| [Enderton] p. 26 | Exercise 5 | unissb 4902 |
| [Enderton] p. 26 | Exercise 10 | pwel 5343 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5545 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5041 iinin2 5040 iinun2 5033 iunin1 5032 iunin1f 32812 iunin2 5031 uniin1 5035 uniin2 5036 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5039 iundif2 5034 |
| [Enderton] p. 32 | Exercise 20 | unineq 4243 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5060 |
| [Enderton] p. 33 | Exercise 25 | iununi 5061 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5068 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7758 iunpwss 5069 |
| [Enderton] p. 36 | Definition | opthwiener 5488 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5422 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4907 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5443 rnex 7895 rnexg 7887 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5895 rnuni 6137 |
| [Enderton] p. 42 | Definition of a function | dffun7 6552 dffun8 6553 |
| [Enderton] p. 43 | Definition of function value | funfv2 6959 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6594 |
| [Enderton] p. 44 | Definition (d) | dfima2 6055 dfima3 6056 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6968 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10445 ac7g 10446 df-ac 10088 dfac2 10103 dfac2a 10101 dfac2b 10102 dfac3 10093 dfac7 10104 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7234 |
| [Enderton] p. 52 | Definition | df-map 8814 |
| [Enderton] p. 53 | Exercise 21 | coass 6257 |
| [Enderton] p. 53 | Exercise 27 | dmco 6246 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6601 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6095 |
| [Enderton] p. 54 | Remark | ixpf 8906 ixpssmap 8918 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8884 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10455 ac9s 10465 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39205 erref 8703 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39208 erthi 8739 |
| [Enderton] p. 57 | Definition | df-ec 8684 |
| [Enderton] p. 58 | Definition | df-qs 8688 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8684 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5891 |
| [Enderton] p. 68 | Definition of successor | df-suc 6356 |
| [Enderton] p. 71 | Definition | df-tr 5213 dftr4 5218 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6431 unisucg 6430 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6431 unisucg 6430 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5228 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5230 trintALT 45454 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8578 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8580 onasuc 8501 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7403 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8579 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8581 onmsuc 8502 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8596 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8583 nnacom 8591 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8597 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8598 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8600 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8584 nnmsucr 8599 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8612 |
| [Enderton] p. 129 | Definition | df-en 8932 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7354 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9987 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16259 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9179 |
| [Enderton] p. 135 | Corollary 6C | php3 9181 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9178 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9210 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9212 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9141 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9145 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9117 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10151 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10152 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10147 dju1en 10143 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9288 unifi 9289 unifi2 9290 |
| [Enderton] p. 144 | Corollary 6K | undif2 4434 unfi 9143 unfi2 9258 |
| [Enderton] p. 145 | Figure 38 | ffoss 7931 |
| [Enderton] p. 145 | Definition | df-dom 8933 |
| [Enderton] p. 146 | Example 1 | domen 8946 domeng 8947 |
| [Enderton] p. 146 | Example 3 | nndomo 9190 nnsdom 9611 nnsdomg 9247 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10155 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9118 xpdom1 9052 xpdom1g 9050 xpdom2g 9049 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9124 |
| [Enderton] p. 151 | Theorem 6M | zorn 10479 zorng 10476 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10464 dfac5 10100 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10548 |
| [Enderton] p. 164 | Example | infdif 10179 |
| [Enderton] p. 168 | Definition | df-po 5560 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6465 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6397 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6464 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6405 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7823 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7768 |
| [Enderton] p. 194 | Remark | onprc 7765 |
| [Enderton] p. 194 | Exercise 16 | suc11 6459 |
| [Enderton] p. 197 | Definition | df-card 9913 |
| [Enderton] p. 197 | Theorem 7P | carden 10523 |
| [Enderton] p. 200 | Exercise 25 | tfis 7839 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9736 |
| [Enderton] p. 202 | Definition | df-r1 9724 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9746 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9827 rankval4b 35408 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9563 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9817 rankprb 9811 rankpw 9803 rankpwi 9783 rankuniss 9826 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9575 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9576 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10082 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10048 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10062 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8316 |
| [Enderton] p. 222 | Definition of kard | karden 9869 kardex 9868 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8571 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8573 |
| [Enderton] p. 240 | Exercise 25 | oarec 8535 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10221 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17688 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17630 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18599 mrieqv2d 17685 mrieqvd 17684 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17689 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17694 mreexexlem2d 17691 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18605 mreexfidimd 17696 |
| [Frege1879] p. 11 | Statement | df3or2 44356 |
| [Frege1879] p. 12 | Statement | df3an2 44357 dfxor4 44354 dfxor5 44355 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44378 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44379 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44383 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44387 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44388 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44394 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44396 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44397 axfrege8 44395 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 37951 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44400 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44408 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44402 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44401 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44410 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44411 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44414 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44404 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44409 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44406 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44412 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44416 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44415 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44407 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44413 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44403 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44405 rp-frege25 44393 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44398 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44418 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44399 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44419 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44422 axfrege31 44421 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44420 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44423 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44424 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44425 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44426 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44427 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44428 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44429 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44430 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44431 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44433 axfrege41 44432 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44434 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44435 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44436 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44437 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44438 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44439 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44440 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44441 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44442 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44445 ax-frege52c 44476 frege52aid 44446 frege52b 44477 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44450 ax-frege54c 44480 frege54b 44481 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44443 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3749 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44448 frege53aid 44447 frege53b 44478 frege53c 44502 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2765 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44456 frege55aid 44453 frege55b 44485 frege55c 44506 frege55cor1a 44457 frege55lem2a 44455 frege55lem2b 44484 frege55lem2c 44505 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44459 frege56aid 44458 frege56b 44486 frege56c 44507 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44463 ax-frege58b 44489 frege58bid 44490 frege58c 44509 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44461 frege57aid 44460 frege57b 44487 frege57c 44508 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3760 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44465 frege59b 44492 frege59c 44510 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44466 frege60b 44493 frege60c 44511 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44467 frege61b 44494 frege61c 44512 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44468 frege62b 44495 frege62c 44513 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44469 frege63b 44496 frege63c 44514 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44470 frege64b 44497 frege64c 44515 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44471 frege65b 44498 frege65c 44516 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44472 frege66b 44499 frege66c 44517 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44473 frege67b 44500 frege67c 44518 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44474 frege68b 44501 frege68c 44519 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44520 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44521 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44522 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44523 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44524 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44527 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44525 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44526 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44528 frege77d 44334 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44529 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44530 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44531 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44532 frege81d 44335 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44533 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44534 frege83d 44336 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44535 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44536 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44537 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44538 frege87d 44338 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44539 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44540 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44541 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44542 frege91d 44339 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44543 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44544 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44545 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44546 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44550 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44547 frege96d 44337 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44548 frege97d 44340 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44549 frege98d 44341 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44551 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44552 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44553 frege102d 44342 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44554 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44555 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44556 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44557 frege106d 44343 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44558 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44559 frege108d 44344 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44560 frege109d 44345 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44561 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44562 frege111d 44347 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44563 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44564 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44565 frege114d 44346 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44566 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44567 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44568 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44569 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44570 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44571 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44572 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44573 frege122d 44348 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44574 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44575 frege124d 44349 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44576 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44577 frege126d 44350 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44578 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44579 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44580 frege129d 44351 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44581 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44582 frege131d 44352 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44583 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44584 frege133d 44353 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46885 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47208 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46908 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47023 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47043 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47034 meadjunre 47048 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47035 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47036 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47032 meaiunle 47041 meaiunlelem 47040 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47053 meaiuninc2 47054 meaiuninc3 47057 meaiuninc3v 47056 meaiunincf 47055 meaiuninclem 47052 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47059 meaiininc2 47060 meaiininclem 47058 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47078 caragendifcl 47086 caratheodory 47100 omelesplit 47090 |
| [Fremlin1] p. 19 | Definition 113A | isome 47066 isomennd 47103 isomenndlem 47102 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47088 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47107 voncmpl 47193 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47070 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47095 carageniuncllem1 47093 carageniuncllem2 47094 caragenuncl 47085 caragenuncllem 47084 caragenunicl 47096 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47104 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47098 caratheodorylem2 47099 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47107 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47166 hoidmv1lelem1 47163 hoidmv1lelem2 47164 hoidmv1lelem3 47165 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47210 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47166 hoidmvle 47172 hoidmvlelem1 47167 hoidmvlelem2 47168 hoidmvlelem3 47169 hoidmvlelem4 47170 hoidmvlelem5 47171 hsphoidmvle2 47157 hsphoif 47148 hsphoival 47151 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47120 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47128 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47155 hoidmvn0val 47156 hoidmvval 47149 hoidmvval0 47159 hoidmvval0b 47162 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47160 hsphoidmvle 47158 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47109 df-voln 47111 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47176 ovn0 47138 ovn0lem 47137 ovnf 47135 ovnome 47145 ovnssle 47133 ovnsslelem 47132 ovnsupge0 47129 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47175 ovnhoilem1 47173 ovnhoilem2 47174 vonhoi 47239 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47192 hoidifhspf 47190 hoidifhspval 47180 hoidifhspval2 47187 hoidifhspval3 47191 hspmbl 47201 hspmbllem1 47198 hspmbllem2 47199 hspmbllem3 47200 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47193 vonmea 47146 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47144 ovnsubadd2 47218 ovnsubadd2lem 47217 ovnsubaddlem1 47142 ovnsubaddlem2 47143 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47203 hoimbl2 47237 hoimbllem 47202 hspdifhsp 47188 opnvonmbl 47206 opnvonmbllem2 47205 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47208 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47251 iccvonmbllem 47250 ioovonmbl 47249 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47257 vonicclem2 47256 vonioo 47254 vonioolem2 47253 vonn0icc 47260 vonn0icc2 47264 vonn0ioo 47259 vonn0ioo2 47262 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47261 snvonmbl 47258 vonct 47265 vonsn 47263 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46931 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46930 subsaliuncllem 46929 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47297 salpreimalegt 47281 salpreimaltle 47298 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47300 issmff 47306 issmflem 47299 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47317 issmflelem 47316 smfpreimale 47326 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47328 issmfgtlem 47327 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47268 issmf 47300 issmff 47306 issmfge 47342 issmfgelem 47341 issmfgt 47328 issmfgtlem 47327 issmfle 47317 issmflelem 47316 issmflem 47299 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47279 salpreimagtlt 47302 salpreimalelt 47301 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47342 issmfgelem 47341 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47325 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47323 cnfsmf 47312 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47339 decsmflem 47338 incsmf 47314 incsmflem 47313 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47273 pimconstlt1 47274 smfconst 47321 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47337 smfaddlem1 47335 smfaddlem2 47336 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47368 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47367 smfmullem1 47363 smfmullem2 47364 smfmullem3 47365 smfmullem4 47366 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47369 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47372 smfpimbor1lem2 47371 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47374 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47362 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47361 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47370 smfresal 47360 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47349 smflim2 47378 smflimlem1 47343 smflimlem2 47344 smflimlem3 47345 smflimlem4 47346 smflimlem5 47347 smflimlem6 47348 smflimmpt 47382 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47386 smfsuplem1 47383 smfsuplem2 47384 smfsuplem3 47385 smfsupmpt 47387 smfsupxr 47388 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47390 smfinflem 47389 smfinfmpt 47391 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47349 smflim2 47378 smflimmpt 47382 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47380 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47410 smfdivdmmbl2 47413 smfinfdmmbl 47421 smfinfdmmbllem 47420 smfsupdmmbl 47417 smfsupdmmbllem 47416 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47400 smflimsuplem2 47393 smflimsuplem6 47397 smflimsuplem7 47398 smflimsuplem8 47399 smflimsupmpt 47401 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47403 smfliminflem 47402 smfliminfmpt 47404 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47268 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47414 fsupdm2 47415 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47405 adddmmbl2 47406 finfdm 47418 finfdm2 47419 fsupdm 47414 fsupdm2 47415 muldmmbl 47407 muldmmbl2 47408 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47418 finfdm2 47419 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25656 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25699 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25709 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38209 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38212 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9595 inf1 9579 inf2 9580 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10884 enqer 10894 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10889 df-nq 10885 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10881 df-plq 10887 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7637 df-mpq 10882 df-mq 10888 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10890 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10948 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10949 ltbtwnnq 10951 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10944 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10945 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10952 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10954 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10966 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10968 |
| [Gleason] p. 122 | Definition | df-1p 10955 |
| [Gleason] p. 122 | Remark (1) | prub 10967 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11006 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10958 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11005 psslinpr 11004 supexpr 11027 suplem1pr 11025 suplem2pr 11026 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10991 addclprlem1 10989 addclprlem2 10990 df-plp 10956 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10995 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10994 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11007 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11016 ltexprlem1 11009 ltexprlem2 11010 ltexprlem3 11011 ltexprlem4 11012 ltexprlem5 11013 ltexprlem6 11014 ltexprlem7 11015 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11018 ltaprlem 11017 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11019 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11020 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10957 mulclpr 10993 mulclprlem 10992 reclem2pr 11021 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11002 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10997 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10996 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11001 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11024 reclem3pr 11022 reclem4pr 11023 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11028 enrer 11036 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11033 df-1r 11034 df-nr 11029 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11031 df-plr 11030 negexsr 11075 recexsr 11080 recexsrlem 11076 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11032 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12204 creur 12203 cru 12201 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11161 axcnre 11137 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15156 crimd 15273 crimi 15234 crre 15155 crred 15272 crrei 15233 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15158 remimd 15239 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15325 absval2d 15489 absval2i 15439 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15182 cjaddd 15261 cjaddi 15229 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15183 cjmuld 15262 cjmuli 15230 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15181 cjcjd 15240 cjcji 15212 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15180 cjreb 15164 cjrebd 15243 cjrebi 15215 cjred 15267 rere 15163 rereb 15161 rerebd 15242 rerebi 15214 rered 15265 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15189 addcjd 15253 addcji 15224 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15279 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15320 abscjd 15494 abscji 15443 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15330 abs00d 15490 abs00i 15440 absne0d 15491 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15363 releabsd 15495 releabsi 15444 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15335 absmuld 15498 absmuli 15446 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15323 sqabsaddi 15447 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15372 abstrid 15500 abstrii 15450 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14089 exp0 14092 expp1 14095 expp1d 14174 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26802 cxpaddd 26840 expadd 14131 expaddd 14175 expaddz 14133 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26811 cxpmuld 26860 expmul 14134 expmuld 14176 expmulz 14135 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26808 mulcxpd 26851 mulexp 14128 mulexpd 14188 mulexpz 14129 |
| [Gleason] p. 140 | Exercise 1 | znnen 16258 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13528 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15673 rlimadd 15684 rlimdiv 15687 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15675 rlimsub 15685 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15674 rlimmul 15686 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15678 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15624 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15645 climcj 15646 climim 15648 climre 15647 rlimabs 15650 rlimcj 15651 rlimim 15653 rlimre 15652 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11236 df-xr 11235 ltxr 13131 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15512 limsupval 15515 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15711 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15720 caucvgb 15721 caucvgbf 46061 caucvgr 15717 climcau 15712 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15858 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15927 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15377 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13852 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21476 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24461 xmet0 24460 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24477 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24468 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24470 mstri 24587 xmettri 24469 xmstri 24586 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24500 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23766 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25430 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24658 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24984 addcn2 15635 mulcn 24986 mulcn2 15637 subcn 24985 subcn2 15636 |
| [Gleason] p. 295 | Remark | bcval3 14333 bcval4 14334 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14348 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14331 df-bc 14330 |
| [Gleason] p. 296 | Remark | bcn0 14337 bcnn 14339 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15874 |
| [Gleason] p. 308 | Equation 2 | ef0 16135 |
| [Gleason] p. 308 | Equation 3 | efcj 16136 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16142 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16147 |
| [Gleason] p. 310 | Equation 14 | sinadd 16210 |
| [Gleason] p. 310 | Equation 15 | cosadd 16211 |
| [Gleason] p. 311 | Equation 17 | sincossq 16222 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16227 sinbnd 16226 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14243 sqeqori 14241 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16116 |
| [Godowski] p. 730 | Equation SF | goeqi 32534 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31929 |
| [Golan] p. 1 | Remark | srgisid 20282 |
| [Golan] p. 1 | Definition | df-srg 20260 |
| [Golan] p. 149 | Definition | df-slmd 33434 |
| [Gonshor] p. 7 | Definition | df-cuts 27911 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27950 lesrecd 27951 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28071 cofcut1d 28072 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28073 cofcut2d 28074 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28075 cofcutr1d 28076 cofcutr2d 28077 |
| [Gonshor] p. 13 | Definition | df-adds 28111 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28127 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28153 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28281 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28301 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28609 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28611 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28610 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28646 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28169 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36522 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17628 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17630 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48808 df-cllaw 48806 df-comlaw 48807 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48820 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48841 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39379 dfmembpart2 39384 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32326 riesz2 32327 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32202 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32434 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32446 elpjidm 32445 pjnmopi 32409 |
| [Halmos] p. 44 | Remark | pjinormi 31948 pjinormii 31937 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32450 pjrn 31968 pjrni 31963 pjvec 31957 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31988 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32415 hmopidmpji 32413 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32452 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32441 pjocvec 31958 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32430 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32433 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32436 pjssdif2i 32435 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32116 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1818 |
| [Hatcher] p. 25 | Definition | df-phtpc 25112 df-phtpy 25091 |
| [Hatcher] p. 26 | Definition | df-pco 25125 df-pi1 25128 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25115 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25170 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22608 df-dmatalt 49029 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48437 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48422 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48434 bgoldbtbnd 48429 bgoldbtbnd 48429 tgblthelfgott 48435 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34946 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34947 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34961 hgt750lemb 34960 hgt750leme 34962 hgt750lemf 34957 hgt750lemg 34958 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48431 tgoldbachgt 34967 tgoldbachgtALTV 48432 tgoldbachgtd 34966 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34948 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30754 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19001 grpoideu 30770 mndideu 18793 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19031 grpoinveu 30780 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19062 grpo2inv 30792 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19075 grpoinvop 30794 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19097 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1791 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1792 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1794 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32681 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32694 cdj3i 32702 cdj3lem1 32695 cdjreui 32693 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32692 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42597 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42527 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42549 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42550 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42547 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42553 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42472 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42567 |
| [Holland95] p. 204 | Definition of involution | df-srng 20912 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40139 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42164 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42117 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40569 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42013 poml4N 40589 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42104 pexmidALTN 40614 pexmidN 40605 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42169 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39760 ldualset 39761 |
| [Holland95] p. 222 | Item 1 | df-lines 40137 df-pointsN 40138 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40539 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40583 omllaw4 39882 pol1N 40546 polcon3N 40553 |
| [Holland95] p. 223 | Definition | df-psubclN 40571 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40542 |
| [Holmes] p. 40 | Definition | df-xrn 38891 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31345 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32443 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32224 eigre 32096 eigrei 32095 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32225 eigorth 32099 eigorthi 32098 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32097 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30569 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30565 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30566 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30567 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30585 frgrregorufr0 30584 frgrregorufrg 30586 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30592 frrusgrord 30601 frrusgrord0 30600 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30348 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30575 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30578 frgrwopreg2 30579 frgrwopregasn 30576 frgrwopregbsn 30577 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30581 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30595 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30598 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30346 numclwlk1 30631 numclwlk1lem1 30629 numclwlk1lem2 30630 numclwwlk1 30621 numclwwlk8 30652 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30572 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30029 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30607 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30633 numclwwlkovh0 30632 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30641 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30238 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30645 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30648 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30651 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30663 natded 30663 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30663 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30663 natded 30663 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30663 |
| [Jech] p. 4 | Definition of class | cv 1562 cvjust 2759 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10552 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10550 alephmul 10551 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10549 infmap2 10188 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9774 |
| [Jech] p. 72 | Equation 9.3 | scott0 9848 scottex 9847 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9827 rankval4b 35408 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9865 |
| [Jech] p. 78 | Note | opthprc 5716 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43504 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43592 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43593 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43516 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43520 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43521 rmyp1 43522 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43523 rmym1 43524 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43514 rmx1 43515 rmxluc 43525 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43518 rmy1 43519 rmyluc 43526 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43528 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43529 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43549 jm2.17b 43550 jm2.17c 43551 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43582 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43586 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43577 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43552 jm2.24nn 43548 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43591 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43597 rmygeid 43553 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43609 |
| [Juillerat] p. 11 | Section *5 | etransc 46855 etransclem47 46853 etransclem48 46854 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46850 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46852 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46838 |
| [Juillerat] p. 13 | Proof | etransclem35 46841 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46844 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46830 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46847 |
| [Juillerat] p. 14 | Proof | etransclem23 46829 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1990 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2035 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2040 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2030 cbvaliw 2029 wl-cbvmotv 38028 wl-motae 38030 wl-moteq 38029 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2009 spimw 1993 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2056 spw 2057 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31777 chabs1i 31779 chabs2 31778 chabs2i 31780 chjass 31794 chjassi 31747 latabs1 18521 latabs2 18522 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32599 ela 32600 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32544 cvrval2 39910 |
| [Kalmbach] p. 16 | Definition | df-ol 39814 df-oml 39815 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31845 cmbri 31851 cmtvalN 39847 df-cm 31844 df-cmtN 39813 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39883 pjoml5 31874 pjoml5i 31849 |
| [Kalmbach] p. 22 | Definition | pjoml2 31872 pjoml2i 31846 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31875 cmcmi 31853 cmcmii 31858 cmtcomN 39885 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39881 omlsi 31665 pjoml 31697 pjomli 31696 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39880 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31857 cmcm3 31876 cmcm3i 31855 cmcm3ii 31860 cmcm4i 31856 cmt3N 39887 cmt4N 39888 cmtbr2N 39889 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31869 cmbr3i 31861 cmtbr3N 39890 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31879 fh1i 31882 fh2 31880 fh2i 31883 omlfh1N 39894 |
| [Kalmbach] p. 65 | Remark | chjatom 32618 chslej 31759 chsleji 31719 shslej 31641 shsleji 31631 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31756 chocini 31715 chsupcl 31601 chsupval2 31671 h0elch 31516 helch 31504 hsupval2 31670 ocin 31557 ococss 31554 shococss 31555 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31573 |
| [Kalmbach] p. 66 | Remark | df-pjh 31656 pjssmi 32426 pjssmii 31942 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31906 osumi 31903 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32461 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32661 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32571 |
| [Kalmbach] p. 140 | Remark | hatomic 32621 hatomici 32620 hatomistici 32623 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39955 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32642 lsatexch 39679 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32616 cvlcvr1 39975 cvr1 40046 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32635 cvexchi 32630 cvrexch 40056 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32625 hlrelat 40038 hlrelat5N 40037 lrelat 39650 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21234 lsmsatcv 39646 spansncv 31914 spansncvi 31913 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39665 spansncv2 32554 |
| [Kalmbach] p. 266 | Definition | df-st 32472 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32110 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10619 fpwwe2 10616 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10620 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10627 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10622 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10624 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10637 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10641 gchxpidm 10642 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10653 gchhar 10652 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10186 unxpwdom 9539 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10643 |
| [Kreyszig] p. 3 | Property M1 | metcl 24450 xmetcl 24449 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24457 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24690 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11923 muleqadd 11846 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24556 |
| [Kreyszig] p. 19 | Remark | mopntopon 24557 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24616 mopnm 24562 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24614 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24619 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24660 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23376 lmmbr 25378 lmmbr2 25379 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23498 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25433 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25396 iscmet2 25414 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25436 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23579 metelcls 25425 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25426 metcld2 25427 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25219 lmodvneg1 20995 nvinv 30900 vcm 30837 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25215 lmod0vs 20985 slmd0vs 33457 vc0 30835 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20986 slmdvs0 33458 vcz 30836 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30952 ngpmet 24721 nrmmetd 24692 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30947 imsdval2 30948 ncvspds 25281 ngpds 24722 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24707 nvnd 30949 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24736 nmge0 24735 nvge0 30934 nvz 30930 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24742 nvabs 30933 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31062 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31006 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31068 blocni 31066 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31067 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25324 ipeq0 21748 ipz 30980 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25336 pythi 31111 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31115 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25358 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15900 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25556 minveco 31145 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31011 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25449 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31134 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32384 leopg 32383 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32402 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31179 |
| [Kulpa] p. 547 | Theorem | poimir 38164 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38163 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38162 |
| [Kulpa] p. 548 | Theorem | broucube 38165 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38157 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38158 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2417 axnul 5260 |
| [Kunen] p. 11 | Axiom 3 | axnul 5260 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5244 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8823 mapvalg 8821 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10494 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7925 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9724 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9766 r1elssi 9765 |
| [Kunen] p. 107 | Exercise 4 | rankop 9818 rankopb 9812 rankuni 9823 rankxplim 9839 rankxpsuc 9842 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45528 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45536 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45535 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45537 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45542 rexabso 45543 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45549 n0abso 45550 ssabso 45548 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45551 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45561 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45556 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45559 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45560 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45555 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45567 wfaxpr 45572 wfaxreg 45574 wfaxrep 45568 wfaxsep 45569 wfaxun 45573 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45558 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45571 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45567 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45566 omelaxinf2 45563 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45576 wfaxinf2 45575 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45589 permaxext 45579 permaxinf2 45587 permaxnul 45582 permaxpow 45583 permaxpr 45584 permaxrep 45580 permaxsep 45581 permaxun 45585 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45577 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45588 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4965 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33972 |
| [Lang] p. | Definition | df-rn 5663 |
| [Lang] p. 3 | Statement | lidrideqd 18717 mndbn0 18798 |
| [Lang] p. 3 | Definition | df-mnd 18783 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18735 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18890 |
| [Lang] p. 5 | Equation | gsumreidx 19978 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48802 |
| [Lang] p. 6 | Example | nn0mnd 48799 |
| [Lang] p. 6 | Equation | gsumxp2 20041 |
| [Lang] p. 6 | Statement | cycsubm 19264 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19137 |
| [Lang] p. 6 | Observation | mndlsmidm 19731 |
| [Lang] p. 7 | Definition | dfgrp2e 19020 |
| [Lang] p. 30 | Definition | df-tocyc 33340 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33385 |
| [Lang] p. 32 | Property (b) | cyc3conja 33390 cycpmconjv 33375 |
| [Lang] p. 53 | Definition | df-cat 17714 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18144 cat1lem 18143 |
| [Lang] p. 54 | Definition | df-iso 17796 |
| [Lang] p. 57 | Definition | df-inito 18031 df-termo 18032 |
| [Lang] p. 58 | Example | irinitoringc 21589 |
| [Lang] p. 58 | Statement | initoeu1 18058 termoeu1 18065 |
| [Lang] p. 62 | Definition | df-func 17905 |
| [Lang] p. 65 | Definition | df-nat 17993 |
| [Lang] p. 91 | Note | df-ringc 20722 |
| [Lang] p. 92 | Statement | mxidlprm 33670 |
| [Lang] p. 92 | Definition | isprmidlc 21434 |
| [Lang] p. 128 | Remark | dsmmlmod 21855 |
| [Lang] p. 129 | Proof | lincscm 49061 lincscmcl 49063 lincsum 49060 lincsumcl 49062 |
| [Lang] p. 129 | Statement | lincolss 49065 |
| [Lang] p. 129 | Observation | dsmmfi 21848 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33934 qusdimsum 33935 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33915 |
| [Lang] p. 147 | Definition | snlindsntor 49102 |
| [Lang] p. 504 | Statement | mat1 22565 matring 22561 |
| [Lang] p. 504 | Definition | df-mamu 22509 |
| [Lang] p. 505 | Statement | mamuass 22520 mamutpos 22576 matassa 22562 mattposvs 22573 tposmap 22575 |
| [Lang] p. 513 | Definition | mdet1 22719 mdetf 22713 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22809 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22705 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22729 |
| [Lang] p. 515 | Definition | df-minmar1 22753 smadiadetr 22793 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22728 mdetralt 22726 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22741 |
| [Lang] p. 518 | Definition | df-madu 22752 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22763 madurid 22762 matinv 22795 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23008 |
| [Lang], p. 190 | Chapter 6 | vieta 33887 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34001 finextalg 34005 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33970 fedgmul 33938 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34032 |
| [Lang], p. 561 | Remark | chpmatply1 22950 |
| [Lang], p. 561 | Definition | df-chpmat 22945 |
| [Lang2] p. 3 | Notations | df-ind 12210 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44908 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44903 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44909 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5260 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2744 wl-df.clab 38013 |
| [Levy] p. 59 | Definition | df-ttrcl 9665 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9711 |
| [Levy] p. 338 | Axiom | df-clel 2840 df-cleq 2757 wl-df.cleq 38014 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38017 |
| [Levy] p. 357 | Definition extends to class variables a relation already valid for set variables, and is therefore conservative. This only sketches the conservativity arguement; for details see Appendix | wl-df.clel 38017 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2840 df-cleq 2757 wl-df.cleq 38014 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2744 wl-df.clab 38013 |
| [Levy] p. 358 | Axiom | df-clab 2744 wl-df.clab 38013 |
| [Levy58] p. 2 | Definition I | isfin1-3 10358 |
| [Levy58] p. 2 | Definition II | df-fin2 10258 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10257 |
| [Levy58] p. 2 | Definition III | df-fin3 10260 |
| [Levy58] p. 3 | Definition V | df-fin5 10261 |
| [Levy58] p. 3 | Definition IV | df-fin4 10259 |
| [Levy58] p. 4 | Definition VI | df-fin6 10262 |
| [Levy58] p. 4 | Definition VII | df-fin7 10263 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10387 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27808 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27819 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27851 nosupbnd1 27836 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27853 nosupbnd2 27838 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27857 noetasuplem4 27858 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27854 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1791 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1792 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1794 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32669 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32673 mdsymi 32672 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32667 mdsymlem6 32669 mdsymlem7 32670 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32671 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32574 ssdmd2 32575 ssmd1 32572 ssmd2 32573 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32570 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32542 df-md 32541 mdbr 32555 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32592 mdslj1i 32580 mdslj2i 32581 mdslle1i 32578 mdslle2i 32579 mdslmd1i 32590 mdslmd2i 32591 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32582 mdsl2bi 32584 mdsl2i 32583 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32596 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32593 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32594 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32571 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32576 mdsl3 32577 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32595 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32690 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39957 hlrelat1 40036 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39675 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32597 cvmdi 32585 cvnbtwn4 32550 cvrnbtwn4 39915 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32598 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39976 cvp 32636 cvrp 40052 lcvp 39676 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32660 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32659 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39969 hlexch4N 40028 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32662 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40079 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40385 atpsubN 40389 df-pointsN 40138 pointpsubN 40387 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40140 pmap11 40398 pmaple 40397 pmapsub 40404 pmapval 40393 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40401 pmap1N 40403 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40406 pmapglb2N 40407 pmapglb2xN 40408 pmapglbx 40405 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40488 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40113 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40432 paddclN 40478 paddidm 40477 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40114 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40474 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40113 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40114 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19736 lsmmod2 19737 lssats 39648 shatomici 32619 shatomistici 32622 shmodi 31651 shmodsi 31650 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32561 mdsymlem7 32670 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31850 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31754 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32676 |
| [Margaris] p. 40 | Rule C | exlimiv 1953 |
| [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 401 df-ex 1803 df-or 861 dfbi2 479 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 30660 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45488 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45489 |
| [Margaris] p. 79 | Rule C | exinst01 45199 exinst11 45200 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1999 19.2g 2226 r19.2z 4456 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2240 rr19.3v 3629 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2196 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1849 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1804 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2219 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2243 19.9h 2323 exlimd 2256 exlimdh 2327 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2199 excomim 2200 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2362 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30661 conventions-labels 30661 conventions-labels 30661 conventions-labels 30661 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1850 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44952 albi 1841 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2263 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2264 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44954 exbi 1870 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2267 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44951 2alimdv 1941 alimd 2250 alimdh 1840 alimdv 1939 ax-4 1832 ralimdaa 3266 ralimdv 3179 ralimdva 3177 ralimdvva 3212 sbcimdv 3815 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2245 19.21h 2324 19.21t 2244 19.21vv 44950 alrimd 2253 alrimdd 2252 alrimdh 1886 alrimdv 1952 alrimi 2251 alrimih 1847 alrimiv 1950 alrimivv 1951 bj-alrimdh 37079 hbralrimi 3155 r19.21be 3258 r19.21bi 3257 ralrimd 3270 ralrimdv 3163 ralrimdva 3165 ralrimdvv 3209 ralrimdvva 3220 ralrimi 3263 ralrimia 3264 ralrimiv 3156 ralrimiva 3157 ralrimivv 3206 ralrimivva 3208 ralrimivvva 3211 ralrimivw 3161 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44953 2eximdv 1942 bj-exim 37094 exim 1857 eximd 2254 eximdh 1887 eximdv 1940 rexim 3106 reximd2a 3275 reximdai 3267 reximdd 45724 reximddv 3181 reximddv2 3224 reximddv3 3182 reximdv 3180 reximdv2 3175 reximdva 3178 reximdvai 3176 reximdvva 3213 reximi2 3098 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2249 19.23bi 2229 19.23h 2325 19.23t 2248 exlimdv 1956 exlimdvv 1957 exlimexi 45098 exlimiv 1953 exlimivv 1955 rexlimd3 45720 rexlimdv 3164 rexlimdv3a 3170 rexlimdva 3166 rexlimdva2 3168 rexlimdvaa 3167 rexlimdvv 3221 rexlimdvva 3222 rexlimdvvva 3223 rexlimdvw 3171 rexlimiv 3159 rexlimiva 3158 rexlimivv 3207 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2014 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1903 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1893 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2265 r19.27z 4467 r19.27zv 4468 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2266 19.28vv 44960 r19.28z 4459 r19.28zf 45735 r19.28zv 4463 rr19.28v 3630 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1896 r19.29d2r 3152 r19.29imd 3130 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1904 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2272 19.31vv 44958 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2271 r19.32 47690 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44956 19.33 1907 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2015 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1900 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2268 19.36vv 44957 r19.36zv 4469 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2270 19.37vv 44959 r19.37zv 4464 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1862 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2013 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1910 19.40 1909 r19.40 3131 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2273 19.41rg 45124 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2274 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1905 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2275 r19.44zv 4466 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2276 r19.45zv 4465 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2640 |
| [Mayet] p. 370 | Remark | jpi 32531 largei 32528 stri 32518 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32473 ishst 32475 |
| [Mayet3] p. 10 | Theorem | hstrbi 32527 hstri 32526 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31989 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31990 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32539 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31593 chsupcl 31601 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32621 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32615 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32642 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40619 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18533 latj32 18531 latjass 18529 |
| [Megill] p. 444 | Axiom C5 | ax-5 1933 ax5ALT 39543 |
| [Megill] p. 444 | Section 7 | conventions 30660 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39537 ax-c11n 39524 axc11n 2460 |
| [Megill] p. 446 | Lemma L17 | equtrr 2045 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39532 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39564 hbnae 2466 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2515 sbid 2293 sbidd-misc 50348 sbidd 50347 |
| [Megill] p. 448 | Remark 9.6 | axc14 2497 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39520 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39519 sp 2221 |
| [Megill] p. 448 | Scheme C6' | ax-11 2194 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39521 |
| [Megill] p. 448 | Scheme C8' | ax-7 2031 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39526 |
| [Megill] p. 448 | Scheme C10' | ax-6 1990 ax-c10 39522 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39523 |
| [Megill] p. 448 | Scheme C12' | ax-8 2147 |
| [Megill] p. 448 | Scheme C13' | ax-9 2155 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39527 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39525 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39528 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39540 dral1 2473 dral2-o 39566 dral2 2472 drex1 2475 drex2 2476 drsb1 2529 drsb2 2304 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2209 sbequ 2119 sbid2v 2543 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39533 hba1 2330 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47484 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3835 rspsbca 3836 stdpc4 2101 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39520 ra4 3842 stdpc5 2246 |
| [Mendelson] p. 81 | Rule C | exlimiv 1953 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2051 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2288 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3746 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5488 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4355 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4356 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4232 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4289 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4233 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4097 |
| [Mendelson] p. 231 | Definition of union | dfun3 4231 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5423 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4865 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5543 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4576 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5544 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4892 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5804 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6260 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7762 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6356 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8569 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9116 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9037 xpsneng 9038 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9044 xpcomeng 9045 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9047 |
| [Mendelson] p. 255 | Definition | brsdom 8959 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9040 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8816 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9022 mapsnend 9021 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9122 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9121 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8868 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9025 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9041 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10150 djucomen 10149 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10154 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10148 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8504 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8531 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10531 |
| [Mendelson] p. 281 | Definition | df-r1 9724 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9773 |
| [Mendelson] p. 287 | Axiom system MK | ru 3746 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30519 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30554 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30556 vdgn1frgrv3 30557 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30558 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30551 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30544 2pthfrgrrn 30542 2pthfrgrrn2 30543 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31513 |
| [Monk1] p. 22 | Remark | conventions 30660 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30660 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4193 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5760 ssrelf 32872 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5761 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5168 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6254 coi2 6255 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5901 rn0 5907 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5862 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5670 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5910 rnxp 6160 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5751 xp0 5752 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6070 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6067 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7899 imaexg 7898 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6064 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7060 funfvop 7035 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6925 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6936 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6571 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7242 dff13f 7243 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7207 funrnex 7939 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7235 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6218 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4925 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7991 df-1st 7974 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7992 df-2nd 7975 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9814 ranksnb 9787 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9815 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9816 rankunb 9810 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9798 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9724 r1val2 9797 |
| [Monk1] p. 117 | Lemma | zorn2 10478 zorn2g 10475 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9960 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10533 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9955 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1832 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2031 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2215 ax-c15 39525 ax12v2 2217 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39520 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2194 |
| [Monk2] p. 109 | Lemma 15 | equvini 2489 equvinv 2052 eqvinop 5460 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1933 ax5ALT 39543 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2178 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2194 |
| [Monk2] p. 114 | Lemma 21 | sp 2221 |
| [Monk2] p. 114 | Lemma 22 | axc4 2356 hba1-o 39533 hba1 2330 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2190 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2212 nfra2 3366 nfra2w 3301 |
| [Moore] p. 53 | Part I | df-mre 17628 |
| [Munkres] p. 77 | Example 2 | distop 23113 indistop 23120 indistopon 23119 |
| [Munkres] p. 77 | Example 3 | fctop 23122 fctop2 23123 |
| [Munkres] p. 77 | Example 4 | cctop 23124 |
| [Munkres] p. 78 | Definition of basis | df-bases 23064 isbasis3g 23067 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17486 tgval2 23074 |
| [Munkres] p. 79 | Remark | tgcl 23087 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23081 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23105 tgss3 23104 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23106 basgen2 23107 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37855 topdifinfeq 37856 topdifinffin 37854 topdifinfindis 37852 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23278 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23156 topcld 23153 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23157 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23159 |
| [Munkres] p. 94 | Definition of closure | clsval 23155 |
| [Munkres] p. 94 | Definition of interior | ntrval 23154 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23193 elcls 23191 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23201 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23266 neindisj 23235 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23268 |
| [Munkres] p. 97 | Definition of limit point | islp2 23263 lpval 23257 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23433 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23345 iscn 23353 iscn2 23356 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23398 cncnp2 23399 cncnpi 23396 df-cnp 23346 iscnp 23355 iscnp2 23357 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24661 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25431 |
| [Nathanson] p. 123 | Remark | reprgt 34925 reprinfz1 34926 reprlt 34923 |
| [Nathanson] p. 123 | Definition | df-repr 34913 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34945 |
| [Nathanson] p. 123 | Proposition | breprexp 34937 breprexpnat 34938 itgexpif 34910 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32365 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48430 |
| [Pfenning] p. 17 | Definition XM | natded 30663 |
| [Pfenning] p. 17 | Definition NNC | natded 30663 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 30663 |
| [Pfenning] p. 18 | Rule" | natded 30663 |
| [Pfenning] p. 18 | Definition /\I | natded 30663 |
| [Pfenning] p. 18 | Definition ` `E | natded 30663 natded 30663 natded 30663 natded 30663 natded 30663 |
| [Pfenning] p. 18 | Definition ` `I | natded 30663 natded 30663 natded 30663 natded 30663 natded 30663 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30663 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30663 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30663 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30663 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30663 |
| [Pfenning] p. 127 | Definition =E | natded 30663 |
| [Pfenning] p. 127 | Definition =I | natded 30663 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25322 df-dip 30962 dip0l 30979 ip0l 21746 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25363 ipval 30964 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30975 ipcj 21744 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25325 dipdir 31103 ipdir 21749 ipdiri 31091 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30971 nmsq 25314 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31086 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31088 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31089 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25331 dipass 31106 ipass 21755 ipassi 31102 |
| [Prugovecki] p. 186 | Definition of bra | braval 32205 df-bra 32111 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32112 kbval 32215 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32643 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40524 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32657 atcvat4i 32658 cvrat3 40078 cvrat4 40079 lsatcvat3 39688 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32543 cvrval 39905 df-cv 32540 df-lcv 39655 lspsncv0 21239 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40536 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40537 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2744 rabid 3438 rabidd 45731 wl-df.clab 38013 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2316 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2757 wl-df.cleq 38014 |
| [Quine] p. 19 | Definition 2.9 | conventions 30660 df-v 3459 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2904 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2901 abid2f 2957 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2313 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2121 sbalex 2280 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2840 wl-df.clel 38017 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2765 eqid1 30727 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2772 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3748 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3749 dfsbcq2 3750 |
| [Quine] p. 43 | Theorem 6.8 | vex 3461 |
| [Quine] p. 43 | Theorem 6.9 | isset 3471 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3553 spcgv 3558 spcimgf 3521 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3760 spsbcd 3761 |
| [Quine] p. 44 | Theorem 6.12 | elex 3478 |
| [Quine] p. 44 | Theorem 6.13 | elab 3641 elabg 3638 elabgf 3636 |
| [Quine] p. 44 | Theorem 6.14 | noel 4293 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4679 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4588 df-sn 4586 |
| [Quine] p. 49 | Theorem 7.4 | snss 4746 snssg 4745 |
| [Quine] p. 49 | Theorem 7.5 | prss 4781 prssg 4780 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4724 prid1g 4722 prid2 4725 prid2g 4723 snid 4624 snidg 4622 |
| [Quine] p. 51 | Theorem 7.12 | snex 5401 |
| [Quine] p. 51 | Theorem 7.13 | prex 5400 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4887 unisnALT 45499 unisng 4886 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4891 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4900 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4897 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6495 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47678 dfiota2 6482 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47687 iotaval 6499 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6505 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6501 |
| [Quine] p. 58 | Definition 9.1 | df-op 4592 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5500 opabidw 5499 opelopab 5518 opelopaba 5511 opelopabaf 5520 opelopabf 5521 opelopabg 5514 opelopabga 5508 opelopabgf 5516 oprabid 7432 oprabidw 7431 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5658 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5660 |
| [Quine] p. 64 | Definition 9.15 | df-id 5547 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6590 |
| [Quine] p. 65 | Theorem 10.4 | funi 6557 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6578 funsng 6576 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6527 |
| [Quine] p. 65 | Definition 10.2 | args 6085 dffv4 6868 |
| [Quine] p. 68 | Definition 10.11 | conventions 30660 df-fv 6533 fv2 6866 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14299 nn0opth2i 14298 nn0opthi 14297 omopthi 8635 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8385 |
| [Quine] p. 232 | Equation i | carddom 10526 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6613 funimaexg 6612 |
| [Quine] p. 331 | Axiom system NF | ru 3746 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31345 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30962 polid 31420 polid2i 31418 polidi 31419 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31074 |
| [ReedSimon] p. 195 | Remark | lnophm 32280 lnophmi 32279 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32393 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32395 leopmuli 32394 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32398 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32113 leoppos 32387 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32397 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32386 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48231 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48239 |
| [Roman] p. 4 | Definition | df-dmat 22608 df-dmatalt 49029 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20222 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20308 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49116 |
| [Roman] p. 112 | Note | isldepslvec2 49116 ldepsnlinc 49139 zlmodzxznm 49128 |
| [Roman] p. 112 | Example | zlmodzxzequa 49127 zlmodzxzequap 49130 zlmodzxzldep 49135 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23008 |
| [Rosenlicht] p. 80 | Theorem | heicant 38166 |
| [Rosser] p. 281 | Definition | df-op 4592 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34949 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34950 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48997 pmtr3ncom 19536 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19532 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19475 cayleyth 19476 |
| [Rudin] p. 164 | Equation 27 | efcan 16140 |
| [Rudin] p. 164 | Equation 30 | efzval 16148 |
| [Rudin] p. 167 | Equation 48 | absefi 16242 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1794 |
| [Sanford] p. 39 | Rule 4 | mptxor 1792 |
| [Sanford] p. 40 | Rule 1 | mptnan 1791 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6106 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6109 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6105 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6103 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17628 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17629 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17629 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17631 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10108 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43651 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10418 axdc3 10426 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20310 isrngo 38408 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31803 |
| [Schechter] p. 276 | Definition of span | df-span 31570 spanval 31594 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23111 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6375 onelord 43840 ordelon 6374 ordelord 6372 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43841 sucidg 6433 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6405 onsuc 7797 ord0 6404 ordsuci 7795 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43842 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5216 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43617 elon2 6361 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6356 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5555 epelg 5553 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9550 epirron 43843 ordirr 6368 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43845 oneptr 43844 ontr1 6397 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6393 oneptri 43846 ordtri3or 6382 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8474 ord0eln0 6406 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6419 onsucss 43855 trsucss 6440 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7802 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6446 ordnbtwn 6445 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43857 ordnexbtwnsuc 43856 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10373 onsucf1lem 43858 onsucf1o 43861 onsucf1olem 43859 onsucrn 43860 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43862 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7829 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43851 ordne0gt0 43850 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43853 limnsuc 43854 onsucelab 43852 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9600 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7844 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9603 ordom 7860 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9604 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8614 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7767 ssorduni 7766 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8504 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9607 limom 7866 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8441 df1o2 8448 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8489 oa0suclim 43864 oalim 8505 oasuc 8497 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8490 om0suclim 43865 omlim 8506 omsuc 8499 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8495 oe0m1 8494 oe0suclim 43866 oelim 8507 oesuc 8500 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43818 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43868 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43869 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43870 limexissupab 43872 limiun 43871 limuni 6412 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8511 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8515 om1om1r 43873 om1r 8516 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8508 oaomoecl 43867 oecl 8510 omcl 8509 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43820 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8517 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8518 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43874 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43875 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8585 nnamecl 43876 nnecl 8587 nnmcl 8586 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43877 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8525 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8526 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8533 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43879 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43880 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43882 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8532 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43886 omword1 8546 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43885 oaordnrex 43884 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43881 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43887 omword2 8547 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43888 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43889 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43890 omordi 8539 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8541 omord2com 43891 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43892 df-2o 8442 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43895 oewordi 8565 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43896 oeworde 8567 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43897 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43898 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43894 omnord1ex 43893 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43899 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43901 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43905 oenord1ex 43904 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43906 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8534 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43900 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8552 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8553 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43908 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8571 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43909 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43910 cantnfub2 43911 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43914 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29173 axtgcgrrflx 28689 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29174 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29175 axtgcgrid 28690 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28675 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29186 axtgsegcon 28691 df-trkgcb 28677 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29197 axtg5seg 28692 df-trkgcb 28677 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29198 axtgbtwnid 28693 df-trkgb 28676 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29200 axtgpasch 28694 df-trkgb 28676 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29219 df-trkg2d 34969 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28697 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28698 df-trkg2d 34969 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29222 axtgeucl 28699 df-trkge 28678 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29235 axtgcont 28696 axtgcont1 28695 df-trkgb 28676 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36350 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36352 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36355 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36359 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36360 tgcgrcomimp 28704 tgcgrcoml 28706 tgcgrcomr 28705 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36365 tgcgrtriv 28711 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36369 tg5segofs 34980 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34977 df-ofs 36346 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36371 tgcgrextend 28712 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36373 tgsegconeq 28713 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36385 btwntriv2 36375 tgbtwntriv2 28714 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36376 tgbtwncom 28715 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36379 tgbtwntriv1 28718 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36380 tgbtwnswapid 28719 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36386 btwnintr 36382 tgbtwnexch2 28723 tgbtwnintr 28720 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36388 btwnexch3 36383 tgbtwnexch 28725 tgbtwnexch3 28721 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36387 tgbtwnouttr 28724 tgbtwnouttr2 28722 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29218 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36390 tgbtwndiff 28733 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28726 trisegint 36391 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36407 tgifscgr 28735 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28785 colrot1 28786 colrot2 28787 lncom 28849 lnrot1 28850 lnrot2 28851 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36403 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36408 tgcgrsub 28736 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36418 tgcgrxfr 28745 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28744 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36404 df-cgrg 28738 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28738 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36419 tgbtwnxfr 28757 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36425 colinearperm2 36427 colinearperm3 36426 colinearperm4 36428 colinearperm5 36429 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28760 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36402 tgellng 28780 tglng 28773 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36430 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36438 lnxfr 28793 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36439 lnext 28794 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36443 tgfscgr 28795 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36444 lncgr 28796 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36405 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36446 lnid 28797 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36447 tgidinside 28798 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36464 tgbtwnconn1 28802 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36465 tgbtwnconn2 28803 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36466 tgbtwnconn3 28804 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36472 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36470 legov 28812 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28813 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28826 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36473 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36475 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36477 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36478 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36479 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36476 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36481 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28814 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28816 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28817 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28818 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28819 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36488 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36489 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36484 df-outsideof 36483 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36485 ishlg 28829 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28834 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28836 outsideofrflx 36490 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28830 hlcomd 28831 outsideofcom 36491 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28837 outsideoftr 36492 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28845 outsideofeu 36494 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36501 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36502 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36495 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36510 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36511 tglineelsb2 28859 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36513 linerflx1 36512 linerflx2 36514 tglinecom 28862 tglinerflx1 28860 tglinerflx2 28861 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36516 tglinethru 28863 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36500 tglng 28773 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28821 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36519 tglinethrueu 28866 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36520 tglineineq 28870 tglineinsn 28871 tglineinteq 28873 tglineintmo 28869 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28877 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28878 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28879 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28897 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28893 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28885 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28884 ismir 28890 mirbtwn 28889 mircgr 28888 mirfv 28887 mirval 28886 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28895 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28896 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28897 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28900 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28901 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28906 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28903 mirbtwni 28902 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28904 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28916 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28920 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28917 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28918 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28919 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28922 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28923 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28929 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28925 israg 28928 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28930 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28931 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28933 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28934 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28935 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28936 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28937 ragncol 28940 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28938 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28944 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28948 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28945 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28927 isperp 28943 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28946 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28953 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28961 colperpexlem2 28962 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28964 colperpexlem3 28963 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28969 midex 28968 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28966 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28975 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28970 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28979 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28982 opphllem6 28983 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28985 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28694 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28986 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28994 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28989 hpgbr 28991 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28996 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28995 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28997 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28998 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28999 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29000 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29001 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29014 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29016 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29020 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29004 elplng 29010 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29022 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29023 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29036 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29026 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29040 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29041 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29042 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29043 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29044 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29047 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29049 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29027 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29050 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29053 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29054 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29055 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29056 trgcopyeu 29058 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29082 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29061 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29070 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29068 cgrahl2 29069 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29071 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29072 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29074 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29075 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29078 cgrahl 29079 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29083 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29084 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29085 acopyeu 29086 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29093 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29097 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29090 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29105 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29098 isleag 29099 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29107 tgsas1 29106 tgsas2 29108 tgsas3 29109 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29111 tgasa1 29110 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29112 tgsss2 29113 tgsss3 29114 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29122 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29125 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29126 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27393 dchrsum 27391 dchrsum2 27390 sumdchr 27394 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27395 sum2dchr 27396 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20129 ablfacrp2 20130 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27338 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27339 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27346 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27604 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27607 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27661 vmalogdivsum2 27660 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27651 dirith2 27650 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27649 rpvmasum 27648 rpvmasum2 27634 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27609 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27647 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27614 dchrisumlem1 27611 dchrisumlem2 27612 dchrisumlem3 27613 dchrisumlema 27610 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27617 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27646 dchrmusumlem 27644 dchrvmasumlem 27645 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27616 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27618 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27642 dchrisum0re 27635 dchrisumn0 27643 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27628 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27632 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27633 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27688 pntrsumbnd2 27689 pntrsumo1 27687 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27652 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27654 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27656 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27659 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27664 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27665 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27670 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27672 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27673 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27681 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27682 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27679 selberg3lem2 27680 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27683 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27677 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27690 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27691 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27692 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27706 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27718 pntlemb 27719 pntlemc 27717 pntlemd 27716 pntlemg 27720 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27718 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27710 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27715 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27718 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27731 pntleml 27733 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34050 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34037 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34069 constrinvcl 34080 constrmulcl 34078 constrnegcl 34070 constrsqrtcl 34086 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34056 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34066 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34088 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34098 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4261 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4362 dif0 4334 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4448 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4432 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4252 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4253 |
| [Stoll] p. 20 | Remark | invdif 4234 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4594 |
| [Stoll] p. 43 | Definition | uniiun 5019 |
| [Stoll] p. 44 | Definition | intiin 5020 |
| [Stoll] p. 45 | Definition | df-iin 4955 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4954 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 406 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4261 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44909 |
| [Suppes] p. 22 | Theorem 2 | eq0 4305 eq0f 4302 |
| [Suppes] p. 22 | Theorem 4 | eqss 3954 eqssd 3956 eqssi 3955 |
| [Suppes] p. 23 | Theorem 5 | ss0 4359 ss0b 4358 |
| [Suppes] p. 23 | Theorem 6 | sstr 3947 sstrALT2 45408 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4059 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4061 |
| [Suppes] p. 23 | Theorem 9 | psstr 4064 |
| [Suppes] p. 23 | Theorem 10 | pssss 4054 |
| [Suppes] p. 25 | Theorem 12 | elin 3923 elun 4109 |
| [Suppes] p. 26 | Theorem 15 | inidm 4181 |
| [Suppes] p. 26 | Theorem 16 | in0 4352 |
| [Suppes] p. 27 | Theorem 23 | unidm 4113 |
| [Suppes] p. 27 | Theorem 24 | un0 4351 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4133 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4141 |
| [Suppes] p. 27 | Theorem 27 | unss 4145 |
| [Suppes] p. 27 | Theorem 28 | indir 4241 |
| [Suppes] p. 27 | Theorem 29 | undir 4242 |
| [Suppes] p. 28 | Theorem 32 | difid 4332 |
| [Suppes] p. 29 | Theorem 33 | difin 4227 |
| [Suppes] p. 29 | Theorem 34 | indif 4235 |
| [Suppes] p. 29 | Theorem 35 | undif1 4433 |
| [Suppes] p. 29 | Theorem 36 | difun2 4438 |
| [Suppes] p. 29 | Theorem 37 | difin0 4431 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4429 |
| [Suppes] p. 29 | Theorem 39 | difundi 4245 |
| [Suppes] p. 29 | Theorem 40 | difindi 4247 |
| [Suppes] p. 30 | Theorem 41 | nalset 5269 |
| [Suppes] p. 39 | Theorem 61 | uniss 4876 |
| [Suppes] p. 39 | Theorem 65 | uniop 5489 |
| [Suppes] p. 41 | Theorem 70 | intsn 4945 |
| [Suppes] p. 42 | Theorem 71 | intpr 4943 intprg 4942 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5444 |
| [Suppes] p. 42 | Theorem 78 | intun 4941 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4992 dfiun2g 4990 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4993 |
| [Suppes] p. 47 | Theorem 86 | elpw 4562 elpw2 5295 elpw2g 5294 elpwg 4561 elpwgdedVD 45490 |
| [Suppes] p. 47 | Theorem 87 | pwid 4581 |
| [Suppes] p. 47 | Theorem 89 | pw0 4773 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4774 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5667 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5810 xpindir 5811 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5721 xpundir 5722 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9547 |
| [Suppes] p. 58 | Theorem 2 | relss 5759 |
| [Suppes] p. 59 | Theorem 4 | eldm 5881 eldm2 5882 eldm2g 5880 eldmg 5879 |
| [Suppes] p. 59 | Definition 3 | df-dm 5662 |
| [Suppes] p. 60 | Theorem 6 | dmin 5892 |
| [Suppes] p. 60 | Theorem 8 | rnun 6133 |
| [Suppes] p. 60 | Theorem 9 | rnin 6134 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5869 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5859 brcnvg 5856 |
| [Suppes] p. 62 | Equation 5 | elcnv 5853 elcnv2 5854 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6097 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6132 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6130 |
| [Suppes] p. 63 | Definition | dftrrels2 39170 |
| [Suppes] p. 63 | Theorem 20 | co02 6252 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5956 |
| [Suppes] p. 63 | Definition 7 | df-co 5661 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5866 |
| [Suppes] p. 64 | Theorem 27 | coass 6257 |
| [Suppes] p. 65 | Theorem 31 | resundi 5983 |
| [Suppes] p. 65 | Theorem 34 | elima 6058 elima2 6059 elima3 6060 elimag 6057 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6138 |
| [Suppes] p. 66 | Theorem 40 | dminss 6142 |
| [Suppes] p. 66 | Theorem 41 | imainss 6143 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6146 |
| [Suppes] p. 81 | Definition 34 | dfec2 8685 |
| [Suppes] p. 82 | Theorem 72 | elec 8729 elecALTV 38782 elecg 8727 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39206 erth 8737 erth2 8738 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39209 erdisj 8740 |
| [Suppes] p. 83 | Definition 35, | df-parts 39379 dfmembpart2 39384 |
| [Suppes] p. 89 | Theorem 96 | map0b 8869 |
| [Suppes] p. 89 | Theorem 97 | map0 8873 map0g 8870 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8874 mapsnd 8872 |
| [Suppes] p. 89 | Theorem 99 | mapss 8875 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10040 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10039 |
| [Suppes] p. 92 | Theorem 1 | enref 8970 enrefg 8969 |
| [Suppes] p. 92 | Theorem 2 | ensym 8988 ensymb 8987 ensymi 8989 |
| [Suppes] p. 92 | Theorem 3 | entr 8991 |
| [Suppes] p. 92 | Theorem 4 | unen 9030 |
| [Suppes] p. 94 | Theorem 15 | endom 8964 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8985 |
| [Suppes] p. 94 | Theorem 17 | domtr 8992 |
| [Suppes] p. 95 | Theorem 18 | sbth 9073 |
| [Suppes] p. 97 | Theorem 23 | canth2 9106 canth2g 9107 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9077 df-sdom 8934 dfsdom2 9076 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9090 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9079 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9078 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9088 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8967 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9091 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9086 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9016 fundmeng 9017 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9051 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9087 |
| [Suppes] p. 104 | Theorem 37 | fofi 9261 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9266 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9266 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10523 |
| [Suppes] p. 130 | Definition 3 | df-tr 5213 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7767 |
| [Suppes] p. 134 | Definition 6 | df-suc 6356 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7885 finds 7881 finds1 7884 finds2 7883 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9609 isfinite2 9246 isfiniteg 9248 unbnn 9244 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10891 df-ltpq 10883 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7847 tfinds 7844 tfinds2 7848 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8524 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8526 |
| [Suppes] p. 211 | Theorem 25 | oaass 8534 |
| [Suppes] p. 225 | Definition 8 | iscard2 9950 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10535 |
| [Suppes] p. 228 | Theorem 59 | harcard 9952 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10038 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6402 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7780 onminsb 7781 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10545 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10042 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10049 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10043 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9914 |
| [Suppes] p. 242 | Theorem 6 | weth 10467 |
| [Suppes] p. 242 | Theorem 8 | entric 10529 |
| [Suppes] p. 242 | Theorem 9 | carden 10523 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36059 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36063 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2737 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2757 wl-df.cleq 38014 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2840 wl-df.clel 38017 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2759 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2785 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7404 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3746 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5383 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4610 elpr2 4612 elpr2g 4611 elprg 4608 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4600 elsn2 4627 elsn2g 4626 elsng 4599 velsn 4601 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5440 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4595 sneqr 4801 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4606 dfsn2 4598 dfsn2ALT 4607 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7728 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5449 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5436 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5420 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7731 unexg 7730 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4653 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4869 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3914 df-un 3912 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4885 uniprg 4884 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5339 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4651 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6422 elsucg 6420 sstr2 3946 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4114 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4164 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4127 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4182 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4239 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4240 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3927 df-ss 3924 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4560 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4142 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3925 sseqin2 4178 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3961 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4191 inss2 4192 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4003 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4879 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5421 sspwimp 45491 sspwimpALT 45498 sspwimpALT2 45501 sspwimpcf 45493 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5428 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5232 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3418 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5262 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3910 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37025 dfnul2 4291 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4332 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4308 n0f 4304 neq0 4307 neq0f 4303 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9546 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9689 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9704 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3459 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5275 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4357 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5282 ssexg 5284 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5278 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9558 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9550 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4322 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4091 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4255 undif3VD 45455 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4092 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4099 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3080 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3090 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7740 xpexg 7737 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5659 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6596 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6775 fun11 6599 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6538 svrelfun 6597 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5868 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5870 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5664 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5665 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5661 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6184 dfrel2 6179 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5668 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5789 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5796 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5809 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5995 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5975 opelresi 5977 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6002 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5991 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5996 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6567 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6101 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6565 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6777 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2639 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30660 df-fv 6533 fv3 6889 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7910 cnvexg 7909 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7894 dmexg 7886 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7895 rnexg 7887 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45027 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7905 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6884 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47766 tz6.12-1-afv2 47833 tz6.12-1 6894 tz6.12-afv 47765 tz6.12-afv2 47832 tz6.12 6895 tz6.12c-afv2 47834 tz6.12c 6893 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47829 tz6.12-2 6858 tz6.12i-afv2 47835 tz6.12i 6897 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6528 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6529 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6531 wfo 6523 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6530 wf1 6522 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6532 wf1o 6524 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7015 eqfnfv2 7016 eqfnfv2f 7019 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6969 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7205 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7203 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6613 funimaexg 6612 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5106 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5561 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5613 dffr3 6092 eliniseg 6087 iniseg 6090 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5552 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5629 fr3nr 7759 frirr 5628 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5605 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7761 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5616 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5638 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6338 tz6.26i 6339 wefrc 5646 wereu2 5649 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6340 wfii 6341 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6534 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7317 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7318 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7324 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7325 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7326 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7330 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7337 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7339 |
| [TakeutiZaring] p. 35 | Notation | wtr 5212 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45028 tz7.2 5635 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5217 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6363 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6371 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6372 ordelordALT 45111 ordelordALTVD 45440 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6378 ordelssne 6377 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6376 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6380 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7769 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7770 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6354 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6382 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45123 ordon 7764 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7765 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7837 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6398 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5214 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7779 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7815 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6456 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6455 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7766 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4900 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6356 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6432 sucidg 6433 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7797 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6446 ordnbtwn 6445 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7812 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6355 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7865 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7870 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7825 ordelsuc 7804 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7806 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7835 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7852 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7873 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7874 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7875 |
| [TakeutiZaring] p. 43 | Remark | omon 7862 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9592 omex 9600 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7860 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7880 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7877 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7878 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7855 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4923 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5231 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4924 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5305 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7782 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6401 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4909 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9617 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7777 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8350 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8372 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8373 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8374 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8381 tz7.44-2 8382 tz7.44-3 8383 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8342 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8337 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8321 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8420 tz7.49c 8421 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8418 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8417 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8419 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2685 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9983 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9984 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8505 oasuc 8497 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7845 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8508 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8489 oa0r 8511 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8509 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8521 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8593 nnaordi 8592 oaord 8520 oaordi 8519 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5010 uniss2 4903 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8523 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8528 oawordex 8530 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8585 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8622 |
| [TakeutiZaring] p. 60 | Remark | oancom 9608 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8533 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8590 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8525 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8492 omlim 8506 omsuc 8499 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8490 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8587 nnmcl 8586 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8606 nnmordi 8605 omord 8541 omordi 8539 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8542 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8610 omwordri 8545 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8512 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8515 om1r 8516 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8548 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8550 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8551 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8552 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8553 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8582 oe0 8495 oelim 8507 oesuc 8500 onesuc 8503 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8493 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8560 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8561 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8494 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8518 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8562 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8568 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8566 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8567 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8571 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8573 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9685 tz9.1 9686 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9724 r10 9728 r1lim 9732 r1limg 9731 r1suc 9730 r1sucg 9729 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9740 r1ord2 9741 r1ordg 9738 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9750 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9775 tz9.13 9751 tz9.13g 9752 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9725 rankval 9776 rankvalb 9757 rankvalg 9777 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9799 rankelb 9784 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9813 rankval3 9800 rankval3b 9786 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9789 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9755 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9794 rankr1c 9781 rankr1g 9792 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9795 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9809 rankssb 9808 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9802 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9801 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10447 dfac3 10093 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10002 numth 10444 numth2 10443 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10518 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10519 cardid2 9927 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9934 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10523 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9933 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9918 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9939 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9931 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9126 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9003 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9131 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9055 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9937 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10070 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9178 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9186 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10071 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9183 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10060 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10038 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9946 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10187 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9270 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8935 isfi 8960 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9187 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10506 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9048 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10498 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10157 unxpdom 9207 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9948 cardsdomelir 9947 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9209 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9986 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8814 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10534 infxpidm2 9989 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10178 infxp 10185 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9060 pw2f1o 9058 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9119 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10459 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10454 ac6s5 10463 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10515 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10516 uniimadomf 10517 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10246 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10241 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10225 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10222 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10229 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10236 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10245 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10555 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10223 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10248 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10069 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10068 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10080 alephfp2 10081 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10672 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10084 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10542 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10556 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10557 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39519 |
| [Tarski] p. 67 | Scheme B5 | sp 2221 |
| [Tarski] p. 68 | Lemma 6 | avril1 30723 equid 2035 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2040 |
| [Tarski] p. 70 | Lemma 14 | spim 2421 spime 2423 spimew 1994 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2215 ax-c15 39525 ax12i 1989 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2121 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1991 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1933 ax5ALT 39543 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2031 ax-8 2147 ax-9 2155 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28691 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28692 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28694 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28694 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28695 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16289 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38170 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38172 |
| [Weierstrass] p. 272 | Definition | df-mdet 22703 mdetuni 22740 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 916 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 881 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 932 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 37951 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44388 imim2 59 wl-luk-imim2 37946 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47611 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 909 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2692 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 915 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 37949 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 907 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 910 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45500 wl-luk-notnotr 37950 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44418 axfrege28 44417 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 880 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 937 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 37943 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 902 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30661 pm2.27 43 wl-luk-pm2.27 37941 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 935 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38882 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 936 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1102 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 919 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 894 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 895 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 864 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 901 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 903 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 912 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 904 pm2.67 905 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 911 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 913 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 944 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 474 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 476 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 464 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 407 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 814 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 453 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 487 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 489 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 776 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 819 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 633 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 497 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 820 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 478 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 818 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 845 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 817 bitr 816 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 573 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 917 pm4.25 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 465 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1023 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 883 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 473 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 934 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 644 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 930 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 648 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1103 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1021 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1067 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1038 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 840 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 866 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 554 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 409 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 869 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 402 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 862 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 566 pm4.71d 570 pm4.71i 568 pm4.71r 567 pm4.71rd 571 pm4.71ri 569 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 536 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 949 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 526 pm4.76 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 947 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1019 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 397 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1039 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1040 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 391 impexp 455 pm4.87 856 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 835 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1028 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1027 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 390 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 836 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1063 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1064 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 914 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 582 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 392 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 843 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 848 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 837 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 846 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 393 pm5.41 394 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 551 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1033 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1034 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1043 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1044 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37076 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44932 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44933 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1893 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44934 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44935 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44936 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1916 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44937 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44938 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44939 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44940 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44941 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44943 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44944 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44945 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44942 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2126 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44948 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44949 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2104 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2197 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1852 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1853 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44950 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44951 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44952 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44953 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44955 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44954 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1910 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44957 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44958 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44956 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1851 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44959 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44960 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1869 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44961 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2380 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1883 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44966 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44962 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44963 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44964 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44965 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44970 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44967 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44968 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44969 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44971 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2599 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44981 pm13.13b 44982 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44983 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3041 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3042 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3628 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44989 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44990 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44984 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45126 pm13.193 44985 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44986 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44987 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44988 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44995 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44994 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44993 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3809 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44996 pm14.122b 44997 pm14.122c 44998 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44999 pm14.123b 45000 pm14.123c 45001 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45003 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45002 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45004 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6506 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45005 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6507 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45006 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45008 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2663 eupickbi 2666 sbaniota 45009 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45007 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2614 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45010 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30660 df-fv 6533 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9975 pm54.43lem 9974 |
| [Young] p. 141 | Definition of operator ordering | leop2 32385 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32391 idleop 32392 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43417 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43424 pellexlem1 43418 |