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 17726 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17726 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18143 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17747 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 48730 prsthinc 48721 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 48751 df-mndtc 48751 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17770 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17842 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17830 invisoinvl 17851 |
| [Adamek] p. 28 | Example 3.13 | idinv 17850 idiso 17849 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17835 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17809 df-iso 17810 dfiso2 17833 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17816 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17867 |
| [Adamek] p. 29 | Definition 3.15 | cic 17860 df-cic 17857 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17922 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17831 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17832 isoco 17838 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17922 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17945 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17938 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 48687 prsthinc 48721 thincciso 48716 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 48751 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17952 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18178 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18236 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17972 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17971 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18236 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17996 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18002 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18001 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18221 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18221 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17939 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18166 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17990 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17989 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18175 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 18166 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17902 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17903 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17914 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17873 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 18005 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18011 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18034 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18038 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18012 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18040 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 18051 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21513 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18052 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18079 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18083 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18053 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21514 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18086 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17808 |
| [Adamek] p. 185 | Section 10.67 | updjud 10003 |
| [Adamek] p. 478 | Item Rng | df-ringc 20668 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48282 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48304 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14619 df-pfx 14719 df-substr 14689 df-word 14563 lencl 14581 wrd0 14587 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24750 df-nmoo 30777 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32185 hmopidmchi 32183 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32233 pjcmul2i 32234 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31950 unoplin 31952 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31951 unopadj2 31970 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32045 lnopunii 32044 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32118 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27979 |
| [Alling] p. 184 | Axiom B | bdayfo 27740 |
| [Alling] p. 184 | Axiom O | sltso 27739 |
| [Alling] p. 184 | Axiom SD | nodense 27755 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27841 |
| [Alling] p. 185 | Theorem | conway 27862 |
| [Alling] p. 185 | Axiom FE | noeta 27806 |
| [Alling] p. 186 | Theorem 4 | slerec 27882 |
| [Alling], p. 2 | Definition | rp-brsslt 43385 |
| [Alling], p. 3 | Note | nla0001 43388 nla0002 43386 nla0003 43387 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11474 addcan2d 11494 addcan2i 11484 addcand 11493 addcani 11483 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11526 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11584 negsubd 11653 negsubi 11614 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11586 negnegd 11638 negnegi 11606 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11723 subdid 11746 subdii 11739 subdir 11724 subdird 11747 subdiri 11740 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11469 mul01d 11489 mul01i 11480 mul02 11468 mul02d 11488 mul02i 11479 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11927 mulcan2d 11924 mulcand 11923 mulcani 11929 |
| [Apostol] p. 18 | Theorem I.8 | receu 11935 xreceu 32886 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11965 divrecd 12073 divreci 12039 divreczi 12032 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11991 recreci 12026 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11930 mul0ord 11940 mul0ori 11938 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11729 mul2negd 11745 mul2negi 11738 mulneg1 11726 mulneg1d 11743 mulneg1i 11736 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 12009 divadddivd 12114 divadddivi 12056 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11994 divmuldivd 12111 divmuldivi 12054 rdivmuldivd 20439 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11995 divdivdivd 12117 divdivdivi 12057 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13079 rpaddcld 13114 rpmulcl 13080 rpmulcld 13115 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13089 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13092 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11416 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11883 ltadd1dd 11901 ltadd1i 11844 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12144 ltmul1a 12143 ltmul1i 12213 ltmul1ii 12223 ltmul2 12145 ltmul2d 13141 ltmul2dd 13155 ltmul2i 12216 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11810 msqgt0d 11857 msqgt0i 11827 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11812 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11796 lt0neg1d 11859 ltneg 11790 ltnegd 11868 ltnegi 11834 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11775 lt2addd 11913 lt2addi 11852 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13058 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12140 recgt0d 12229 recgt0i 12200 recgt0ii 12201 |
| [Apostol] p. 22 | Definition of integers | df-z 12640 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12307 |
| [Apostol] p. 22 | Definition of rationals | df-q 13014 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9523 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12549 |
| [Apostol] p. 26 | Theorem I.29 | arch 12550 archd 45067 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12746 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12551 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 13012 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 13011 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13261 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16387 zneo 12726 zneoALTV 47543 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26790 msqsqrtd 15489 resqrtth 15304 sqrtth 15413 sqrtthi 15419 sqsqrtd 15488 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12296 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12978 |
| [Apostol] p. 361 | Remark | crreczi 14277 |
| [Apostol] p. 363 | Remark | absgt0i 15448 |
| [Apostol] p. 363 | Example | abssubd 15502 abssubi 15452 |
| [ApostolNT] p. 7 | Remark | fmtno0 47414 fmtno1 47415 fmtno2 47424 fmtno3 47425 fmtno4 47426 fmtno5fac 47456 fmtnofz04prm 47451 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47402 |
| [ApostolNT] p. 8 | Definition | df-ppi 27161 |
| [ApostolNT] p. 14 | Definition | df-dvds 16303 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16318 |
| [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 16331 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16333 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16319 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16320 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16325 |
| [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 16541 dfgcd2 16593 |
| [ApostolNT] p. 16 | Definition | isprm2 16729 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16700 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16962 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16559 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16594 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16596 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16574 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16566 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16758 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16760 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16975 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16969 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16451 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16634 |
| [ApostolNT] p. 24 | Definition | df-mu 27162 |
| [ApostolNT] p. 25 | Definition | df-phi 16813 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27252 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16837 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16823 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16827 |
| [ApostolNT] p. 32 | Definition | df-vma 27159 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27254 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27278 |
| [ApostolNT] p. 38 | Remark | df-sgm 27163 |
| [ApostolNT] p. 38 | Definition | df-sgm 27163 |
| [ApostolNT] p. 75 | Definition | df-chp 27160 df-cht 27158 |
| [ApostolNT] p. 104 | Definition | congr 16711 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16306 |
| [ApostolNT] p. 106 | Definition | moddvds 16313 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16394 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16395 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13939 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13976 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14287 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16336 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16714 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17121 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16716 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16830 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16848 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16831 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27133 |
| [ApostolNT] p. 179 | Definition | df-lgs 27357 lgsprme0 27401 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27402 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27378 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27393 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27450 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27469 2lgsoddprm 27478 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27436 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27445 |
| [ApostolNT] p. 188 | Definition | df-lgs 27357 lgs1 27403 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27394 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27396 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27404 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27405 |
| [Baer] p. 40 | Property (b) | mapdord 41595 |
| [Baer] p. 40 | Property (c) | mapd11 41596 |
| [Baer] p. 40 | Property (e) | mapdin 41619 mapdlsm 41621 |
| [Baer] p. 40 | Property (f) | mapd0 41622 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41582 mapd1o 41605 |
| [Baer] p. 41 | Property (g) | mapdat 41624 |
| [Baer] p. 44 | Part (1) | mapdpg 41663 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41758 mapdheq 41685 mapdheq2 41686 mapdheq2biN 41687 |
| [Baer] p. 45 | Part (3) | baerlem3 41670 |
| [Baer] p. 46 | Part (4) | mapdheq4 41689 mapdheq4lem 41688 |
| [Baer] p. 46 | Part (5) | baerlem5a 41671 baerlem5abmN 41675 baerlem5amN 41673 baerlem5b 41672 baerlem5bmN 41674 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41778 hdmap1l6a 41766 hdmap1l6e 41771 hdmap1l6f 41772 hdmap1l6g 41773 hdmap1l6lem1 41764 hdmap1l6lem2 41765 mapdh6N 41704 mapdh6aN 41692 mapdh6eN 41697 mapdh6fN 41698 mapdh6gN 41699 mapdh6lem1N 41690 mapdh6lem2N 41691 |
| [Baer] p. 48 | Part 9 | hdmapval 41785 |
| [Baer] p. 48 | Part 10 | hdmap10 41797 |
| [Baer] p. 48 | Part 11 | hdmapadd 41800 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41774 mapdh6hN 41700 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41710 mapdh75d 41711 mapdh75e 41709 mapdh75fN 41712 mapdh7cN 41706 mapdh7dN 41707 mapdh7eN 41705 mapdh7fN 41708 |
| [Baer] p. 48 | Part (8) | mapdh8 41745 mapdh8a 41732 mapdh8aa 41733 mapdh8ab 41734 mapdh8ac 41735 mapdh8ad 41736 mapdh8b 41737 mapdh8c 41738 mapdh8d 41740 mapdh8d0N 41739 mapdh8e 41741 mapdh8g 41742 mapdh8i 41743 mapdh8j 41744 |
| [Baer] p. 48 | Part (9) | mapdh9a 41746 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41726 |
| [Baer] p. 49 | Part 12 | hdmap11 41805 hdmapeq0 41801 hdmapf1oN 41822 hdmapneg 41803 hdmaprnN 41821 hdmaprnlem1N 41806 hdmaprnlem3N 41807 hdmaprnlem3uN 41808 hdmaprnlem4N 41810 hdmaprnlem6N 41811 hdmaprnlem7N 41812 hdmaprnlem8N 41813 hdmaprnlem9N 41814 hdmapsub 41804 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41825 hdmap14lem10 41834 hdmap14lem1a 41823 hdmap14lem2N 41826 hdmap14lem2a 41824 hdmap14lem3 41827 hdmap14lem8 41832 hdmap14lem9 41833 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41835 hdmap14lem12 41836 hdmap14lem13 41837 hdmap14lem14 41838 hdmap14lem15 41839 hgmapval 41844 |
| [Baer] p. 50 | Part 15 | hgmapadd 41851 hgmapmul 41852 hgmaprnlem2N 41854 hgmapvs 41848 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41858 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41874 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41875 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41876 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41877 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41879 hgmapvv 41883 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41878 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41880 |
| [Baer] p. 111 | Line 15 | hdmapg 41887 hdmapglem7 41886 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26791 2irrexpqALT 26861 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2572 |
| [BellMachover] p. 460 | Notation | df-mo 2543 |
| [BellMachover] p. 460 | Definition | mo3 2567 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2711 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2715 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5309 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5317 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37030 bm1.3ii 5320 |
| [BellMachover] p. 466 | Problem | axpow2 5385 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5386 |
| [BellMachover] p. 466 | Axiom Union | axun2 7772 |
| [BellMachover] p. 468 | Definition | df-ord 6398 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6413 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6420 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6415 |
| [BellMachover] p. 471 | Definition of N | df-om 7904 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7837 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6400 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9711 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7919 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9833 |
| [BellMachover] p. 478 | Definition | rankval2 9887 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9851 r1ord3g 9848 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9664 |
| [BellMachover] p. 488 | Axiom AC | ac5 10546 dfac4 10191 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10179 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39275 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32385 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32427 chirredi 32426 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32415 |
| [Beran] p. 3 | Definition of join | sshjval3 31386 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31648 cmcm2i 31625 cmcm2ii 31630 cmt2N 39206 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31649 lecmi 31634 lecmii 31635 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31623 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31652 cm2ji 31657 cm2mi 31658 |
| [Beran] p. 95 | Definition | df-sh 31239 issh2 31241 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31118 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31131 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31122 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31860 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31862 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31861 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31863 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31114 his1i 31132 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31115 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31116 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31117 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31000 dfhnorm2 31154 normval 31156 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31216 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31005 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31273 |
| [Beran] p. 96 | Definition of converge | df-hlim 31004 hlimi 31220 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31165 norm-i 31161 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31169 norm-ii 31170 normlem0 31141 normlem1 31142 normlem2 31143 normlem3 31144 normlem4 31145 normlem5 31146 normlem6 31147 normlem7 31148 normlem7tALT 31151 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31171 norm-iii 31172 |
| [Beran] p. 98 | Remark 3.4 | bcs 31213 bcsiALT 31211 bcsiHIL 31212 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31153 normpar 31187 normpari 31186 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31178 normpyth 31177 normpythi 31174 |
| [Beran] p. 99 | Remark | lnfn0 32079 lnfn0i 32074 lnop0 31998 lnop0i 32002 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32058 nmcfnex 32085 nmcfnexi 32083 nmcopex 32061 nmcopexi 32059 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32086 nmcfnlbi 32084 nmcoplb 32062 nmcoplbi 32060 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32088 lnfnconi 32087 lnopcon 32067 lnopconi 32066 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31188 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31185 norm3adifii 31180 norm3dif 31182 norm3difi 31179 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31333 pjhth 31425 pjhtheu 31426 pjpjhth 31457 pjpjhthi 31458 pjth 25492 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31438 ococi 31437 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32093 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32094 riesz4 32096 riesz4i 32095 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32111 cnlnadjeu 32110 cnlnadjeui 32109 cnlnadji 32108 cnlnadjlem1 32099 nmopadjlei 32120 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32123 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32122 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32124 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31968 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32134 nmopcoadji 32133 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32125 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32135 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32132 pjadj2coi 32236 pjadjcoi 32193 |
| [Beran] p. 107 | Definition | df-ch 31253 isch2 31255 |
| [Beran] p. 107 | Remark 3.12 | choccl 31338 isch3 31273 occl 31336 ocsh 31315 shoccl 31337 shocsh 31316 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31440 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31364 |
| [Beran] p. 109 | Property (i) | pjadj2 32219 pjadj3 32220 pjadji 31717 pjadjii 31706 |
| [Beran] p. 109 | Property (ii) | pjidmco 32213 pjidmcoi 32209 pjidmi 31705 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32205 |
| [Beran] p. 111 | Remark | ho0val 31782 pjch1 31702 |
| [Beran] p. 111 | Definition | df-hfmul 31766 df-hfsum 31765 df-hodif 31764 df-homul 31763 df-hosum 31762 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31703 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31726 pjchi 31464 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31471 pjoc2i 31470 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31712 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32197 pjssmii 31713 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32196 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32195 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32200 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32198 pjssge0ii 31714 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32199 pjdifnormii 31715 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1774 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1772 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1775 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1770 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34257 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34265 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34263 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34267 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34287 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34318 df-sitm 34296 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34318 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34295 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29083 isuhgrop 29105 isusgrop 29197 isuspgrop 29196 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47733 df-subgr 29303 uhgrspan1 29338 uhgrspansubgr 29326 |
| [Bollobas] p. 3 | Definition | df-gric 47751 gricuspgr 47771 isuspgrim 47759 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29490 df-clnbgr 47693 df-cusgr 29447 df-nbgr 29368 fusgrmaxsize 29500 |
| [Bollobas] p. 4 | Definition | df-upwlks 47857 df-wlks 29635 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29586 finsumvtxdgeven 29588 fusgr1th 29587 fusgrvtxdgonume 29590 vtxdgoddnumeven 29589 |
| [Bollobas] p. 5 | Notation | df-pths 29752 |
| [Bollobas] p. 5 | Definition | df-crcts 29822 df-cycls 29823 df-trls 29728 df-wlkson 29636 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29094 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 47923 df-cllaw 47909 df-mgm 18678 df-mgm2 47942 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 47924 df-asslaw 47911 df-sgrp 18757 df-sgrp2 47944 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 47943 df-comlaw 47910 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18773 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33012 mndlactf1o 33016 mndractf1 33014 mndractf1o 33017 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20262 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20180 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33646 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33650 assarrginv 33649 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33530 dfufd2 33543 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7323 fcofo 7324 |
| [BourbakiTop1] p. | Remark | xnegmnf 13272 xnegpnf 13271 |
| [BourbakiTop1] p. | Remark | rexneg 13273 |
| [BourbakiTop1] p. | Remark 3 | ust0 24249 ustfilxp 24242 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24119 |
| [BourbakiTop1] p. | Criterion | ishmeo 23788 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24314 iducn 24313 snfil 23893 |
| [BourbakiTop1] p. | Example 2 | neifil 23909 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24096 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24334 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33903 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23892 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24306 df-ust 24230 filintn0 23890 filn0 23891 istgp 24106 ucnprima 24312 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24317 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24328 df-usp 24287 df-utop 24261 trust 24259 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33802 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23145 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23298 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24235 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24238 |
| [BourbakiTop1] p. | Property V_ii | innei 23154 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23162 neissex 23156 |
| [BourbakiTop1] p. | Proposition 1 | neips 23142 neiss 23138 ucncn 24315 ustund 24251 ustuqtop 24276 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23296 neiptopreu 23162 utop2nei 24280 utop3cls 24281 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24322 uspreg 24304 utopreg 24282 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23720 imasncls 23721 imasnopn 23719 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24029 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24237 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24239 |
| [BourbakiTop1] p. | Property V_iii | elnei 23140 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24333 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24236 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24240 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23416 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23875 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22921 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33799 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 45983 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 45985 stoweid 45984 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45922 stoweidlem10 45931 stoweidlem14 45935 stoweidlem15 45936 stoweidlem35 45956 stoweidlem36 45957 stoweidlem37 45958 stoweidlem38 45959 stoweidlem40 45961 stoweidlem41 45962 stoweidlem43 45964 stoweidlem44 45965 stoweidlem46 45967 stoweidlem5 45926 stoweidlem50 45971 stoweidlem52 45973 stoweidlem53 45974 stoweidlem55 45976 stoweidlem56 45977 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 45944 stoweidlem24 45945 stoweidlem27 45948 stoweidlem28 45949 stoweidlem30 45951 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 45955 stoweidlem59 45980 stoweidlem60 45981 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 45966 stoweidlem49 45970 stoweidlem7 45928 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 45952 stoweidlem39 45960 stoweidlem42 45963 stoweidlem48 45969 stoweidlem51 45972 stoweidlem54 45975 stoweidlem57 45978 stoweidlem58 45979 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 45946 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 45938 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 45932 stoweidlem13 45934 stoweidlem26 45947 stoweidlem61 45982 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 45939 |
| [Bruck] p. 1 | Section I.1 | df-clintop 47923 df-mgm 18678 df-mgm2 47942 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18757 df-sgrp2 47944 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19079 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5250 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30435 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30435 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30435 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30435 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30435 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30435 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30435 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30435 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30435 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30435 |
| [Clemente] p. 14 | Proof 5.11 | natded 30435 |
| [Clemente] p. 14 | Definition E` `n | natded 30435 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30437 ex-natded5.2 30436 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30440 ex-natded5.3 30439 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30442 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30444 ex-natded5.7 30443 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30446 ex-natded5.8 30445 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30448 ex-natded5.13 30447 |
| [Clemente] p. 32 | Definition I` `n | natded 30435 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30435 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30435 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30435 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30449 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30450 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30452 ex-natded9.26 30451 |
| [Cohen] p. 301 | Remark | relogoprlem 26651 |
| [Cohen] p. 301 | Property 2 | relogmul 26652 relogmuld 26685 |
| [Cohen] p. 301 | Property 3 | relogdiv 26653 relogdivd 26686 |
| [Cohen] p. 301 | Property 4 | relogexp 26656 |
| [Cohen] p. 301 | Property 1a | log1 26645 |
| [Cohen] p. 301 | Property 1b | loge 26646 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26848 |
| [Cohen4] p. 349 | Property | relogbf 26852 |
| [Cohen4] p. 352 | Definition | elogb 26831 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26838 |
| [Cohen4] p. 361 | Property 3 | logbrec 26843 relogbdiv 26840 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26836 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26841 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26829 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26830 |
| [Cohen4] p. 367 | Property | logbchbase 26832 |
| [Cohen4] p. 377 | Property 2 | logblt 26845 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34250 sxbrsigalem4 34252 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18627 acsinfd 18626 acsinfdimd 18628 acsmap2d 18625 acsmapd 18624 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34255 |
| [Connell] p. 57 | Definition | df-scmat 22518 df-scmatalt 48128 |
| [Conway] p. 4 | Definition | slerec 27882 |
| [Conway] p. 5 | Definition | addsval 28013 addsval2 28014 df-adds 28011 df-muls 28151 df-negs 28071 |
| [Conway] p. 7 | Theorem | 0slt1s 27892 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27928 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27927 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27826 |
| [Conway] p. 17 | Theorem 3 | addsass 28056 addsassd 28057 addscom 28017 addscomd 28018 addsrid 28015 addsridd 28016 |
| [Conway] p. 17 | Definition | df-0s 27887 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28094 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28091 negsidd 28092 |
| [Conway] p. 18 | Theorem 5 | sleadd1 28040 sleadd1d 28046 |
| [Conway] p. 18 | Definition | df-1s 27888 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28086 negscld 28087 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28031 |
| [Conway] p. 19 | Note | mulsunif2 28214 |
| [Conway] p. 19 | Theorem 7 | addsdi 28199 addsdid 28200 addsdird 28201 mulnegs1d 28204 mulnegs2d 28205 mulsass 28210 mulsassd 28211 mulscom 28183 mulscomd 28184 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28178 mulscld 28179 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28182 sltmul 28180 sltmuld 28181 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28188 mulsgt0d 28189 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28260 |
| [Conway] p. 24 | Definition | df-reno 28444 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28449 remulscl 28452 renegscl 28448 |
| [Conway] p. 27 | Definition | df-ons 28293 elons2 28299 |
| [Conway] p. 27 | Theorem 14 | sltonex 28302 |
| [Conway] p. 29 | Remark | madebday 27956 newbday 27958 oldbday 27957 |
| [Conway] p. 29 | Definition | df-made 27904 df-new 27906 df-old 27905 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13912 |
| [Crawley] p. 1 | Definition of poset | df-poset 18383 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39343 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40147 dalaw 39843 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41922 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39947 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40063 df-ldil 40061 isldil 40067 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40062 df-trnN 40064 isltrn 40076 ltrnu 40078 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39748 cdlema2N 39749 exatleN 39361 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39433 cdlemb 39751 cdlemb2 39998 cdlemb3 40563 idltrn 40107 l1cvat 39011 lhpat 40000 lhpat2 40002 lshpat 39012 ltrnel 40096 ltrnmw 40108 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40148 cdlemc2 40149 ltrnnidn 40131 trlat 40126 trljat1 40123 trljat2 40124 trljat3 40125 trlne 40142 trlnidat 40130 trlnle 40143 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39948 |
| [Crawley] p. 113 | Lemma C | cdlemc 40154 cdlemc3 40150 cdlemc4 40151 |
| [Crawley] p. 113 | Lemma D | cdlemd 40164 cdlemd1 40155 cdlemd2 40156 cdlemd3 40157 cdlemd4 40158 cdlemd5 40159 cdlemd6 40160 cdlemd7 40161 cdlemd8 40162 cdlemd9 40163 cdleme31sde 40342 cdleme31se 40339 cdleme31se2 40340 cdleme31snd 40343 cdleme32a 40398 cdleme32b 40399 cdleme32c 40400 cdleme32d 40401 cdleme32e 40402 cdleme32f 40403 cdleme32fva 40394 cdleme32fva1 40395 cdleme32fvcl 40397 cdleme32le 40404 cdleme48fv 40456 cdleme4gfv 40464 cdleme50eq 40498 cdleme50f 40499 cdleme50f1 40500 cdleme50f1o 40503 cdleme50laut 40504 cdleme50ldil 40505 cdleme50lebi 40497 cdleme50rn 40502 cdleme50rnlem 40501 cdlemeg49le 40468 cdlemeg49lebilem 40496 |
| [Crawley] p. 113 | Lemma E | cdleme 40517 cdleme00a 40166 cdleme01N 40178 cdleme02N 40179 cdleme0a 40168 cdleme0aa 40167 cdleme0b 40169 cdleme0c 40170 cdleme0cp 40171 cdleme0cq 40172 cdleme0dN 40173 cdleme0e 40174 cdleme0ex1N 40180 cdleme0ex2N 40181 cdleme0fN 40175 cdleme0gN 40176 cdleme0moN 40182 cdleme1 40184 cdleme10 40211 cdleme10tN 40215 cdleme11 40227 cdleme11a 40217 cdleme11c 40218 cdleme11dN 40219 cdleme11e 40220 cdleme11fN 40221 cdleme11g 40222 cdleme11h 40223 cdleme11j 40224 cdleme11k 40225 cdleme11l 40226 cdleme12 40228 cdleme13 40229 cdleme14 40230 cdleme15 40235 cdleme15a 40231 cdleme15b 40232 cdleme15c 40233 cdleme15d 40234 cdleme16 40242 cdleme16aN 40216 cdleme16b 40236 cdleme16c 40237 cdleme16d 40238 cdleme16e 40239 cdleme16f 40240 cdleme16g 40241 cdleme19a 40260 cdleme19b 40261 cdleme19c 40262 cdleme19d 40263 cdleme19e 40264 cdleme19f 40265 cdleme1b 40183 cdleme2 40185 cdleme20aN 40266 cdleme20bN 40267 cdleme20c 40268 cdleme20d 40269 cdleme20e 40270 cdleme20f 40271 cdleme20g 40272 cdleme20h 40273 cdleme20i 40274 cdleme20j 40275 cdleme20k 40276 cdleme20l 40279 cdleme20l1 40277 cdleme20l2 40278 cdleme20m 40280 cdleme20y 40259 cdleme20zN 40258 cdleme21 40294 cdleme21d 40287 cdleme21e 40288 cdleme22a 40297 cdleme22aa 40296 cdleme22b 40298 cdleme22cN 40299 cdleme22d 40300 cdleme22e 40301 cdleme22eALTN 40302 cdleme22f 40303 cdleme22f2 40304 cdleme22g 40305 cdleme23a 40306 cdleme23b 40307 cdleme23c 40308 cdleme26e 40316 cdleme26eALTN 40318 cdleme26ee 40317 cdleme26f 40320 cdleme26f2 40322 cdleme26f2ALTN 40321 cdleme26fALTN 40319 cdleme27N 40326 cdleme27a 40324 cdleme27cl 40323 cdleme28c 40329 cdleme3 40194 cdleme30a 40335 cdleme31fv 40347 cdleme31fv1 40348 cdleme31fv1s 40349 cdleme31fv2 40350 cdleme31id 40351 cdleme31sc 40341 cdleme31sdnN 40344 cdleme31sn 40337 cdleme31sn1 40338 cdleme31sn1c 40345 cdleme31sn2 40346 cdleme31so 40336 cdleme35a 40405 cdleme35b 40407 cdleme35c 40408 cdleme35d 40409 cdleme35e 40410 cdleme35f 40411 cdleme35fnpq 40406 cdleme35g 40412 cdleme35h 40413 cdleme35h2 40414 cdleme35sn2aw 40415 cdleme35sn3a 40416 cdleme36a 40417 cdleme36m 40418 cdleme37m 40419 cdleme38m 40420 cdleme38n 40421 cdleme39a 40422 cdleme39n 40423 cdleme3b 40186 cdleme3c 40187 cdleme3d 40188 cdleme3e 40189 cdleme3fN 40190 cdleme3fa 40193 cdleme3g 40191 cdleme3h 40192 cdleme4 40195 cdleme40m 40424 cdleme40n 40425 cdleme40v 40426 cdleme40w 40427 cdleme41fva11 40434 cdleme41sn3aw 40431 cdleme41sn4aw 40432 cdleme41snaw 40433 cdleme42a 40428 cdleme42b 40435 cdleme42c 40429 cdleme42d 40430 cdleme42e 40436 cdleme42f 40437 cdleme42g 40438 cdleme42h 40439 cdleme42i 40440 cdleme42k 40441 cdleme42ke 40442 cdleme42keg 40443 cdleme42mN 40444 cdleme42mgN 40445 cdleme43aN 40446 cdleme43bN 40447 cdleme43cN 40448 cdleme43dN 40449 cdleme5 40197 cdleme50ex 40516 cdleme50ltrn 40514 cdleme51finvN 40513 cdleme51finvfvN 40512 cdleme51finvtrN 40515 cdleme6 40198 cdleme7 40206 cdleme7a 40200 cdleme7aa 40199 cdleme7b 40201 cdleme7c 40202 cdleme7d 40203 cdleme7e 40204 cdleme7ga 40205 cdleme8 40207 cdleme8tN 40212 cdleme9 40210 cdleme9a 40208 cdleme9b 40209 cdleme9tN 40214 cdleme9taN 40213 cdlemeda 40255 cdlemedb 40254 cdlemednpq 40256 cdlemednuN 40257 cdlemefr27cl 40360 cdlemefr32fva1 40367 cdlemefr32fvaN 40366 cdlemefrs32fva 40357 cdlemefrs32fva1 40358 cdlemefs27cl 40370 cdlemefs32fva1 40380 cdlemefs32fvaN 40379 cdlemesner 40253 cdlemeulpq 40177 |
| [Crawley] p. 114 | Lemma E | 4atex 40033 4atexlem7 40032 cdleme0nex 40247 cdleme17a 40243 cdleme17c 40245 cdleme17d 40455 cdleme17d1 40246 cdleme17d2 40452 cdleme18a 40248 cdleme18b 40249 cdleme18c 40250 cdleme18d 40252 cdleme4a 40196 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40282 cdleme21at 40285 cdleme21b 40283 cdleme21c 40284 cdleme21ct 40286 cdleme21f 40289 cdleme21g 40290 cdleme21h 40291 cdleme21i 40292 cdleme22gb 40251 |
| [Crawley] p. 116 | Lemma F | cdlemf 40520 cdlemf1 40518 cdlemf2 40519 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40524 cdlemg16 40614 cdlemg28 40661 cdlemg28a 40650 cdlemg28b 40660 cdlemg3a 40554 cdlemg42 40686 cdlemg43 40687 cdlemg44 40690 cdlemg44a 40688 cdlemg46 40692 cdlemg47 40693 cdlemg9 40591 ltrnco 40676 ltrncom 40695 tgrpabl 40708 trlco 40684 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40700 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40634 cdlemg17b 40619 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40713 df-edring 40714 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40717 |
| [Crawley] p. 118 | Remark | tendopltp 40737 |
| [Crawley] p. 118 | Lemma H | cdlemh 40774 cdlemh1 40772 cdlemh2 40773 |
| [Crawley] p. 118 | Lemma I | cdlemi 40777 cdlemi1 40775 cdlemi2 40776 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40778 cdlemj2 40779 cdlemj3 40780 tendocan 40781 |
| [Crawley] p. 118 | Lemma K | cdlemk 40931 cdlemk1 40788 cdlemk10 40800 cdlemk11 40806 cdlemk11t 40903 cdlemk11ta 40886 cdlemk11tb 40888 cdlemk11tc 40902 cdlemk11u-2N 40846 cdlemk11u 40828 cdlemk12 40807 cdlemk12u-2N 40847 cdlemk12u 40829 cdlemk13-2N 40833 cdlemk13 40809 cdlemk14-2N 40835 cdlemk14 40811 cdlemk15-2N 40836 cdlemk15 40812 cdlemk16-2N 40837 cdlemk16 40814 cdlemk16a 40813 cdlemk17-2N 40838 cdlemk17 40815 cdlemk18-2N 40843 cdlemk18-3N 40857 cdlemk18 40825 cdlemk19-2N 40844 cdlemk19 40826 cdlemk19u 40927 cdlemk1u 40816 cdlemk2 40789 cdlemk20-2N 40849 cdlemk20 40831 cdlemk21-2N 40848 cdlemk21N 40830 cdlemk22-3 40858 cdlemk22 40850 cdlemk23-3 40859 cdlemk24-3 40860 cdlemk25-3 40861 cdlemk26-3 40863 cdlemk26b-3 40862 cdlemk27-3 40864 cdlemk28-3 40865 cdlemk29-3 40868 cdlemk3 40790 cdlemk30 40851 cdlemk31 40853 cdlemk32 40854 cdlemk33N 40866 cdlemk34 40867 cdlemk35 40869 cdlemk36 40870 cdlemk37 40871 cdlemk38 40872 cdlemk39 40873 cdlemk39u 40925 cdlemk4 40791 cdlemk41 40877 cdlemk42 40898 cdlemk42yN 40901 cdlemk43N 40920 cdlemk45 40904 cdlemk46 40905 cdlemk47 40906 cdlemk48 40907 cdlemk49 40908 cdlemk5 40793 cdlemk50 40909 cdlemk51 40910 cdlemk52 40911 cdlemk53 40914 cdlemk54 40915 cdlemk55 40918 cdlemk55u 40923 cdlemk56 40928 cdlemk5a 40792 cdlemk5auN 40817 cdlemk5u 40818 cdlemk6 40794 cdlemk6u 40819 cdlemk7 40805 cdlemk7u-2N 40845 cdlemk7u 40827 cdlemk8 40795 cdlemk9 40796 cdlemk9bN 40797 cdlemki 40798 cdlemkid 40893 cdlemkj-2N 40839 cdlemkj 40820 cdlemksat 40803 cdlemksel 40802 cdlemksv 40801 cdlemksv2 40804 cdlemkuat 40823 cdlemkuel-2N 40841 cdlemkuel-3 40855 cdlemkuel 40822 cdlemkuv-2N 40840 cdlemkuv2-2 40842 cdlemkuv2-3N 40856 cdlemkuv2 40824 cdlemkuvN 40821 cdlemkvcl 40799 cdlemky 40883 cdlemkyyN 40919 tendoex 40932 |
| [Crawley] p. 120 | Remark | dva1dim 40942 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40933 cdleml2N 40934 cdleml3N 40935 cdleml4N 40936 cdleml5N 40937 cdleml6 40938 cdleml7 40939 cdleml8 40940 cdleml9 40941 dia1dim 41018 |
| [Crawley] p. 120 | Lemma M | dia11N 41005 diaf11N 41006 dialss 41003 diaord 41004 dibf11N 41118 djajN 41094 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 40989 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41075 dia2dimlem1 41021 dia2dimlem2 41022 dia2dimlem3 41023 dia2dimlem4 41024 dia2dimlem5 41025 diaf1oN 41087 diarnN 41086 dvheveccl 41069 dvhopN 41073 |
| [Crawley] p. 121 | Lemma N | cdlemn 41169 cdlemn10 41163 cdlemn11 41168 cdlemn11a 41164 cdlemn11b 41165 cdlemn11c 41166 cdlemn11pre 41167 cdlemn2 41152 cdlemn2a 41153 cdlemn3 41154 cdlemn4 41155 cdlemn4a 41156 cdlemn5 41158 cdlemn5pre 41157 cdlemn6 41159 cdlemn7 41160 cdlemn8 41161 cdlemn9 41162 diclspsn 41151 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41130 |
| [Crawley] p. 122 | Lemma N | dih11 41222 dihf11 41224 dihjust 41174 dihjustlem 41173 dihord 41221 dihord1 41175 dihord10 41180 dihord11b 41179 dihord11c 41181 dihord2 41184 dihord2a 41176 dihord2b 41177 dihord2cN 41178 dihord2pre 41182 dihord2pre2 41183 dihordlem6 41170 dihordlem7 41171 dihordlem7b 41172 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41187 dihfval 41188 dihval 41189 |
| [Diestel] p. 3 | Definition | df-gric 47751 df-grim 47748 isuspgrim 47759 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29447 df-nbgr 29368 |
| [Diestel] p. 3 | Definition by | df-grisom 47747 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47733 df-subgr 29303 uhgrspan1 29338 uhgrspansubgr 29326 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29590 vtxdgoddnumeven 29589 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29094 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33810 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33822 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33814 zarcls1 33815 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33825 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33828 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33831 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3979 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9716 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8886 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9724 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10049 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10624 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5323 |
| [Enderton] p. 19 | Definition | df-tp 4653 |
| [Enderton] p. 26 | Exercise 5 | unissb 4963 |
| [Enderton] p. 26 | Exercise 10 | pwel 5399 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5591 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5102 iinin2 5101 iinun2 5096 iunin1 5095 iunin1f 32580 iunin2 5094 uniin1 32574 uniin2 32575 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5100 iundif2 5097 |
| [Enderton] p. 32 | Exercise 20 | unineq 4307 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5121 |
| [Enderton] p. 33 | Exercise 25 | iununi 5122 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5129 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7806 iunpwss 5130 |
| [Enderton] p. 36 | Definition | opthwiener 5533 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5470 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4969 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5490 rnex 7950 rnexg 7942 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5939 rnuni 6180 |
| [Enderton] p. 42 | Definition of a function | dffun7 6605 dffun8 6606 |
| [Enderton] p. 43 | Definition of function value | funfv2 7010 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6647 |
| [Enderton] p. 44 | Definition (d) | dfima2 6091 dfima3 6092 |
| [Enderton] p. 47 | Theorem 3H | fvco2 7019 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10542 ac7g 10543 df-ac 10185 dfac2 10201 dfac2a 10199 dfac2b 10200 dfac3 10190 dfac7 10202 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7283 |
| [Enderton] p. 52 | Definition | df-map 8886 |
| [Enderton] p. 53 | Exercise 21 | coass 6296 |
| [Enderton] p. 53 | Exercise 27 | dmco 6285 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6654 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6132 |
| [Enderton] p. 54 | Remark | ixpf 8978 ixpssmap 8990 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8956 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10552 ac9s 10562 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38566 erref 8783 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38569 erthi 8816 |
| [Enderton] p. 57 | Definition | df-ec 8765 |
| [Enderton] p. 58 | Definition | df-qs 8769 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8765 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5935 |
| [Enderton] p. 68 | Definition of successor | df-suc 6401 |
| [Enderton] p. 71 | Definition | df-tr 5284 dftr4 5290 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6474 unisucg 6473 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6474 unisucg 6473 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5299 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5301 trintALT 44852 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8660 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8662 onasuc 8584 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7451 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8661 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8663 onmsuc 8585 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8678 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8665 nnacom 8673 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8679 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8680 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8682 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8666 nnmsucr 8681 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8694 |
| [Enderton] p. 129 | Definition | df-en 9004 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7401 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10084 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16261 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9273 |
| [Enderton] p. 135 | Corollary 6C | php3 9275 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9272 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9319 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9321 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9234 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9240 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9207 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10249 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10250 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10245 dju1en 10241 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9411 unifi 9412 unifi2 9413 |
| [Enderton] p. 144 | Corollary 6K | undif2 4500 unfi 9238 unfi2 9376 |
| [Enderton] p. 145 | Figure 38 | ffoss 7986 |
| [Enderton] p. 145 | Definition | df-dom 9005 |
| [Enderton] p. 146 | Example 1 | domen 9021 domeng 9022 |
| [Enderton] p. 146 | Example 3 | nndomo 9296 nnsdom 9723 nnsdomg 9363 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10253 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9208 xpdom1 9137 xpdom1g 9135 xpdom2g 9134 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9214 |
| [Enderton] p. 151 | Theorem 6M | zorn 10576 zorng 10573 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10561 dfac5 10198 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10644 |
| [Enderton] p. 164 | Example | infdif 10277 |
| [Enderton] p. 168 | Definition | df-po 5607 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6509 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6441 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6508 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6449 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7875 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7816 |
| [Enderton] p. 194 | Remark | onprc 7813 |
| [Enderton] p. 194 | Exercise 16 | suc11 6502 |
| [Enderton] p. 197 | Definition | df-card 10008 |
| [Enderton] p. 197 | Theorem 7P | carden 10620 |
| [Enderton] p. 200 | Exercise 25 | tfis 7892 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9845 |
| [Enderton] p. 202 | Definition | df-r1 9833 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9855 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9936 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9675 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9926 rankprb 9920 rankpw 9912 rankpwi 9892 rankuniss 9935 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9687 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9688 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10179 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10145 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10159 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8397 |
| [Enderton] p. 222 | Definition of kard | karden 9964 kardex 9963 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8653 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8655 |
| [Enderton] p. 240 | Exercise 25 | oarec 8618 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10319 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17700 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17646 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18623 mrieqv2d 17697 mrieqvd 17696 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17701 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17706 mreexexlem2d 17703 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18629 mreexfidimd 17708 |
| [Frege1879] p. 11 | Statement | df3or2 43730 |
| [Frege1879] p. 12 | Statement | df3an2 43731 dfxor4 43728 dfxor5 43729 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43752 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43753 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43757 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43761 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43762 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43768 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43770 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43771 axfrege8 43769 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37411 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43774 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43782 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43776 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43775 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43784 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43785 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43788 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43778 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43783 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43780 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43786 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43790 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43789 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43781 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43787 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43777 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43779 rp-frege25 43767 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43772 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43792 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43773 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43793 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43796 axfrege31 43795 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43794 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43797 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43798 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43799 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43800 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43801 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43802 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43803 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43804 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43805 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43807 axfrege41 43806 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43808 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43809 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43810 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43811 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43812 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43813 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43814 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43815 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43816 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43819 ax-frege52c 43850 frege52aid 43820 frege52b 43851 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43824 ax-frege54c 43854 frege54b 43855 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43817 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3806 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43822 frege53aid 43821 frege53b 43852 frege53c 43876 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2740 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43830 frege55aid 43827 frege55b 43859 frege55c 43880 frege55cor1a 43831 frege55lem2a 43829 frege55lem2b 43858 frege55lem2c 43879 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43833 frege56aid 43832 frege56b 43860 frege56c 43881 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43837 ax-frege58b 43863 frege58bid 43864 frege58c 43883 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43835 frege57aid 43834 frege57b 43861 frege57c 43882 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3817 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43839 frege59b 43866 frege59c 43884 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43840 frege60b 43867 frege60c 43885 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43841 frege61b 43868 frege61c 43886 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43842 frege62b 43869 frege62c 43887 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43843 frege63b 43870 frege63c 43888 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43844 frege64b 43871 frege64c 43889 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43845 frege65b 43872 frege65c 43890 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43846 frege66b 43873 frege66c 43891 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43847 frege67b 43874 frege67c 43892 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43848 frege68b 43875 frege68c 43893 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43894 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43895 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43896 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43897 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43898 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43901 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43899 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43900 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43902 frege77d 43708 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43903 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43904 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43905 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43906 frege81d 43709 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43907 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43908 frege83d 43710 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43909 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43910 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43911 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43912 frege87d 43712 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43913 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43914 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43915 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43916 frege91d 43713 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43917 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43918 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43919 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43920 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43924 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43921 frege96d 43711 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43922 frege97d 43714 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43923 frege98d 43715 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43925 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43926 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43927 frege102d 43716 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43928 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43929 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43930 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43931 frege106d 43717 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43932 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43933 frege108d 43718 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43934 frege109d 43719 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43935 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43936 frege111d 43721 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43937 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43938 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43939 frege114d 43720 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43940 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43941 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43942 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43943 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43944 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43945 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43946 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43947 frege122d 43722 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43948 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43949 frege124d 43723 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43950 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43951 frege126d 43724 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43952 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43953 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43954 frege129d 43725 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43955 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43956 frege131d 43726 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43957 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43958 frege133d 43727 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46234 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46557 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46257 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46372 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46392 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46383 meadjunre 46397 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46384 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46385 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46381 meaiunle 46390 meaiunlelem 46389 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46402 meaiuninc2 46403 meaiuninc3 46406 meaiuninc3v 46405 meaiunincf 46404 meaiuninclem 46401 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46408 meaiininc2 46409 meaiininclem 46407 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46427 caragendifcl 46435 caratheodory 46449 omelesplit 46439 |
| [Fremlin1] p. 19 | Definition 113A | isome 46415 isomennd 46452 isomenndlem 46451 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46437 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46456 voncmpl 46542 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46419 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46444 carageniuncllem1 46442 carageniuncllem2 46443 caragenuncl 46434 caragenuncllem 46433 caragenunicl 46445 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46453 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46447 caratheodorylem2 46448 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46456 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46515 hoidmv1lelem1 46512 hoidmv1lelem2 46513 hoidmv1lelem3 46514 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46559 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46515 hoidmvle 46521 hoidmvlelem1 46516 hoidmvlelem2 46517 hoidmvlelem3 46518 hoidmvlelem4 46519 hoidmvlelem5 46520 hsphoidmvle2 46506 hsphoif 46497 hsphoival 46500 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46469 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46477 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46504 hoidmvn0val 46505 hoidmvval 46498 hoidmvval0 46508 hoidmvval0b 46511 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46509 hsphoidmvle 46507 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46458 df-voln 46460 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46525 ovn0 46487 ovn0lem 46486 ovnf 46484 ovnome 46494 ovnssle 46482 ovnsslelem 46481 ovnsupge0 46478 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46524 ovnhoilem1 46522 ovnhoilem2 46523 vonhoi 46588 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46541 hoidifhspf 46539 hoidifhspval 46529 hoidifhspval2 46536 hoidifhspval3 46540 hspmbl 46550 hspmbllem1 46547 hspmbllem2 46548 hspmbllem3 46549 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46542 vonmea 46495 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46493 ovnsubadd2 46567 ovnsubadd2lem 46566 ovnsubaddlem1 46491 ovnsubaddlem2 46492 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46552 hoimbl2 46586 hoimbllem 46551 hspdifhsp 46537 opnvonmbl 46555 opnvonmbllem2 46554 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46557 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46600 iccvonmbllem 46599 ioovonmbl 46598 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46606 vonicclem2 46605 vonioo 46603 vonioolem2 46602 vonn0icc 46609 vonn0icc2 46613 vonn0ioo 46608 vonn0ioo2 46611 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46610 snvonmbl 46607 vonct 46614 vonsn 46612 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46280 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46279 subsaliuncllem 46278 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46646 salpreimalegt 46630 salpreimaltle 46647 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46649 issmff 46655 issmflem 46648 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46666 issmflelem 46665 smfpreimale 46675 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46677 issmfgtlem 46676 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46617 issmf 46649 issmff 46655 issmfge 46691 issmfgelem 46690 issmfgt 46677 issmfgtlem 46676 issmfle 46666 issmflelem 46665 issmflem 46648 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46628 salpreimagtlt 46651 salpreimalelt 46650 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46691 issmfgelem 46690 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46674 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46672 cnfsmf 46661 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46688 decsmflem 46687 incsmf 46663 incsmflem 46662 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46622 pimconstlt1 46623 smfconst 46670 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46686 smfaddlem1 46684 smfaddlem2 46685 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46717 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46716 smfmullem1 46712 smfmullem2 46713 smfmullem3 46714 smfmullem4 46715 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46718 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46721 smfpimbor1lem2 46720 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46723 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46711 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46710 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46719 smfresal 46709 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46698 smflim2 46727 smflimlem1 46692 smflimlem2 46693 smflimlem3 46694 smflimlem4 46695 smflimlem5 46696 smflimlem6 46697 smflimmpt 46731 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46735 smfsuplem1 46732 smfsuplem2 46733 smfsuplem3 46734 smfsupmpt 46736 smfsupxr 46737 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46739 smfinflem 46738 smfinfmpt 46740 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46698 smflim2 46727 smflimmpt 46731 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46729 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46759 smfdivdmmbl2 46762 smfinfdmmbl 46770 smfinfdmmbllem 46769 smfsupdmmbl 46766 smfsupdmmbllem 46765 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46749 smflimsuplem2 46742 smflimsuplem6 46746 smflimsuplem7 46747 smflimsuplem8 46748 smflimsupmpt 46750 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46752 smfliminflem 46751 smfliminfmpt 46753 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46617 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46763 fsupdm2 46764 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46754 adddmmbl2 46755 finfdm 46767 finfdm2 46768 fsupdm 46763 fsupdm2 46764 muldmmbl 46756 muldmmbl2 46757 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46767 finfdm2 46768 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25590 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25633 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25643 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37658 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37661 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9707 inf1 9691 inf2 9692 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10980 enqer 10990 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10985 df-nq 10981 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10977 df-plq 10983 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7687 df-mpq 10978 df-mq 10984 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10986 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11044 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11045 ltbtwnnq 11047 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11040 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11041 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11048 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11050 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11062 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11064 |
| [Gleason] p. 122 | Definition | df-1p 11051 |
| [Gleason] p. 122 | Remark (1) | prub 11063 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11102 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11054 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11101 psslinpr 11100 supexpr 11123 suplem1pr 11121 suplem2pr 11122 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11087 addclprlem1 11085 addclprlem2 11086 df-plp 11052 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11091 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11090 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11103 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11112 ltexprlem1 11105 ltexprlem2 11106 ltexprlem3 11107 ltexprlem4 11108 ltexprlem5 11109 ltexprlem6 11110 ltexprlem7 11111 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11114 ltaprlem 11113 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11115 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11116 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11053 mulclpr 11089 mulclprlem 11088 reclem2pr 11117 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11098 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11093 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11092 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11097 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11120 reclem3pr 11118 reclem4pr 11119 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11124 enrer 11132 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11129 df-1r 11130 df-nr 11125 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11127 df-plr 11126 negexsr 11171 recexsr 11176 recexsrlem 11172 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11128 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12288 creur 12287 cru 12285 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11257 axcnre 11233 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15164 crimd 15281 crimi 15242 crre 15163 crred 15280 crrei 15241 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15166 remimd 15247 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15333 absval2d 15494 absval2i 15446 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15190 cjaddd 15269 cjaddi 15237 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15191 cjmuld 15270 cjmuli 15238 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15189 cjcjd 15248 cjcji 15220 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15188 cjreb 15172 cjrebd 15251 cjrebi 15223 cjred 15275 rere 15171 rereb 15169 rerebd 15250 rerebi 15222 rered 15273 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15197 addcjd 15261 addcji 15232 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15287 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15328 abscjd 15499 abscji 15450 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15338 abs00d 15495 abs00i 15447 absne0d 15496 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15370 releabsd 15500 releabsi 15451 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15343 absmuld 15503 absmuli 15453 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15331 sqabsaddi 15454 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15379 abstrid 15505 abstrii 15457 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14113 exp0 14116 expp1 14119 expp1d 14197 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26739 cxpaddd 26777 expadd 14155 expaddd 14198 expaddz 14157 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26748 cxpmuld 26797 expmul 14158 expmuld 14199 expmulz 14159 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26745 mulcxpd 26788 mulexp 14152 mulexpd 14211 mulexpz 14153 |
| [Gleason] p. 140 | Exercise 1 | znnen 16260 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13569 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15678 rlimadd 15689 rlimdiv 15694 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15680 rlimsub 15691 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15679 rlimmul 15692 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15683 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15629 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15650 climcj 15651 climim 15653 climre 15652 rlimabs 15655 rlimcj 15656 rlimim 15658 rlimre 15657 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11329 df-xr 11328 ltxr 13178 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15517 limsupval 15520 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15718 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15727 caucvgb 15728 caucvgbf 45405 caucvgr 15724 climcau 15719 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15864 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15931 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15384 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13879 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21381 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24374 xmet0 24373 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24390 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24381 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24383 mstri 24500 xmettri 24382 xmstri 24499 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24413 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23677 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25363 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24574 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24906 addcn2 15640 mulcn 24908 mulcn2 15642 subcn 24907 subcn2 15641 |
| [Gleason] p. 295 | Remark | bcval3 14355 bcval4 14356 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14370 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14353 df-bc 14352 |
| [Gleason] p. 296 | Remark | bcn0 14359 bcnn 14361 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15878 |
| [Gleason] p. 308 | Equation 2 | ef0 16139 |
| [Gleason] p. 308 | Equation 3 | efcj 16140 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16145 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16149 |
| [Gleason] p. 310 | Equation 14 | sinadd 16212 |
| [Gleason] p. 310 | Equation 15 | cosadd 16213 |
| [Gleason] p. 311 | Equation 17 | sincossq 16224 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16229 sinbnd 16228 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14265 sqeqori 14263 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16120 |
| [Godowski] p. 730 | Equation SF | goeqi 32305 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31700 |
| [Golan] p. 1 | Remark | srgisid 20236 |
| [Golan] p. 1 | Definition | df-srg 20214 |
| [Golan] p. 149 | Definition | df-slmd 33180 |
| [Gonshor] p. 7 | Definition | df-scut 27846 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27882 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27972 cofcut1d 27973 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27974 cofcut2d 27975 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27976 cofcutr1d 27977 cofcutr2d 27978 |
| [Gonshor] p. 13 | Definition | df-adds 28011 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28027 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28053 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28174 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28194 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28434 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28438 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28437 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 28068 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36123 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17644 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17646 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 47911 df-cllaw 47909 df-comlaw 47910 |
| [Hall] p. 2 | Section 1.2 | df-clintop 47923 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 47944 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38721 dfmembpart2 38726 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32097 riesz2 32098 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31973 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32205 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32217 elpjidm 32216 pjnmopi 32180 |
| [Halmos] p. 44 | Remark | pjinormi 31719 pjinormii 31708 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32221 pjrn 31739 pjrni 31734 pjvec 31728 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31759 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32186 hmopidmpji 32184 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32223 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32212 pjocvec 31729 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32201 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32204 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32207 pjssdif2i 32206 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31887 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1793 |
| [Hatcher] p. 25 | Definition | df-phtpc 25043 df-phtpy 25022 |
| [Hatcher] p. 26 | Definition | df-pco 25057 df-pi1 25060 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25046 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25102 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22517 df-dmatalt 48127 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47691 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47676 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47688 bgoldbtbnd 47683 bgoldbtbnd 47683 tgblthelfgott 47689 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34619 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34620 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34634 hgt750lemb 34633 hgt750leme 34635 hgt750lemf 34630 hgt750lemg 34631 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47685 tgoldbachgt 34640 tgoldbachgtALTV 47686 tgoldbachgtd 34639 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34621 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30525 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18984 grpoideu 30541 mndideu 18783 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19014 grpoinveu 30551 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19045 grpo2inv 30563 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19058 grpoinvop 30565 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19080 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1766 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1767 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1769 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32452 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32465 cdj3i 32473 cdj3lem1 32466 cdjreui 32464 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32463 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41922 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41848 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41870 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41871 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41868 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41874 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41793 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41888 |
| [Holland95] p. 204 | Definition of involution | df-srng 20863 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39460 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41485 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41438 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39890 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41334 poml4N 39910 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41425 pexmidALTN 39935 pexmidN 39926 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41490 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39080 ldualset 39081 |
| [Holland95] p. 222 | Item 1 | df-lines 39458 df-pointsN 39459 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39860 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39904 omllaw4 39202 pol1N 39867 polcon3N 39874 |
| [Holland95] p. 223 | Definition | df-psubclN 39892 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39863 |
| [Holmes] p. 40 | Definition | df-xrn 38327 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31116 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32214 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31995 eigre 31867 eigrei 31866 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31996 eigorth 31870 eigorthi 31869 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31868 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30341 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30337 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30338 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30339 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30357 frgrregorufr0 30356 frgrregorufrg 30358 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30364 frrusgrord 30373 frrusgrord0 30372 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30120 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30347 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30350 frgrwopreg2 30351 frgrwopregasn 30348 frgrwopregbsn 30349 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30353 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30367 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30370 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30118 numclwlk1 30403 numclwlk1lem1 30401 numclwlk1lem2 30402 numclwwlk1 30393 numclwwlk8 30424 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30344 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29807 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30379 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30405 numclwwlkovh0 30404 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30413 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30010 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30417 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30420 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30423 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30435 natded 30435 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30435 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30435 natded 30435 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30435 |
| [Jech] p. 4 | Definition of class | cv 1536 cvjust 2734 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10648 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10646 alephmul 10647 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10645 infmap2 10286 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9883 |
| [Jech] p. 72 | Equation 9.3 | scott0 9955 scottex 9954 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9936 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9960 |
| [Jech] p. 78 | Note | opthprc 5764 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42872 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42960 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42961 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42884 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42888 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42889 rmyp1 42890 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42891 rmym1 42892 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42882 rmx1 42883 rmxluc 42893 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42886 rmy1 42887 rmyluc 42894 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42896 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42897 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42917 jm2.17b 42918 jm2.17c 42919 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42950 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42954 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42945 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42920 jm2.24nn 42916 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42959 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42965 rmygeid 42921 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 42977 |
| [Juillerat] p. 11 | Section *5 | etransc 46204 etransclem47 46202 etransclem48 46203 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46199 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46201 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46187 |
| [Juillerat] p. 13 | Proof | etransclem35 46190 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46193 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46179 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46196 |
| [Juillerat] p. 14 | Proof | etransclem23 46178 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1967 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2011 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2016 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2006 cbvaliw 2005 wl-cbvmotv 37467 wl-motae 37469 wl-moteq 37468 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1995 spimw 1970 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2032 spw 2033 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31548 chabs1i 31550 chabs2 31549 chabs2i 31551 chjass 31565 chjassi 31518 latabs1 18545 latabs2 18546 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32370 ela 32371 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32315 cvrval2 39230 |
| [Kalmbach] p. 16 | Definition | df-ol 39134 df-oml 39135 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31616 cmbri 31622 cmtvalN 39167 df-cm 31615 df-cmtN 39133 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39203 pjoml5 31645 pjoml5i 31620 |
| [Kalmbach] p. 22 | Definition | pjoml2 31643 pjoml2i 31617 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31646 cmcmi 31624 cmcmii 31629 cmtcomN 39205 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39201 omlsi 31436 pjoml 31468 pjomli 31467 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39200 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31628 cmcm3 31647 cmcm3i 31626 cmcm3ii 31631 cmcm4i 31627 cmt3N 39207 cmt4N 39208 cmtbr2N 39209 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31640 cmbr3i 31632 cmtbr3N 39210 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31650 fh1i 31653 fh2 31651 fh2i 31654 omlfh1N 39214 |
| [Kalmbach] p. 65 | Remark | chjatom 32389 chslej 31530 chsleji 31490 shslej 31412 shsleji 31402 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31527 chocini 31486 chsupcl 31372 chsupval2 31442 h0elch 31287 helch 31275 hsupval2 31441 ocin 31328 ococss 31325 shococss 31326 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31344 |
| [Kalmbach] p. 66 | Remark | df-pjh 31427 pjssmi 32197 pjssmii 31713 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31677 osumi 31674 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32232 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32432 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32342 |
| [Kalmbach] p. 140 | Remark | hatomic 32392 hatomici 32391 hatomistici 32394 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39275 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32413 lsatexch 38999 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32387 cvlcvr1 39295 cvr1 39367 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32406 cvexchi 32401 cvrexch 39377 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32396 hlrelat 39359 hlrelat5N 39358 lrelat 38970 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21166 lsmsatcv 38966 spansncv 31685 spansncvi 31684 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 38985 spansncv2 32325 |
| [Kalmbach] p. 266 | Definition | df-st 32243 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31881 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10715 fpwwe2 10712 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10716 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10723 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10718 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10720 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10733 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10737 gchxpidm 10738 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10749 gchhar 10748 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10284 unxpwdom 9658 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10739 |
| [Kreyszig] p. 3 | Property M1 | metcl 24363 xmetcl 24362 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24370 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24606 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 12011 muleqadd 11934 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24469 |
| [Kreyszig] p. 19 | Remark | mopntopon 24470 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24532 mopnm 24475 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24530 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24535 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24576 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23287 lmmbr 25311 lmmbr2 25312 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23409 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25366 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25329 iscmet2 25347 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25369 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23490 metelcls 25358 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25359 metcld2 25360 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25151 lmodvneg1 20925 nvinv 30671 vcm 30608 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25147 lmod0vs 20915 slmd0vs 33203 vc0 30606 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20916 slmdvs0 33204 vcz 30607 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30723 ngpmet 24637 nrmmetd 24608 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30718 imsdval2 30719 ncvspds 25214 ngpds 24638 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24623 nvnd 30720 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24652 nmge0 24651 nvge0 30705 nvz 30701 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24658 nvabs 30704 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30833 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30777 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30839 blocni 30837 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30838 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25257 ipeq0 21679 ipz 30751 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25269 pythi 30882 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30886 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25291 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15904 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25489 minveco 30916 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30782 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25382 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30905 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32155 leopg 32154 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32173 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30950 |
| [Kulpa] p. 547 | Theorem | poimir 37613 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37612 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37611 |
| [Kulpa] p. 548 | Theorem | broucube 37614 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37606 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37607 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2391 axnul 5323 |
| [Kunen] p. 11 | Axiom 3 | axnul 5323 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7995 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8896 mapvalg 8894 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10591 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7979 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9833 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9875 r1elssi 9874 |
| [Kunen] p. 107 | Exercise 4 | rankop 9927 rankopb 9921 rankuni 9932 rankxplim 9948 rankxpsuc 9951 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44910 |
| [Kunen2] p. 112 | Part of Corollaray II.2.5 | wfaxext 44911 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 5027 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33675 |
| [Lang] p. | Definition | df-rn 5711 |
| [Lang] p. 3 | Statement | lidrideqd 18707 mndbn0 18788 |
| [Lang] p. 3 | Definition | df-mnd 18773 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18725 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18876 |
| [Lang] p. 5 | Equation | gsumreidx 19959 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 47905 |
| [Lang] p. 6 | Example | nn0mnd 47902 |
| [Lang] p. 6 | Equation | gsumxp2 20022 |
| [Lang] p. 6 | Statement | cycsubm 19242 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19120 |
| [Lang] p. 6 | Observation | mndlsmidm 19712 |
| [Lang] p. 7 | Definition | dfgrp2e 19003 |
| [Lang] p. 30 | Definition | df-tocyc 33100 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33145 |
| [Lang] p. 32 | Property (b) | cyc3conja 33150 cycpmconjv 33135 |
| [Lang] p. 53 | Definition | df-cat 17726 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18164 cat1lem 18163 |
| [Lang] p. 54 | Definition | df-iso 17810 |
| [Lang] p. 57 | Definition | df-inito 18051 df-termo 18052 |
| [Lang] p. 58 | Example | irinitoringc 21513 |
| [Lang] p. 58 | Statement | initoeu1 18078 termoeu1 18085 |
| [Lang] p. 62 | Definition | df-func 17922 |
| [Lang] p. 65 | Definition | df-nat 18011 |
| [Lang] p. 91 | Note | df-ringc 20668 |
| [Lang] p. 92 | Statement | mxidlprm 33463 |
| [Lang] p. 92 | Definition | isprmidlc 33440 |
| [Lang] p. 128 | Remark | dsmmlmod 21788 |
| [Lang] p. 129 | Proof | lincscm 48159 lincscmcl 48161 lincsum 48158 lincsumcl 48160 |
| [Lang] p. 129 | Statement | lincolss 48163 |
| [Lang] p. 129 | Observation | dsmmfi 21781 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33640 qusdimsum 33641 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33620 |
| [Lang] p. 147 | Definition | snlindsntor 48200 |
| [Lang] p. 504 | Statement | mat1 22474 matring 22470 |
| [Lang] p. 504 | Definition | df-mamu 22416 |
| [Lang] p. 505 | Statement | mamuass 22427 mamutpos 22485 matassa 22471 mattposvs 22482 tposmap 22484 |
| [Lang] p. 513 | Definition | mdet1 22628 mdetf 22622 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22718 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22614 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22638 |
| [Lang] p. 515 | Definition | df-minmar1 22662 smadiadetr 22702 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22637 mdetralt 22635 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22650 |
| [Lang] p. 518 | Definition | df-madu 22661 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22672 madurid 22671 matinv 22704 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22917 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33674 fedgmul 33644 |
| [Lang], p. 561 | Remark | chpmatply1 22859 |
| [Lang], p. 561 | Definition | df-chpmat 22854 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44303 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44298 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44304 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5323 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2718 |
| [Levy] p. 59 | Definition | df-ttrcl 9777 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9820 |
| [Levy] p. 338 | Axiom | df-clel 2819 df-cleq 2732 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2819 df-cleq 2732 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2718 |
| [Levy] p. 358 | Axiom | df-clab 2718 |
| [Levy58] p. 2 | Definition I | isfin1-3 10455 |
| [Levy58] p. 2 | Definition II | df-fin2 10355 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10354 |
| [Levy58] p. 2 | Definition III | df-fin3 10357 |
| [Levy58] p. 3 | Definition V | df-fin5 10358 |
| [Levy58] p. 3 | Definition IV | df-fin4 10356 |
| [Levy58] p. 4 | Definition VI | df-fin6 10359 |
| [Levy58] p. 4 | Definition VII | df-fin7 10360 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10484 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27749 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27760 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27792 nosupbnd1 27777 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27794 nosupbnd2 27779 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27798 noetasuplem4 27799 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27795 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1766 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1767 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1769 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32440 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32444 mdsymi 32443 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32438 mdsymlem6 32440 mdsymlem7 32441 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32442 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32345 ssdmd2 32346 ssmd1 32343 ssmd2 32344 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32341 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32313 df-md 32312 mdbr 32326 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32363 mdslj1i 32351 mdslj2i 32352 mdslle1i 32349 mdslle2i 32350 mdslmd1i 32361 mdslmd2i 32362 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32353 mdsl2bi 32355 mdsl2i 32354 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32367 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32364 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32365 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32342 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32347 mdsl3 32348 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32366 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32461 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39277 hlrelat1 39357 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 38995 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32368 cvmdi 32356 cvnbtwn4 32321 cvrnbtwn4 39235 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32369 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39296 cvp 32407 cvrp 39373 lcvp 38996 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32431 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32430 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39289 hlexch4N 39349 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32433 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39400 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39706 atpsubN 39710 df-pointsN 39459 pointpsubN 39708 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39461 pmap11 39719 pmaple 39718 pmapsub 39725 pmapval 39714 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39722 pmap1N 39724 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39727 pmapglb2N 39728 pmapglb2xN 39729 pmapglbx 39726 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39809 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39434 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39753 paddclN 39799 paddidm 39798 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39435 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39795 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39434 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39435 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19717 lsmmod2 19718 lssats 38968 shatomici 32390 shatomistici 32393 shmodi 31422 shmodsi 31421 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32332 mdsymlem7 32441 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31621 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31525 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32447 |
| [Margaris] p. 40 | Rule C | exlimiv 1929 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1778 df-or 847 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30432 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44886 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44887 |
| [Margaris] p. 79 | Rule C | exinst01 44596 exinst11 44597 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1976 19.2g 2189 r19.2z 4518 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2203 rr19.3v 3680 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2160 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1824 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1779 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2182 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2206 19.9h 2290 exlimd 2219 exlimdh 2294 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2163 excomim 2164 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2331 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30433 conventions-labels 30433 conventions-labels 30433 conventions-labels 30433 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1825 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44347 albi 1816 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2226 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2227 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44349 exbi 1845 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2230 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44346 2alimdv 1917 alimd 2213 alimdh 1815 alimdv 1915 ax-4 1807 ralimdaa 3266 ralimdv 3175 ralimdva 3173 ralimdvva 3212 sbcimdv 3878 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2208 19.21h 2291 19.21t 2207 19.21vv 44345 alrimd 2216 alrimdd 2215 alrimdh 1862 alrimdv 1928 alrimi 2214 alrimih 1822 alrimiv 1926 alrimivv 1927 hbralrimi 3150 r19.21be 3258 r19.21bi 3257 ralrimd 3270 ralrimdv 3158 ralrimdva 3160 ralrimdvv 3209 ralrimdvva 3217 ralrimi 3263 ralrimia 3264 ralrimiv 3151 ralrimiva 3152 ralrimivv 3206 ralrimivva 3208 ralrimivvva 3211 ralrimivw 3156 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44348 2eximdv 1918 exim 1832 eximd 2217 eximdh 1863 eximdv 1916 rexim 3093 reximd2a 3275 reximdai 3267 reximdd 45053 reximddv 3177 reximddv2 3221 reximddv3 3178 reximdv 3176 reximdv2 3170 reximdva 3174 reximdvai 3171 reximdvva 3213 reximi2 3085 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2212 19.23bi 2192 19.23h 2292 19.23t 2211 exlimdv 1932 exlimdvv 1933 exlimexi 44495 exlimiv 1929 exlimivv 1931 rexlimd3 45046 rexlimdv 3159 rexlimdv3a 3165 rexlimdva 3161 rexlimdva2 3163 rexlimdvaa 3162 rexlimdvv 3218 rexlimdvva 3219 rexlimdvvva 3220 rexlimdvw 3166 rexlimiv 3154 rexlimiva 3153 rexlimivv 3207 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1985 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1879 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1869 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2228 r19.27z 4528 r19.27zv 4529 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2229 19.28vv 44355 r19.28z 4521 r19.28zf 45064 r19.28zv 4524 rr19.28v 3681 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1872 r19.29d2r 3146 r19.29imd 3124 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1880 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2235 19.31vv 44353 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2234 r19.32 47013 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44351 19.33 1883 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1986 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1876 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2231 19.36vv 44352 r19.36zv 4530 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2233 19.37vv 44354 r19.37zv 4525 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1837 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1984 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1886 19.40 1885 r19.40 3125 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2236 19.41rg 44521 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2237 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1881 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2238 r19.44zv 4527 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2239 r19.45zv 4526 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2613 |
| [Mayet] p. 370 | Remark | jpi 32302 largei 32299 stri 32289 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32244 ishst 32246 |
| [Mayet3] p. 10 | Theorem | hstrbi 32298 hstri 32297 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31760 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31761 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32310 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31364 chsupcl 31372 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32392 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32386 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32413 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39940 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18557 latj32 18555 latjass 18553 |
| [Megill] p. 444 | Axiom C5 | ax-5 1909 ax5ALT 38863 |
| [Megill] p. 444 | Section 7 | conventions 30432 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38857 ax-c11n 38844 axc11n 2434 |
| [Megill] p. 446 | Lemma L17 | equtrr 2021 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38852 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38884 hbnae 2440 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2489 sbid 2256 sbidd-misc 48811 sbidd 48810 |
| [Megill] p. 448 | Remark 9.6 | axc14 2471 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38840 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38839 sp 2184 |
| [Megill] p. 448 | Scheme C6' | ax-11 2158 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38841 |
| [Megill] p. 448 | Scheme C8' | ax-7 2007 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38846 |
| [Megill] p. 448 | Scheme C10' | ax-6 1967 ax-c10 38842 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38843 |
| [Megill] p. 448 | Scheme C12' | ax-8 2110 |
| [Megill] p. 448 | Scheme C13' | ax-9 2118 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38847 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38845 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38848 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38860 dral1 2447 dral2-o 38886 dral2 2446 drex1 2449 drex2 2450 drsb1 2503 drsb2 2267 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2174 sbequ 2083 sbid2v 2517 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38853 hba1 2297 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46807 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3901 rspsbca 3902 stdpc4 2068 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38840 ra4 3908 stdpc5 2209 |
| [Mendelson] p. 81 | Rule C | exlimiv 1929 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2027 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2251 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3802 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5533 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4421 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4422 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4296 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4353 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4297 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4164 |
| [Mendelson] p. 231 | Definition of union | dfun3 4295 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5471 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4928 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5589 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4640 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5590 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4955 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5850 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6299 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7810 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6401 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8651 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9206 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9121 xpsneng 9122 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9129 xpcomeng 9130 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9132 |
| [Mendelson] p. 255 | Definition | brsdom 9035 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9124 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8888 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9102 mapsnend 9101 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9212 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9211 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8940 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9105 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9125 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10248 djucomen 10247 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10252 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10246 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8587 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8614 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10628 |
| [Mendelson] p. 281 | Definition | df-r1 9833 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9882 |
| [Mendelson] p. 287 | Axiom system MK | ru 3802 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30291 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30326 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30328 vdgn1frgrv3 30329 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30330 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30323 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30316 2pthfrgrrn 30314 2pthfrgrrn2 30315 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31284 |
| [Monk1] p. 22 | Remark | conventions 30432 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30432 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4260 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5806 ssrelf 32637 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5808 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5229 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6293 coi2 6294 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5945 rn0 5950 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6173 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5718 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5953 rnxp 6201 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5798 xp0 6189 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6106 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6103 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7954 imaexALTV 38286 imaexg 7953 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6100 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7109 funfvop 7083 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6976 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6987 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6624 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7292 dff13f 7293 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7256 funrnex 7994 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7284 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6258 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4988 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8047 df-1st 8030 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8048 df-2nd 8031 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9923 ranksnb 9896 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9924 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9925 rankunb 9919 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9907 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9833 r1val2 9906 |
| [Monk1] p. 117 | Lemma | zorn2 10575 zorn2g 10572 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10055 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10630 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10050 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1807 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2007 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2178 ax-c15 38845 ax12v2 2180 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38840 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2158 |
| [Monk2] p. 109 | Lemma 15 | equvini 2463 equvinv 2028 eqvinop 5507 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1909 ax5ALT 38863 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2141 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2158 |
| [Monk2] p. 114 | Lemma 21 | sp 2184 |
| [Monk2] p. 114 | Lemma 22 | axc4 2325 hba1-o 38853 hba1 2297 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2154 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2177 nfra2 3384 nfra2w 3305 |
| [Moore] p. 53 | Part I | df-mre 17644 |
| [Munkres] p. 77 | Example 2 | distop 23023 indistop 23030 indistopon 23029 |
| [Munkres] p. 77 | Example 3 | fctop 23032 fctop2 23033 |
| [Munkres] p. 77 | Example 4 | cctop 23034 |
| [Munkres] p. 78 | Definition of basis | df-bases 22974 isbasis3g 22977 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17503 tgval2 22984 |
| [Munkres] p. 79 | Remark | tgcl 22997 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22991 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23015 tgss3 23014 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23016 basgen2 23017 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37315 topdifinfeq 37316 topdifinffin 37314 topdifinfindis 37312 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23189 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23067 topcld 23064 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23068 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23070 |
| [Munkres] p. 94 | Definition of closure | clsval 23066 |
| [Munkres] p. 94 | Definition of interior | ntrval 23065 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23104 elcls 23102 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23112 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23177 neindisj 23146 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23179 |
| [Munkres] p. 97 | Definition of limit point | islp2 23174 lpval 23168 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23344 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23256 iscn 23264 iscn2 23267 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23309 cncnp2 23310 cncnpi 23307 df-cnp 23257 iscnp 23266 iscnp2 23268 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24577 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25364 |
| [Nathanson] p. 123 | Remark | reprgt 34598 reprinfz1 34599 reprlt 34596 |
| [Nathanson] p. 123 | Definition | df-repr 34586 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34618 |
| [Nathanson] p. 123 | Proposition | breprexp 34610 breprexpnat 34611 itgexpif 34583 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32136 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47684 |
| [Pfenning] p. 17 | Definition XM | natded 30435 |
| [Pfenning] p. 17 | Definition NNC | natded 30435 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30435 |
| [Pfenning] p. 18 | Rule" | natded 30435 |
| [Pfenning] p. 18 | Definition /\I | natded 30435 |
| [Pfenning] p. 18 | Definition ` `E | natded 30435 natded 30435 natded 30435 natded 30435 natded 30435 |
| [Pfenning] p. 18 | Definition ` `I | natded 30435 natded 30435 natded 30435 natded 30435 natded 30435 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30435 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30435 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30435 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30435 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30435 |
| [Pfenning] p. 127 | Definition =E | natded 30435 |
| [Pfenning] p. 127 | Definition =I | natded 30435 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25255 df-dip 30733 dip0l 30750 ip0l 21677 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25296 ipval 30735 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30746 ipcj 21675 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25258 dipdir 30874 ipdir 21680 ipdiri 30862 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30742 nmsq 25247 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30857 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30859 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30860 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25264 dipass 30877 ipass 21686 ipassi 30873 |
| [Prugovecki] p. 186 | Definition of bra | braval 31976 df-bra 31882 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31883 kbval 31986 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32414 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39845 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32428 atcvat4i 32429 cvrat3 39399 cvrat4 39400 lsatcvat3 39008 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32314 cvrval 39225 df-cv 32311 df-lcv 38975 lspsncv0 21171 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39857 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39858 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2718 rabid 3465 rabidd 45060 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2283 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2732 |
| [Quine] p. 19 | Definition 2.9 | conventions 30432 df-v 3490 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2884 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2881 abid2f 2942 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2277 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2085 sbalex 2243 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2819 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2740 eqid1 30499 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2747 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3805 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3806 dfsbcq2 3807 |
| [Quine] p. 43 | Theorem 6.8 | vex 3492 |
| [Quine] p. 43 | Theorem 6.9 | isset 3502 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3604 spcgv 3609 spcimgf 3562 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3817 spsbcd 3818 |
| [Quine] p. 44 | Theorem 6.12 | elex 3509 |
| [Quine] p. 44 | Theorem 6.13 | elab 3694 elabg 3690 elabgf 3688 |
| [Quine] p. 44 | Theorem 6.14 | noel 4360 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4742 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4651 df-sn 4649 |
| [Quine] p. 49 | Theorem 7.4 | snss 4810 snssg 4808 |
| [Quine] p. 49 | Theorem 7.5 | prss 4845 prssg 4844 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4787 prid1g 4785 prid2 4788 prid2g 4786 snid 4684 snidg 4682 |
| [Quine] p. 51 | Theorem 7.12 | snex 5451 |
| [Quine] p. 51 | Theorem 7.13 | prex 5452 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4950 unisnALT 44897 unisng 4949 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4954 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4961 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4959 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6540 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47001 dfiota2 6526 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47010 iotaval 6544 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6551 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6546 |
| [Quine] p. 58 | Definition 9.1 | df-op 4655 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5544 opabidw 5543 opelopab 5561 opelopaba 5555 opelopabaf 5563 opelopabf 5564 opelopabg 5557 opelopabga 5552 opelopabgf 5559 oprabid 7480 oprabidw 7479 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5706 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5708 |
| [Quine] p. 64 | Definition 9.15 | df-id 5593 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6643 |
| [Quine] p. 65 | Theorem 10.4 | funi 6610 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6631 funsng 6629 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6575 |
| [Quine] p. 65 | Definition 10.2 | args 6122 dffv4 6917 |
| [Quine] p. 68 | Definition 10.11 | conventions 30432 df-fv 6581 fv2 6915 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14321 nn0opth2i 14320 nn0opthi 14319 omopthi 8717 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8466 |
| [Quine] p. 232 | Equation i | carddom 10623 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6666 funimaexg 6664 |
| [Quine] p. 331 | Axiom system NF | ru 3802 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31116 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30733 polid 31191 polid2i 31189 polidi 31190 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30845 |
| [ReedSimon] p. 195 | Remark | lnophm 32051 lnophmi 32050 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32164 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32166 leopmuli 32165 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32169 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31884 leoppos 32158 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32168 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32157 |
| [Roman] p. 4 | Definition | df-dmat 22517 df-dmatalt 48127 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20180 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20262 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48214 |
| [Roman] p. 112 | Note | isldepslvec2 48214 ldepsnlinc 48237 zlmodzxznm 48226 |
| [Roman] p. 112 | Example | zlmodzxzequa 48225 zlmodzxzequap 48228 zlmodzxzldep 48233 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22917 |
| [Rosenlicht] p. 80 | Theorem | heicant 37615 |
| [Rosser] p. 281 | Definition | df-op 4655 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34622 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34623 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48091 pmtr3ncom 19517 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19513 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19456 cayleyth 19457 |
| [Rudin] p. 164 | Equation 27 | efcan 16144 |
| [Rudin] p. 164 | Equation 30 | efzval 16150 |
| [Rudin] p. 167 | Equation 48 | absefi 16244 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1769 |
| [Sanford] p. 39 | Rule 4 | mptxor 1767 |
| [Sanford] p. 40 | Rule 1 | mptnan 1766 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6147 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6150 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6144 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6142 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17644 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17645 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17645 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17647 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10206 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43019 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10515 axdc3 10523 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20264 isrngo 37857 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31574 |
| [Schechter] p. 276 | Definition of span | df-span 31341 spanval 31365 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23021 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6420 onelord 43212 ordelon 6419 ordelord 6417 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43213 sucidg 6476 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6449 onsuc 7847 ord0 6448 ordsuci 7844 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43214 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5287 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 42985 elon2 6406 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6401 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5602 epelg 5600 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9666 epirron 43215 ordirr 6413 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43217 oneptr 43216 ontr1 6441 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 43219 oneptri 43218 ordtri3or 6427 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8557 ord0eln0 6450 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6462 onsucss 43228 trsucss 6483 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7854 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6489 ordnbtwn 6488 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43230 ordnexbtwnsuc 43229 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10470 onsucf1lem 43231 onsucf1o 43234 onsucf1olem 43232 onsucrn 43233 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43235 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7882 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43224 ordne0gt0 43223 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43226 limnsuc 43227 onsucelab 43225 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9712 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7897 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9715 ordom 7913 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9716 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8696 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7815 ssorduni 7814 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8587 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9719 limom 7919 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8522 df1o2 8529 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8572 oa0suclim 43237 oalim 8588 oasuc 8580 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8573 om0suclim 43238 omlim 8589 omsuc 8582 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8578 oe0m1 8577 oe0suclim 43239 oelim 8590 oesuc 8583 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43190 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43241 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43242 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43243 limexissupab 43245 limiun 43244 limuni 6456 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8594 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8598 om1om1r 43246 om1r 8599 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8591 oaomoecl 43240 oecl 8593 omcl 8592 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43192 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8600 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8601 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43247 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43248 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8667 nnamecl 43249 nnecl 8669 nnmcl 8668 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43250 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8608 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8609 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8616 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43252 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43253 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43255 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8615 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43259 omword1 8629 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43258 oaordnrex 43257 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43254 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43260 omword2 8630 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43261 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43262 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43263 omordi 8622 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8624 omord2com 43264 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43265 df-2o 8523 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43268 oewordi 8647 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43269 oeworde 8649 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43270 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43271 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43267 omnord1ex 43266 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43272 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43274 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43278 oenord1ex 43277 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43279 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8617 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43273 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8635 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8636 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43281 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8653 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43282 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43283 cantnfub2 43284 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43287 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28947 axtgcgrrflx 28488 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28948 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28949 axtgcgrid 28489 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28474 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28960 axtgsegcon 28490 df-trkgcb 28476 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28971 axtg5seg 28491 df-trkgcb 28476 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28972 axtgbtwnid 28492 df-trkgb 28475 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28974 axtgpasch 28493 df-trkgb 28475 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28993 df-trkg2d 34642 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28496 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28497 df-trkg2d 34642 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28996 axtgeucl 28498 df-trkge 28477 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29009 axtgcont 28495 axtgcont1 28494 df-trkgb 28475 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35951 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35953 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35956 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35960 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35961 tgcgrcomimp 28503 tgcgrcoml 28505 tgcgrcomr 28504 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35966 tgcgrtriv 28510 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35970 tg5segofs 34650 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34647 df-ofs 35947 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35972 tgcgrextend 28511 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35974 tgsegconeq 28512 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 35986 btwntriv2 35976 tgbtwntriv2 28513 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 35977 tgbtwncom 28514 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 35980 tgbtwntriv1 28517 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 35981 tgbtwnswapid 28518 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 35987 btwnintr 35983 tgbtwnexch2 28522 tgbtwnintr 28519 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 35989 btwnexch3 35984 tgbtwnexch 28524 tgbtwnexch3 28520 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 35988 tgbtwnouttr 28523 tgbtwnouttr2 28521 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28992 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 35991 tgbtwndiff 28532 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28525 trisegint 35992 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36008 tgifscgr 28534 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28584 colrot1 28585 colrot2 28586 lncom 28648 lnrot1 28649 lnrot2 28650 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36004 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36009 tgcgrsub 28535 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36019 tgcgrxfr 28544 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28543 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36005 df-cgrg 28537 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28537 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36020 tgbtwnxfr 28556 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36026 colinearperm2 36028 colinearperm3 36027 colinearperm4 36029 colinearperm5 36030 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28559 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36003 tgellng 28579 tglng 28572 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36031 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36039 lnxfr 28592 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36040 lnext 28593 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36044 tgfscgr 28594 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36045 lncgr 28595 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36006 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36047 lnid 28596 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36048 tgidinside 28597 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36065 tgbtwnconn1 28601 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36066 tgbtwnconn2 28602 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36067 tgbtwnconn3 28603 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36073 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36071 legov 28611 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28612 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28625 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36074 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36076 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36078 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36079 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36080 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36077 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36082 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28613 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28615 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28616 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28617 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28618 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36089 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36090 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36085 df-outsideof 36084 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36086 ishlg 28628 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28633 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28635 outsideofrflx 36091 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28629 hlcomd 28630 outsideofcom 36092 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28636 outsideoftr 36093 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28644 outsideofeu 36095 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36102 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36103 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36096 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36111 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36112 tglineelsb2 28658 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36114 linerflx1 36113 linerflx2 36115 tglinecom 28661 tglinerflx1 28659 tglinerflx2 28660 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36117 tglinethru 28662 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36101 tglng 28572 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28620 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36120 tglinethrueu 28665 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36121 tglineineq 28669 tglineinteq 28671 tglineintmo 28668 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28675 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28676 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28677 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28692 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28688 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28680 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28679 ismir 28685 mirbtwn 28684 mircgr 28683 mirfv 28682 mirval 28681 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28690 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28691 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28692 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28695 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28696 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28701 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28698 mirbtwni 28697 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28699 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28711 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28715 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28712 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28713 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28714 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28717 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28718 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28724 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28720 israg 28723 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28725 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28726 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28728 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28729 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28730 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28731 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28732 ragncol 28735 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28733 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28739 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28743 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28740 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28722 isperp 28738 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28741 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28748 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28756 colperpexlem2 28757 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28759 colperpexlem3 28758 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28764 midex 28763 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28761 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28770 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28765 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28774 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28777 opphllem6 28778 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28780 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28493 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28781 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28789 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28784 hpgbr 28786 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28791 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28790 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28792 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28793 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28794 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28795 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28796 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28810 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28800 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28814 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28815 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28816 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28817 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28818 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28821 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28823 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28801 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28824 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28827 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28828 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28829 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28830 trgcopyeu 28832 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28856 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28835 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28844 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28842 cgrahl2 28843 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28845 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28846 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28848 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28849 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28852 cgrahl 28853 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28857 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28858 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28859 acopyeu 28860 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28867 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28871 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28864 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28879 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28872 isleag 28873 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28881 tgsas1 28880 tgsas2 28882 tgsas3 28883 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28885 tgasa1 28884 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28886 tgsss2 28887 tgsss3 28888 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27333 dchrsum 27331 dchrsum2 27330 sumdchr 27334 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27335 sum2dchr 27336 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20110 ablfacrp2 20111 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27278 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27279 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27286 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27544 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27547 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27601 vmalogdivsum2 27600 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27591 dirith2 27590 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27589 rpvmasum 27588 rpvmasum2 27574 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27549 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27587 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27554 dchrisumlem1 27551 dchrisumlem2 27552 dchrisumlem3 27553 dchrisumlema 27550 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27557 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27586 dchrmusumlem 27584 dchrvmasumlem 27585 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27556 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27558 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27582 dchrisum0re 27575 dchrisumn0 27583 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27568 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27572 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27573 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27628 pntrsumbnd2 27629 pntrsumo1 27627 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27592 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27594 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27596 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27599 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27604 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27605 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27610 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27612 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27613 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27621 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27622 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27619 selberg3lem2 27620 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27623 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27617 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27630 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27631 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27632 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27646 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27658 pntlemb 27659 pntlemc 27657 pntlemd 27656 pntlemg 27660 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27658 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27650 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27655 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27658 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27671 pntleml 27673 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4325 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4428 dif0 4400 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4515 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4498 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4316 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4317 |
| [Stoll] p. 20 | Remark | invdif 4298 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4657 |
| [Stoll] p. 43 | Definition | uniiun 5081 |
| [Stoll] p. 44 | Definition | intiin 5082 |
| [Stoll] p. 45 | Definition | df-iin 5018 |
| [Stoll] p. 45 | Definition indexed union | df-iun 5017 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4325 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44304 |
| [Suppes] p. 22 | Theorem 2 | eq0 4373 eq0f 4370 |
| [Suppes] p. 22 | Theorem 4 | eqss 4024 eqssd 4026 eqssi 4025 |
| [Suppes] p. 23 | Theorem 5 | ss0 4425 ss0b 4424 |
| [Suppes] p. 23 | Theorem 6 | sstr 4017 sstrALT2 44806 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4126 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4127 |
| [Suppes] p. 23 | Theorem 9 | psstr 4130 |
| [Suppes] p. 23 | Theorem 10 | pssss 4121 |
| [Suppes] p. 25 | Theorem 12 | elin 3992 elun 4176 |
| [Suppes] p. 26 | Theorem 15 | inidm 4248 |
| [Suppes] p. 26 | Theorem 16 | in0 4418 |
| [Suppes] p. 27 | Theorem 23 | unidm 4180 |
| [Suppes] p. 27 | Theorem 24 | un0 4417 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4201 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4209 |
| [Suppes] p. 27 | Theorem 27 | unss 4213 |
| [Suppes] p. 27 | Theorem 28 | indir 4305 |
| [Suppes] p. 27 | Theorem 29 | undir 4306 |
| [Suppes] p. 28 | Theorem 32 | difid 4398 |
| [Suppes] p. 29 | Theorem 33 | difin 4291 |
| [Suppes] p. 29 | Theorem 34 | indif 4299 |
| [Suppes] p. 29 | Theorem 35 | undif1 4499 |
| [Suppes] p. 29 | Theorem 36 | difun2 4504 |
| [Suppes] p. 29 | Theorem 37 | difin0 4497 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4495 |
| [Suppes] p. 29 | Theorem 39 | difundi 4309 |
| [Suppes] p. 29 | Theorem 40 | difindi 4311 |
| [Suppes] p. 30 | Theorem 41 | nalset 5331 |
| [Suppes] p. 39 | Theorem 61 | uniss 4939 |
| [Suppes] p. 39 | Theorem 65 | uniop 5534 |
| [Suppes] p. 41 | Theorem 70 | intsn 5008 |
| [Suppes] p. 42 | Theorem 71 | intpr 5006 intprg 5005 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5491 |
| [Suppes] p. 42 | Theorem 78 | intun 5004 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 5056 dfiun2g 5053 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 5057 |
| [Suppes] p. 47 | Theorem 86 | elpw 4626 elpw2 5352 elpw2g 5351 elpwg 4625 elpwgdedVD 44888 |
| [Suppes] p. 47 | Theorem 87 | pwid 4644 |
| [Suppes] p. 47 | Theorem 89 | pw0 4837 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4838 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5715 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5858 xpindir 5859 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5768 xpundir 5769 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9665 |
| [Suppes] p. 58 | Theorem 2 | relss 5805 |
| [Suppes] p. 59 | Theorem 4 | eldm 5925 eldm2 5926 eldm2g 5924 eldmg 5923 |
| [Suppes] p. 59 | Definition 3 | df-dm 5710 |
| [Suppes] p. 60 | Theorem 6 | dmin 5936 |
| [Suppes] p. 60 | Theorem 8 | rnun 6177 |
| [Suppes] p. 60 | Theorem 9 | rnin 6178 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5913 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5907 brcnvg 5904 |
| [Suppes] p. 62 | Equation 5 | elcnv 5901 elcnv2 5902 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6134 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6176 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6174 |
| [Suppes] p. 63 | Definition | dftrrels2 38531 |
| [Suppes] p. 63 | Theorem 20 | co02 6291 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5997 |
| [Suppes] p. 63 | Definition 7 | df-co 5709 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5910 |
| [Suppes] p. 64 | Theorem 27 | coass 6296 |
| [Suppes] p. 65 | Theorem 31 | resundi 6023 |
| [Suppes] p. 65 | Theorem 34 | elima 6094 elima2 6095 elima3 6096 elimag 6093 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6181 |
| [Suppes] p. 66 | Theorem 40 | dminss 6184 |
| [Suppes] p. 66 | Theorem 41 | imainss 6185 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6188 |
| [Suppes] p. 81 | Definition 34 | dfec2 8766 |
| [Suppes] p. 82 | Theorem 72 | elec 8809 elecALTV 38222 elecg 8807 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38567 erth 8814 erth2 8815 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38570 erdisj 8817 |
| [Suppes] p. 83 | Definition 35, | df-parts 38721 dfmembpart2 38726 |
| [Suppes] p. 89 | Theorem 96 | map0b 8941 |
| [Suppes] p. 89 | Theorem 97 | map0 8945 map0g 8942 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8946 mapsnd 8944 |
| [Suppes] p. 89 | Theorem 99 | mapss 8947 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10137 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10136 |
| [Suppes] p. 92 | Theorem 1 | enref 9045 enrefg 9044 |
| [Suppes] p. 92 | Theorem 2 | ensym 9063 ensymb 9062 ensymi 9064 |
| [Suppes] p. 92 | Theorem 3 | entr 9066 |
| [Suppes] p. 92 | Theorem 4 | unen 9112 |
| [Suppes] p. 94 | Theorem 15 | endom 9039 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9060 |
| [Suppes] p. 94 | Theorem 17 | domtr 9067 |
| [Suppes] p. 95 | Theorem 18 | sbth 9159 |
| [Suppes] p. 97 | Theorem 23 | canth2 9196 canth2g 9197 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9163 df-sdom 9006 dfsdom2 9162 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9180 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9165 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9164 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9178 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9042 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9181 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9176 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9096 fundmeng 9097 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9136 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9177 |
| [Suppes] p. 104 | Theorem 37 | fofi 9379 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9385 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9385 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10620 |
| [Suppes] p. 130 | Definition 3 | df-tr 5284 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7815 |
| [Suppes] p. 134 | Definition 6 | df-suc 6401 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7940 finds 7936 finds1 7939 finds2 7938 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9721 isfinite2 9362 isfiniteg 9365 unbnn 9360 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10987 df-ltpq 10979 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7900 tfinds 7897 tfinds2 7901 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8607 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8609 |
| [Suppes] p. 211 | Theorem 25 | oaass 8617 |
| [Suppes] p. 225 | Definition 8 | iscard2 10045 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10632 |
| [Suppes] p. 228 | Theorem 59 | harcard 10047 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10135 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6446 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7829 onminsb 7830 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10641 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10139 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10146 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10140 |
| [Suppes] p. 229 | Definition 12 | df-aleph 10009 |
| [Suppes] p. 242 | Theorem 6 | weth 10564 |
| [Suppes] p. 242 | Theorem 8 | entric 10626 |
| [Suppes] p. 242 | Theorem 9 | carden 10620 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35658 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35662 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2711 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2732 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2819 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2734 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2763 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7452 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3802 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5439 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4672 elpr2 4674 elpr2g 4673 elprg 4670 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4663 elsn2 4687 elsn2g 4686 elsng 4662 velsn 4664 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5487 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4658 sneqr 4865 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4668 dfsn2 4661 dfsn2ALT 4669 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7776 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5496 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5484 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5468 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7779 unexg 7778 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4714 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4932 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3983 df-un 3981 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4948 uniprg 4947 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5395 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4712 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6465 elsucg 6463 sstr2 4015 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4181 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4230 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4195 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4249 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4303 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4304 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3996 df-ss 3993 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4624 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4210 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3994 sseqin2 4244 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 4031 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4258 inss2 4259 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4073 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4942 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5469 sspwimp 44889 sspwimpALT 44896 sspwimpALT2 44899 sspwimpcf 44891 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5476 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5303 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3444 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5325 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3979 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4355 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4398 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4376 n0f 4372 neq0 4375 neq0f 4371 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9664 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9801 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9803 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3490 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5333 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4423 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5339 ssexg 5341 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5335 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9671 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9666 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4389 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4158 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4319 undif3VD 44853 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4159 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4166 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3068 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3077 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7788 xpexg 7785 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5707 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6649 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6826 fun11 6652 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6589 svrelfun 6650 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5912 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5914 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5712 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5713 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5709 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6225 dfrel2 6220 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5716 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5835 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5842 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5856 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6035 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 6015 opelresi 6017 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6041 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6031 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6036 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6620 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6138 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6618 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6828 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2612 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30432 df-fv 6581 fv3 6938 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7965 cnvexg 7964 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7949 dmexg 7941 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7950 rnexg 7942 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44423 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7960 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6933 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47089 tz6.12-1-afv2 47156 tz6.12-1 6943 tz6.12-afv 47088 tz6.12-afv2 47155 tz6.12 6945 tz6.12c-afv2 47157 tz6.12c 6942 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47152 tz6.12-2 6908 tz6.12i-afv2 47158 tz6.12i 6948 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6576 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6577 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6579 wfo 6571 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6578 wf1 6570 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6580 wf1o 6572 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7064 eqfnfv2 7065 eqfnfv2f 7068 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 7020 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7254 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7252 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6666 funimaexg 6664 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5167 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5608 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5661 dffr3 6129 eliniseg 6124 iniseg 6127 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5599 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5677 fr3nr 7807 frirr 5676 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5652 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7809 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5664 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5686 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6379 tz6.26i 6381 wefrc 5694 wereu2 5697 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6382 wfii 6384 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6582 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7365 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7366 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7372 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7373 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7374 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7378 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7385 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7387 |
| [TakeutiZaring] p. 35 | Notation | wtr 5283 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44424 tz7.2 5683 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5289 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6408 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6416 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6417 ordelordALT 44508 ordelordALTVD 44838 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6423 ordelssne 6422 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6421 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6425 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7817 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7818 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6399 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6427 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44520 ordon 7812 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7813 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7890 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6442 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5285 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7828 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7867 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6499 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6498 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7814 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4961 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6401 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6475 sucidg 6476 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7847 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6489 ordnbtwn 6488 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7864 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6400 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7918 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7923 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7878 ordelsuc 7856 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7858 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7888 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7905 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7927 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7929 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7930 |
| [TakeutiZaring] p. 43 | Remark | omon 7915 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9704 omex 9712 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7913 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7935 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7931 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7932 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7908 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4986 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5302 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4987 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5362 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7831 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6445 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4971 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9729 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7826 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8432 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8453 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8454 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8455 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8462 tz7.44-2 8463 tz7.44-3 8464 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8423 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8418 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8402 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8501 tz7.49c 8502 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8499 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8498 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8500 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2659 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10080 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10081 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8588 oasuc 8580 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7898 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8591 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8572 oa0r 8594 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8592 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8604 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8675 nnaordi 8674 oaord 8603 oaordi 8602 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5072 uniss2 4965 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8606 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8611 oawordex 8613 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8667 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8704 |
| [TakeutiZaring] p. 60 | Remark | oancom 9720 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8616 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8672 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8608 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8575 omlim 8589 omsuc 8582 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8573 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8669 nnmcl 8668 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8688 nnmordi 8687 omord 8624 omordi 8622 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8625 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8692 omwordri 8628 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8595 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8598 om1r 8599 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8631 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8633 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8634 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8635 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8636 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8664 oe0 8578 oelim 8590 oesuc 8583 onesuc 8586 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8576 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8642 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8643 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8577 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8601 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8644 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8650 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8648 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8649 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8653 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8655 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9797 tz9.1 9798 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9833 r10 9837 r1lim 9841 r1limg 9840 r1suc 9839 r1sucg 9838 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9849 r1ord2 9850 r1ordg 9847 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9859 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9884 tz9.13 9860 tz9.13g 9861 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9834 rankval 9885 rankvalb 9866 rankvalg 9886 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9908 rankelb 9893 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9922 rankval3 9909 rankval3b 9895 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9898 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9864 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9903 rankr1c 9890 rankr1g 9901 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9904 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9918 rankssb 9917 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9911 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9910 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10544 dfac3 10190 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10099 numth 10541 numth2 10540 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10615 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10616 cardid2 10022 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10029 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10620 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 10028 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 10013 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10034 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 10026 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9216 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9078 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9221 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9140 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10032 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10167 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9272 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9291 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10168 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9277 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10157 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10135 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10041 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10285 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9390 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 9007 isfi 9036 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9293 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10603 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9133 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10595 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10255 unxpdom 9316 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10043 cardsdomelir 10042 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9318 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10083 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8886 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10631 infxpidm2 10086 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10276 infxp 10283 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9145 pw2f1o 9143 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9209 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10556 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10551 ac6s5 10560 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10612 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10613 uniimadomf 10614 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10343 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10338 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10323 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10320 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10326 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10333 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10342 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10651 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10321 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10345 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10166 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10165 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10177 alephfp2 10178 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10768 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10181 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10638 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10652 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10653 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38839 |
| [Tarski] p. 67 | Scheme B5 | sp 2184 |
| [Tarski] p. 68 | Lemma 6 | avril1 30495 equid 2011 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2016 |
| [Tarski] p. 70 | Lemma 14 | spim 2395 spime 2397 spimew 1971 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2178 ax-c15 38845 ax12i 1966 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2085 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1968 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1909 ax5ALT 38863 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2007 ax-8 2110 ax-9 2118 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28490 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28491 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28493 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28493 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28494 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16291 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37619 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37621 |
| [Weierstrass] p. 272 | Definition | df-mdet 22612 mdetuni 22649 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 902 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 867 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 918 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 968 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37411 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43762 imim2 58 wl-luk-imim2 37406 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 46934 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2666 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 901 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37409 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 893 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 896 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 44898 wl-luk-notnotr 37410 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43792 axfrege28 43791 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 866 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 923 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37403 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 888 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 940 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30433 pm2.27 42 wl-luk-pm2.27 37401 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 921 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38319 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 922 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 970 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 971 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 969 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 905 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 943 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 880 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 881 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 850 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 887 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 941 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 942 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 890 pm2.67 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 897 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 930 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 972 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 992 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 802 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 621 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 961 pm3.44 960 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 964 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 903 pm4.25 904 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1008 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 869 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 920 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 632 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 916 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 636 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 977 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1006 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1023 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 997 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 999 pm4.45 998 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 852 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 982 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 984 pm4.56 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 990 pm4.57 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 855 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 848 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 950 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 962 pm4.77 963 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 933 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1004 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1024 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1025 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 842 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 945 pm5.11g 944 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 947 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1013 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1012 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 900 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1002 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 954 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1005 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1018 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 949 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1001 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1028 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1029 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44327 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44328 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1869 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44329 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44330 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44331 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1892 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44332 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44333 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44334 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44335 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44336 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44338 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44339 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44340 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44337 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2090 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44343 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44344 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2070 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2161 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1827 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1828 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44345 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44346 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44347 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44348 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44350 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44349 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1886 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44352 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44353 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44351 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1826 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44354 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44355 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1844 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44356 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2352 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1859 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44361 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44357 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44358 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44359 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44360 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44365 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44362 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44363 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44364 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44366 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2572 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44376 pm13.13b 44377 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44378 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3028 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3029 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3679 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44384 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44385 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44379 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44523 pm13.193 44380 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44381 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44382 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44383 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44390 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44389 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44388 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3872 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44391 pm14.122b 44392 pm14.122c 44393 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44394 pm14.123b 44395 pm14.123c 44396 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44398 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44397 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44399 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6554 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44400 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6555 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44401 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44403 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2636 eupickbi 2639 sbaniota 44404 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44402 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2587 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44406 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30432 df-fv 6581 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10070 pm54.43lem 10069 |
| [Young] p. 141 | Definition of operator ordering | leop2 32156 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32162 idleop 32163 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42784 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42791 pellexlem1 42785 |