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 17804 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17804 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18213 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17825 0funcg 50115 df-termc 50503 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50580 prsthinc 50494 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50608 df-mndtc 50608 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50604 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17848 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50596 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50621 oppgoppchom 50620 oppgoppcid 50622 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17918 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17906 invisoinvl 17927 |
| [Adamek] p. 28 | Example 3.13 | idinv 17926 idiso 17925 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17911 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17885 df-iso 17886 dfiso2 17909 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17892 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17943 cicerALT 50076 |
| [Adamek] p. 29 | Definition 3.15 | cic 17936 df-cic 17933 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17995 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17907 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17908 isoco 17914 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17995 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 18018 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50334 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 18011 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50604 discthing 50491 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50448 prsthinc 50494 thincciso 50483 thincciso2 50485 thincciso3 50486 thinccisod 50484 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50608 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 18025 cofucla 50126 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 50192 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18248 catcisoi 50430 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18303 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 18044 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 18043 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18303 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 18068 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18074 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18073 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18288 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18288 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 50162 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 50153 funcoppc 18012 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18236 elcatchom 50427 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 18062 fthoppf 50194 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 18061 fulloppf 50193 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18245 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 50115 df-catc 18236 |
| [Adamek] p. 45 | Exercise 3G | incat 50631 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50634 nelsubc3 50101 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 50181 imasubc2 50182 imasubc3 50186 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17975 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17976 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 50101 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17987 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17949 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 50190 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 50189 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 50191 ressffth 18077 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50632 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18083 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18104 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18108 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18084 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18110 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 50115 df-inito 18121 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 50115 df-termc 50503 initc 50121 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21747 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18122 oppctermo 50266 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18149 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18153 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50267 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18123 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21748 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18156 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17884 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50499 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50498 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50463 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17919 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17921 |
| [Adamek] p. 185 | Section 10.67 | updjud 9987 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50675 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50675 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50675 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50676 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50676 |
| [Adamek] p. 478 | Item Rng | df-ringc 20860 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49582 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49604 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14684 df-pfx 14789 df-substr 14757 df-word 14627 lencl 14646 wrd0 14652 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24989 df-nmoo 31281 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32689 hmopidmchi 32687 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32737 pjcmul2i 32738 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32454 unoplin 32456 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32455 unopadj2 32474 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32549 lnopunii 32548 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32622 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28247 |
| [Alling] p. 184 | Axiom B | bdayfo 27968 |
| [Alling] p. 184 | Axiom O | ltsso 27967 |
| [Alling] p. 184 | Axiom SD | nodense 27983 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 28075 |
| [Alling] p. 185 | Theorem | conway 28099 |
| [Alling] p. 185 | Axiom FE | noeta 28034 |
| [Alling] p. 186 | Theorem 4 | lesrec 28119 lesrecd 28120 |
| [Alling], p. 2 | Definition | rp-brsslt 44367 |
| [Alling], p. 3 | Note | nla0001 44370 nla0002 44368 nla0003 44369 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11466 addcan2d 11486 addcan2i 11476 addcand 11485 addcani 11475 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11519 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11578 negsubd 11647 negsubi 11608 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11580 negnegd 11632 negnegi 11600 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11719 subdid 11742 subdii 11735 subdir 11720 subdird 11743 subdiri 11736 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11461 mul01d 11481 mul01i 11472 mul02 11460 mul02d 11480 mul02i 11471 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11923 mulcan2d 11920 mulcand 11919 mulcani 11925 |
| [Apostol] p. 18 | Theorem I.8 | receu 11931 xreceu 33422 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11960 divrecd 12066 divreci 12032 divreczi 12025 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11984 recreci 12019 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11926 mul0ord 11934 mul0ori 11933 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11725 mul2negd 11741 mul2negi 11734 mulneg1 11722 mulneg1d 11739 mulneg1i 11732 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 12002 divadddivd 12107 divadddivi 12049 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11987 divmuldivd 12104 divmuldivi 12047 rdivmuldivd 20605 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11988 divdivdivd 12110 divdivdivi 12050 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13114 rpaddcld 13149 rpmulcl 13115 rpmulcld 13150 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13124 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13127 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11408 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11879 ltadd1dd 11897 ltadd1i 11840 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12137 ltmul1a 12136 ltmul1i 12205 ltmul1ii 12215 ltmul2 12138 ltmul2d 13176 ltmul2dd 13190 ltmul2i 12208 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11806 msqgt0d 11853 msqgt0i 11823 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11808 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11792 lt0neg1d 11855 ltneg 11786 ltnegd 11864 ltnegi 11830 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11771 lt2addd 11909 lt2addi 11848 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13091 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12133 recgt0d 12221 recgt0i 12192 recgt0ii 12193 |
| [Apostol] p. 22 | Definition of integers | df-z 12664 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12319 |
| [Apostol] p. 22 | Definition of rationals | df-q 13046 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9424 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12572 |
| [Apostol] p. 26 | Theorem I.29 | arch 12573 archd 46098 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12772 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12574 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 13044 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 13043 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13299 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16477 zneo 12752 zneoALTV 48689 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 27022 msqsqrtd 15578 resqrtth 15390 sqrtth 15500 sqrtthi 15506 sqsqrtd 15577 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12308 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 13010 |
| [Apostol] p. 361 | Remark | crreczi 14340 |
| [Apostol] p. 363 | Remark | absgt0i 15535 |
| [Apostol] p. 363 | Example | abssubd 15591 abssubi 15539 |
| [ApostolNT] p. 7 | Remark | fmtno0 48547 fmtno1 48548 fmtno2 48557 fmtno3 48558 fmtno4 48559 fmtno5fac 48589 fmtnofz04prm 48584 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48535 |
| [ApostolNT] p. 8 | Definition | df-ppi 27391 |
| [ApostolNT] p. 14 | Definition | df-dvds 16391 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16407 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16432 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16427 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16420 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16422 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16408 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16409 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16414 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16449 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16451 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16453 |
| [ApostolNT] p. 15 | Definition | df-gcd 16633 dfgcd2 16684 |
| [ApostolNT] p. 16 | Definition | isprm2 16820 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16791 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 17055 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16651 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16685 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16687 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16666 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16658 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16850 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16852 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 17068 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 17062 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16541 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16725 |
| [ApostolNT] p. 24 | Definition | df-mu 27392 |
| [ApostolNT] p. 25 | Definition | df-phi 16905 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27482 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16930 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16915 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16919 |
| [ApostolNT] p. 32 | Definition | df-vma 27389 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27484 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27507 |
| [ApostolNT] p. 38 | Remark | df-sgm 27393 |
| [ApostolNT] p. 38 | Definition | df-sgm 27393 |
| [ApostolNT] p. 75 | Definition | df-chp 27390 df-cht 27388 |
| [ApostolNT] p. 104 | Definition | congr 16802 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16394 |
| [ApostolNT] p. 106 | Definition | moddvds 16401 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16484 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16485 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13997 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 14037 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14350 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16426 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16805 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17214 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16807 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16922 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16941 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16923 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27363 |
| [ApostolNT] p. 179 | Definition | df-lgs 27586 lgsprme0 27630 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27631 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27607 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27622 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27679 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27698 2lgsoddprm 27707 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27665 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27674 |
| [ApostolNT] p. 188 | Definition | df-lgs 27586 lgs1 27632 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27623 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27625 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27633 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27634 |
| [Baer] p. 40 | Property (b) | mapdord 42615 |
| [Baer] p. 40 | Property (c) | mapd11 42616 |
| [Baer] p. 40 | Property (e) | mapdin 42639 mapdlsm 42641 |
| [Baer] p. 40 | Property (f) | mapd0 42642 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42602 mapd1o 42625 |
| [Baer] p. 41 | Property (g) | mapdat 42644 |
| [Baer] p. 44 | Part (1) | mapdpg 42683 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42778 mapdheq 42705 mapdheq2 42706 mapdheq2biN 42707 |
| [Baer] p. 45 | Part (3) | baerlem3 42690 |
| [Baer] p. 46 | Part (4) | mapdheq4 42709 mapdheq4lem 42708 |
| [Baer] p. 46 | Part (5) | baerlem5a 42691 baerlem5abmN 42695 baerlem5amN 42693 baerlem5b 42692 baerlem5bmN 42694 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42798 hdmap1l6a 42786 hdmap1l6e 42791 hdmap1l6f 42792 hdmap1l6g 42793 hdmap1l6lem1 42784 hdmap1l6lem2 42785 mapdh6N 42724 mapdh6aN 42712 mapdh6eN 42717 mapdh6fN 42718 mapdh6gN 42719 mapdh6lem1N 42710 mapdh6lem2N 42711 |
| [Baer] p. 48 | Part 9 | hdmapval 42805 |
| [Baer] p. 48 | Part 10 | hdmap10 42817 |
| [Baer] p. 48 | Part 11 | hdmapadd 42820 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42794 mapdh6hN 42720 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42730 mapdh75d 42731 mapdh75e 42729 mapdh75fN 42732 mapdh7cN 42726 mapdh7dN 42727 mapdh7eN 42725 mapdh7fN 42728 |
| [Baer] p. 48 | Part (8) | mapdh8 42765 mapdh8a 42752 mapdh8aa 42753 mapdh8ab 42754 mapdh8ac 42755 mapdh8ad 42756 mapdh8b 42757 mapdh8c 42758 mapdh8d 42760 mapdh8d0N 42759 mapdh8e 42761 mapdh8g 42762 mapdh8i 42763 mapdh8j 42764 |
| [Baer] p. 48 | Part (9) | mapdh9a 42766 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42746 |
| [Baer] p. 49 | Part 12 | hdmap11 42825 hdmapeq0 42821 hdmapf1oN 42842 hdmapneg 42823 hdmaprnN 42841 hdmaprnlem1N 42826 hdmaprnlem3N 42827 hdmaprnlem3uN 42828 hdmaprnlem4N 42830 hdmaprnlem6N 42831 hdmaprnlem7N 42832 hdmaprnlem8N 42833 hdmaprnlem9N 42834 hdmapsub 42824 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42845 hdmap14lem10 42854 hdmap14lem1a 42843 hdmap14lem2N 42846 hdmap14lem2a 42844 hdmap14lem3 42847 hdmap14lem8 42852 hdmap14lem9 42853 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42855 hdmap14lem12 42856 hdmap14lem13 42857 hdmap14lem14 42858 hdmap14lem15 42859 hgmapval 42864 |
| [Baer] p. 50 | Part 15 | hgmapadd 42871 hgmapmul 42872 hgmaprnlem2N 42874 hgmapvs 42868 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42878 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42894 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42895 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42896 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42897 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42899 hgmapvv 42903 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42898 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42900 |
| [Baer] p. 111 | Line 15 | hdmapg 42907 hdmapglem7 42906 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 27023 2irrexpqALT 27092 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2594 |
| [BellMachover] p. 460 | Notation | df-mo 2564 |
| [BellMachover] p. 460 | Definition | mo3 2589 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2732 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2736 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5238 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5248 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37899 sepex 5254 |
| [BellMachover] p. 466 | Problem | axpow2 5328 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5329 |
| [BellMachover] p. 466 | Axiom Union | axun2 7736 |
| [BellMachover] p. 468 | Definition | df-ord 6354 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6369 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6376 onelond 36870 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6371 |
| [BellMachover] p. 471 | Definition of N | df-om 7861 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7798 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6356 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9621 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7876 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9746 |
| [BellMachover] p. 478 | Definition | rankval2 9800 rankval2b 9808 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9764 r1ord3g 9761 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9568 |
| [BellMachover] p. 488 | Axiom AC | ac5 10527 dfac4 10173 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10161 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40296 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32889 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32931 chirredi 32930 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32919 |
| [Beran] p. 3 | Definition of join | sshjval3 31890 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 32152 cmcm2i 32129 cmcm2ii 32134 cmt2N 40227 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 32153 lecmi 32138 lecmii 32139 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 32127 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 32156 cm2ji 32161 cm2mi 32162 |
| [Beran] p. 95 | Definition | df-sh 31743 issh2 31745 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31622 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31635 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31626 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32364 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32366 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32365 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32367 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31618 his1i 31636 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31619 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31620 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31621 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31504 dfhnorm2 31658 normval 31660 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31720 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31509 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31777 |
| [Beran] p. 96 | Definition of converge | df-hlim 31508 hlimi 31724 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31669 norm-i 31665 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31673 norm-ii 31674 normlem0 31645 normlem1 31646 normlem2 31647 normlem3 31648 normlem4 31649 normlem5 31650 normlem6 31651 normlem7 31652 normlem7tALT 31655 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31675 norm-iii 31676 |
| [Beran] p. 98 | Remark 3.4 | bcs 31717 bcsiALT 31715 bcsiHIL 31716 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31657 normpar 31691 normpari 31690 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31682 normpyth 31681 normpythi 31678 |
| [Beran] p. 99 | Remark | lnfn0 32583 lnfn0i 32578 lnop0 32502 lnop0i 32506 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32562 nmcfnex 32589 nmcfnexi 32587 nmcopex 32565 nmcopexi 32563 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32590 nmcfnlbi 32588 nmcoplb 32566 nmcoplbi 32564 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32592 lnfnconi 32591 lnopcon 32571 lnopconi 32570 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31692 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31689 norm3adifii 31684 norm3dif 31686 norm3difi 31683 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31837 pjhth 31929 pjhtheu 31930 pjpjhth 31961 pjpjhthi 31962 pjth 25722 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31942 ococi 31941 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32597 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32598 riesz4 32600 riesz4i 32599 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32615 cnlnadjeu 32614 cnlnadjeui 32613 cnlnadji 32612 cnlnadjlem1 32603 nmopadjlei 32624 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32627 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32626 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32628 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32472 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32638 nmopcoadji 32637 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32629 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32639 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32636 pjadj2coi 32740 pjadjcoi 32697 |
| [Beran] p. 107 | Definition | df-ch 31757 isch2 31759 |
| [Beran] p. 107 | Remark 3.12 | choccl 31842 isch3 31777 occl 31840 ocsh 31819 shoccl 31841 shocsh 31820 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31944 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31868 |
| [Beran] p. 109 | Property (i) | pjadj2 32723 pjadj3 32724 pjadji 32221 pjadjii 32210 |
| [Beran] p. 109 | Property (ii) | pjidmco 32717 pjidmcoi 32713 pjidmi 32209 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32709 |
| [Beran] p. 111 | Remark | ho0val 32286 pjch1 32206 |
| [Beran] p. 111 | Definition | df-hfmul 32270 df-hfsum 32269 df-hodif 32268 df-homul 32267 df-hosum 32266 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32207 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32230 pjchi 31968 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31975 pjoc2i 31974 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32216 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32701 pjssmii 32217 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32700 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32699 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32704 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32702 pjssge0ii 32218 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32703 pjdifnormii 32219 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1809 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1807 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1810 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1805 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34859 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34867 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34865 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34869 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34889 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34920 df-sitm 34898 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34920 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34897 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29560 isuhgrop 29582 isusgrop 29677 isuspgrop 29676 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48881 df-subgr 29783 uhgrspan1 29818 uhgrspansubgr 29806 |
| [Bollobas] p. 3 | Definition | df-gric 48901 gricuspgr 48938 isuspgrim 48916 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29969 df-clnbgr 48839 df-cusgr 29927 df-nbgr 29848 fusgrmaxsize 29979 |
| [Bollobas] p. 4 | Definition | df-upwlks 49154 df-wlks 30114 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 30065 finsumvtxdgeven 30067 fusgr1th 30066 fusgrvtxdgonume 30069 vtxdgoddnumeven 30068 |
| [Bollobas] p. 5 | Notation | df-pths 30233 |
| [Bollobas] p. 5 | Definition | df-crcts 30307 df-cycls 30308 df-trls 30209 df-wlkson 30115 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29571 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 49219 df-cllaw 49205 df-mgm 18778 df-mgm2 49238 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 49220 df-asslaw 49207 df-sgrp 18870 df-sgrp2 49240 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49239 df-comlaw 49206 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18886 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33521 mndlactf1o 33525 mndractf1 33523 mndractf1o 33526 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20423 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20337 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34199 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34203 assarrginv 34202 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34244 fldextrspunfld 34242 fldextrspunlem1 34241 fldextrspunlem2 34243 fldextrspunlsp 34240 fldextrspunlsplem 34239 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 34003 dfufd2 34016 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7283 fcofo 7284 |
| [BourbakiTop1] p. | Remark | xnegmnf 13310 xnegpnf 13309 |
| [BourbakiTop1] p. | Remark | rexneg 13311 |
| [BourbakiTop1] p. | Remark 3 | ust0 24501 ustfilxp 24494 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24371 |
| [BourbakiTop1] p. | Criterion | ishmeo 24040 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24564 iducn 24563 snfil 24145 |
| [BourbakiTop1] p. | Example 2 | neifil 24161 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24348 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24584 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34523 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24144 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24556 df-ust 24482 filintn0 24142 filn0 24143 istgp 24358 ucnprima 24562 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24567 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24578 df-usp 24538 df-utop 24512 trust 24510 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34422 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23396 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23549 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24487 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24490 |
| [BourbakiTop1] p. | Property V_ii | innei 23405 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23413 neissex 23407 |
| [BourbakiTop1] p. | Proposition 1 | neips 23393 neiss 23389 ucncn 24565 ustund 24503 ustuqtop 24527 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23547 neiptopreu 23413 utop2nei 24531 utop3cls 24532 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24572 uspreg 24554 utopreg 24533 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23972 imasncls 23973 imasnopn 23971 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24281 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24489 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24491 |
| [BourbakiTop1] p. | Property V_iii | elnei 23391 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24583 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24488 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24492 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23667 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24127 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23174 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34419 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46994 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46996 stoweid 46995 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46933 stoweidlem10 46942 stoweidlem14 46946 stoweidlem15 46947 stoweidlem35 46967 stoweidlem36 46968 stoweidlem37 46969 stoweidlem38 46970 stoweidlem40 46972 stoweidlem41 46973 stoweidlem43 46975 stoweidlem44 46976 stoweidlem46 46978 stoweidlem5 46937 stoweidlem50 46982 stoweidlem52 46984 stoweidlem53 46985 stoweidlem55 46987 stoweidlem56 46988 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46955 stoweidlem24 46956 stoweidlem27 46959 stoweidlem28 46960 stoweidlem30 46962 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46966 stoweidlem59 46991 stoweidlem60 46992 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46977 stoweidlem49 46981 stoweidlem7 46939 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46963 stoweidlem39 46971 stoweidlem42 46974 stoweidlem48 46980 stoweidlem51 46983 stoweidlem54 46986 stoweidlem57 46989 stoweidlem58 46990 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46957 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46949 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46943 stoweidlem13 46945 stoweidlem26 46958 stoweidlem61 46993 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46950 |
| [Bruck] p. 1 | Section I.1 | df-clintop 49219 df-mgm 18778 df-mgm2 49238 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18870 df-sgrp2 49240 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19211 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5186 |
| [Church] p. 129 | Section II.24 | df-ifp 1079 dfifp2 1080 |
| [Clemente] p. 10 | Definition IT | natded 30938 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30938 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30938 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30938 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30938 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30938 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30938 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30938 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30938 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30938 |
| [Clemente] p. 14 | Proof 5.11 | natded 30938 |
| [Clemente] p. 14 | Definition E` `n | natded 30938 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30940 ex-natded5.2 30939 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30943 ex-natded5.3 30942 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30945 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30947 ex-natded5.7 30946 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30949 ex-natded5.8 30948 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30951 ex-natded5.13 30950 |
| [Clemente] p. 32 | Definition I` `n | natded 30938 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30938 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30938 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30938 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30952 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30953 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30955 ex-natded9.26 30954 |
| [Cohen] p. 301 | Remark | relogoprlem 26883 |
| [Cohen] p. 301 | Property 2 | relogmul 26884 relogmuld 26917 |
| [Cohen] p. 301 | Property 3 | relogdiv 26885 relogdivd 26918 |
| [Cohen] p. 301 | Property 4 | relogexp 26888 |
| [Cohen] p. 301 | Property 1a | log1 26877 |
| [Cohen] p. 301 | Property 1b | loge 26878 |
| [Cohen4] p. 348 | Observation | relogbcxpb 27079 |
| [Cohen4] p. 349 | Property | relogbf 27083 |
| [Cohen4] p. 352 | Definition | elogb 27062 |
| [Cohen4] p. 361 | Property 2 | relogbmul 27069 |
| [Cohen4] p. 361 | Property 3 | logbrec 27074 relogbdiv 27071 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 27067 |
| [Cohen4] p. 361 | Property 6 | relogbexp 27072 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 27060 |
| [Cohen4] p. 361 | Property 1(b) | logb1 27061 |
| [Cohen4] p. 367 | Property | logbchbase 27063 |
| [Cohen4] p. 377 | Property 2 | logblt 27076 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34852 sxbrsigalem4 34854 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18693 acsinfd 18692 acsinfdimd 18694 acsmap2d 18691 acsmapd 18690 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34857 |
| [Connell] p. 57 | Definition | df-scmat 22768 df-scmatalt 49433 |
| [Conway] p. 4 | Definition | lesrec 28119 lesrecd 28120 |
| [Conway] p. 5 | Definition | addsval 28282 addsval2 28283 df-adds 28280 df-muls 28427 df-negs 28341 |
| [Conway] p. 7 | Theorem | 0lt1s 28132 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28782 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28181 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28180 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 28058 |
| [Conway] p. 17 | Theorem 3 | addsass 28325 addsassd 28326 addscom 28286 addscomd 28287 addsrid 28284 addsridd 28285 |
| [Conway] p. 17 | Definition | df-0s 28127 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28364 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28361 negsidd 28362 |
| [Conway] p. 18 | Theorem 5 | leadds1 28309 leadds1d 28315 |
| [Conway] p. 18 | Definition | df-1s 28128 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28356 negscld 28357 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28300 |
| [Conway] p. 19 | Note | mulsunif2 28490 |
| [Conway] p. 19 | Theorem 7 | addsdi 28475 addsdid 28476 addsdird 28477 mulnegs1d 28480 mulnegs2d 28481 mulsass 28486 mulsassd 28487 mulscom 28459 mulscomd 28460 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28454 mulscld 28455 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28458 ltmuls 28456 ltmulsd 28457 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28464 mulsgt0d 28465 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28538 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28124 |
| [Conway] p. 24 | Definition | df-reno 28810 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28819 remulscl 28822 renegscl 28818 |
| [Conway] p. 27 | Definition | df-ons 28572 elons2 28578 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28582 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28584 onswe 28592 |
| [Conway] p. 29 | Remark | madebday 28220 newbday 28222 oldbday 28221 |
| [Conway] p. 29 | Definition | df-made 28147 df-new 28149 df-old 28148 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13970 |
| [Crawley] p. 1 | Definition of poset | df-poset 18449 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40363 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 41167 dalaw 40863 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42938 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40967 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 41083 df-ldil 41081 isldil 41087 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 41082 df-trnN 41084 isltrn 41096 ltrnu 41098 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40768 cdlema2N 40769 exatleN 40381 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40453 cdlemb 40771 cdlemb2 41018 cdlemb3 41583 idltrn 41127 l1cvat 40032 lhpat 41020 lhpat2 41022 lshpat 40033 ltrnel 41116 ltrnmw 41128 |
| [Crawley] p. 112 | Lemma C | cdlemc1 41168 cdlemc2 41169 ltrnnidn 41151 trlat 41146 trljat1 41143 trljat2 41144 trljat3 41145 trlne 41162 trlnidat 41150 trlnle 41163 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40968 |
| [Crawley] p. 113 | Lemma C | cdlemc 41174 cdlemc3 41170 cdlemc4 41171 |
| [Crawley] p. 113 | Lemma D | cdlemd 41184 cdlemd1 41175 cdlemd2 41176 cdlemd3 41177 cdlemd4 41178 cdlemd5 41179 cdlemd6 41180 cdlemd7 41181 cdlemd8 41182 cdlemd9 41183 cdleme31sde 41362 cdleme31se 41359 cdleme31se2 41360 cdleme31snd 41363 cdleme32a 41418 cdleme32b 41419 cdleme32c 41420 cdleme32d 41421 cdleme32e 41422 cdleme32f 41423 cdleme32fva 41414 cdleme32fva1 41415 cdleme32fvcl 41417 cdleme32le 41424 cdleme48fv 41476 cdleme4gfv 41484 cdleme50eq 41518 cdleme50f 41519 cdleme50f1 41520 cdleme50f1o 41523 cdleme50laut 41524 cdleme50ldil 41525 cdleme50lebi 41517 cdleme50rn 41522 cdleme50rnlem 41521 cdlemeg49le 41488 cdlemeg49lebilem 41516 |
| [Crawley] p. 113 | Lemma E | cdleme 41537 cdleme00a 41186 cdleme01N 41198 cdleme02N 41199 cdleme0a 41188 cdleme0aa 41187 cdleme0b 41189 cdleme0c 41190 cdleme0cp 41191 cdleme0cq 41192 cdleme0dN 41193 cdleme0e 41194 cdleme0ex1N 41200 cdleme0ex2N 41201 cdleme0fN 41195 cdleme0gN 41196 cdleme0moN 41202 cdleme1 41204 cdleme10 41231 cdleme10tN 41235 cdleme11 41247 cdleme11a 41237 cdleme11c 41238 cdleme11dN 41239 cdleme11e 41240 cdleme11fN 41241 cdleme11g 41242 cdleme11h 41243 cdleme11j 41244 cdleme11k 41245 cdleme11l 41246 cdleme12 41248 cdleme13 41249 cdleme14 41250 cdleme15 41255 cdleme15a 41251 cdleme15b 41252 cdleme15c 41253 cdleme15d 41254 cdleme16 41262 cdleme16aN 41236 cdleme16b 41256 cdleme16c 41257 cdleme16d 41258 cdleme16e 41259 cdleme16f 41260 cdleme16g 41261 cdleme19a 41280 cdleme19b 41281 cdleme19c 41282 cdleme19d 41283 cdleme19e 41284 cdleme19f 41285 cdleme1b 41203 cdleme2 41205 cdleme20aN 41286 cdleme20bN 41287 cdleme20c 41288 cdleme20d 41289 cdleme20e 41290 cdleme20f 41291 cdleme20g 41292 cdleme20h 41293 cdleme20i 41294 cdleme20j 41295 cdleme20k 41296 cdleme20l 41299 cdleme20l1 41297 cdleme20l2 41298 cdleme20m 41300 cdleme20y 41279 cdleme20zN 41278 cdleme21 41314 cdleme21d 41307 cdleme21e 41308 cdleme22a 41317 cdleme22aa 41316 cdleme22b 41318 cdleme22cN 41319 cdleme22d 41320 cdleme22e 41321 cdleme22eALTN 41322 cdleme22f 41323 cdleme22f2 41324 cdleme22g 41325 cdleme23a 41326 cdleme23b 41327 cdleme23c 41328 cdleme26e 41336 cdleme26eALTN 41338 cdleme26ee 41337 cdleme26f 41340 cdleme26f2 41342 cdleme26f2ALTN 41341 cdleme26fALTN 41339 cdleme27N 41346 cdleme27a 41344 cdleme27cl 41343 cdleme28c 41349 cdleme3 41214 cdleme30a 41355 cdleme31fv 41367 cdleme31fv1 41368 cdleme31fv1s 41369 cdleme31fv2 41370 cdleme31id 41371 cdleme31sc 41361 cdleme31sdnN 41364 cdleme31sn 41357 cdleme31sn1 41358 cdleme31sn1c 41365 cdleme31sn2 41366 cdleme31so 41356 cdleme35a 41425 cdleme35b 41427 cdleme35c 41428 cdleme35d 41429 cdleme35e 41430 cdleme35f 41431 cdleme35fnpq 41426 cdleme35g 41432 cdleme35h 41433 cdleme35h2 41434 cdleme35sn2aw 41435 cdleme35sn3a 41436 cdleme36a 41437 cdleme36m 41438 cdleme37m 41439 cdleme38m 41440 cdleme38n 41441 cdleme39a 41442 cdleme39n 41443 cdleme3b 41206 cdleme3c 41207 cdleme3d 41208 cdleme3e 41209 cdleme3fN 41210 cdleme3fa 41213 cdleme3g 41211 cdleme3h 41212 cdleme4 41215 cdleme40m 41444 cdleme40n 41445 cdleme40v 41446 cdleme40w 41447 cdleme41fva11 41454 cdleme41sn3aw 41451 cdleme41sn4aw 41452 cdleme41snaw 41453 cdleme42a 41448 cdleme42b 41455 cdleme42c 41449 cdleme42d 41450 cdleme42e 41456 cdleme42f 41457 cdleme42g 41458 cdleme42h 41459 cdleme42i 41460 cdleme42k 41461 cdleme42ke 41462 cdleme42keg 41463 cdleme42mN 41464 cdleme42mgN 41465 cdleme43aN 41466 cdleme43bN 41467 cdleme43cN 41468 cdleme43dN 41469 cdleme5 41217 cdleme50ex 41536 cdleme50ltrn 41534 cdleme51finvN 41533 cdleme51finvfvN 41532 cdleme51finvtrN 41535 cdleme6 41218 cdleme7 41226 cdleme7a 41220 cdleme7aa 41219 cdleme7b 41221 cdleme7c 41222 cdleme7d 41223 cdleme7e 41224 cdleme7ga 41225 cdleme8 41227 cdleme8tN 41232 cdleme9 41230 cdleme9a 41228 cdleme9b 41229 cdleme9tN 41234 cdleme9taN 41233 cdlemeda 41275 cdlemedb 41274 cdlemednpq 41276 cdlemednuN 41277 cdlemefr27cl 41380 cdlemefr32fva1 41387 cdlemefr32fvaN 41386 cdlemefrs32fva 41377 cdlemefrs32fva1 41378 cdlemefs27cl 41390 cdlemefs32fva1 41400 cdlemefs32fvaN 41399 cdlemesner 41273 cdlemeulpq 41197 |
| [Crawley] p. 114 | Lemma E | 4atex 41053 4atexlem7 41052 cdleme0nex 41267 cdleme17a 41263 cdleme17c 41265 cdleme17d 41475 cdleme17d1 41266 cdleme17d2 41472 cdleme18a 41268 cdleme18b 41269 cdleme18c 41270 cdleme18d 41272 cdleme4a 41216 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41302 cdleme21at 41305 cdleme21b 41303 cdleme21c 41304 cdleme21ct 41306 cdleme21f 41309 cdleme21g 41310 cdleme21h 41311 cdleme21i 41312 cdleme22gb 41271 |
| [Crawley] p. 116 | Lemma F | cdlemf 41540 cdlemf1 41538 cdlemf2 41539 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41544 cdlemg16 41634 cdlemg28 41681 cdlemg28a 41670 cdlemg28b 41680 cdlemg3a 41574 cdlemg42 41706 cdlemg43 41707 cdlemg44 41710 cdlemg44a 41708 cdlemg46 41712 cdlemg47 41713 cdlemg9 41611 ltrnco 41696 ltrncom 41715 tgrpabl 41728 trlco 41704 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41720 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41654 cdlemg17b 41639 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41733 df-edring 41734 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41737 |
| [Crawley] p. 118 | Remark | tendopltp 41757 |
| [Crawley] p. 118 | Lemma H | cdlemh 41794 cdlemh1 41792 cdlemh2 41793 |
| [Crawley] p. 118 | Lemma I | cdlemi 41797 cdlemi1 41795 cdlemi2 41796 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41798 cdlemj2 41799 cdlemj3 41800 tendocan 41801 |
| [Crawley] p. 118 | Lemma K | cdlemk 41951 cdlemk1 41808 cdlemk10 41820 cdlemk11 41826 cdlemk11t 41923 cdlemk11ta 41906 cdlemk11tb 41908 cdlemk11tc 41922 cdlemk11u-2N 41866 cdlemk11u 41848 cdlemk12 41827 cdlemk12u-2N 41867 cdlemk12u 41849 cdlemk13-2N 41853 cdlemk13 41829 cdlemk14-2N 41855 cdlemk14 41831 cdlemk15-2N 41856 cdlemk15 41832 cdlemk16-2N 41857 cdlemk16 41834 cdlemk16a 41833 cdlemk17-2N 41858 cdlemk17 41835 cdlemk18-2N 41863 cdlemk18-3N 41877 cdlemk18 41845 cdlemk19-2N 41864 cdlemk19 41846 cdlemk19u 41947 cdlemk1u 41836 cdlemk2 41809 cdlemk20-2N 41869 cdlemk20 41851 cdlemk21-2N 41868 cdlemk21N 41850 cdlemk22-3 41878 cdlemk22 41870 cdlemk23-3 41879 cdlemk24-3 41880 cdlemk25-3 41881 cdlemk26-3 41883 cdlemk26b-3 41882 cdlemk27-3 41884 cdlemk28-3 41885 cdlemk29-3 41888 cdlemk3 41810 cdlemk30 41871 cdlemk31 41873 cdlemk32 41874 cdlemk33N 41886 cdlemk34 41887 cdlemk35 41889 cdlemk36 41890 cdlemk37 41891 cdlemk38 41892 cdlemk39 41893 cdlemk39u 41945 cdlemk4 41811 cdlemk41 41897 cdlemk42 41918 cdlemk42yN 41921 cdlemk43N 41940 cdlemk45 41924 cdlemk46 41925 cdlemk47 41926 cdlemk48 41927 cdlemk49 41928 cdlemk5 41813 cdlemk50 41929 cdlemk51 41930 cdlemk52 41931 cdlemk53 41934 cdlemk54 41935 cdlemk55 41938 cdlemk55u 41943 cdlemk56 41948 cdlemk5a 41812 cdlemk5auN 41837 cdlemk5u 41838 cdlemk6 41814 cdlemk6u 41839 cdlemk7 41825 cdlemk7u-2N 41865 cdlemk7u 41847 cdlemk8 41815 cdlemk9 41816 cdlemk9bN 41817 cdlemki 41818 cdlemkid 41913 cdlemkj-2N 41859 cdlemkj 41840 cdlemksat 41823 cdlemksel 41822 cdlemksv 41821 cdlemksv2 41824 cdlemkuat 41843 cdlemkuel-2N 41861 cdlemkuel-3 41875 cdlemkuel 41842 cdlemkuv-2N 41860 cdlemkuv2-2 41862 cdlemkuv2-3N 41876 cdlemkuv2 41844 cdlemkuvN 41841 cdlemkvcl 41819 cdlemky 41903 cdlemkyyN 41939 tendoex 41952 |
| [Crawley] p. 120 | Remark | dva1dim 41962 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41953 cdleml2N 41954 cdleml3N 41955 cdleml4N 41956 cdleml5N 41957 cdleml6 41958 cdleml7 41959 cdleml8 41960 cdleml9 41961 dia1dim 42038 |
| [Crawley] p. 120 | Lemma M | dia11N 42025 diaf11N 42026 dialss 42023 diaord 42024 dibf11N 42138 djajN 42114 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 42009 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 42095 dia2dimlem1 42041 dia2dimlem2 42042 dia2dimlem3 42043 dia2dimlem4 42044 dia2dimlem5 42045 diaf1oN 42107 diarnN 42106 dvheveccl 42089 dvhopN 42093 |
| [Crawley] p. 121 | Lemma N | cdlemn 42189 cdlemn10 42183 cdlemn11 42188 cdlemn11a 42184 cdlemn11b 42185 cdlemn11c 42186 cdlemn11pre 42187 cdlemn2 42172 cdlemn2a 42173 cdlemn3 42174 cdlemn4 42175 cdlemn4a 42176 cdlemn5 42178 cdlemn5pre 42177 cdlemn6 42179 cdlemn7 42180 cdlemn8 42181 cdlemn9 42182 diclspsn 42171 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 42150 |
| [Crawley] p. 122 | Lemma N | dih11 42242 dihf11 42244 dihjust 42194 dihjustlem 42193 dihord 42241 dihord1 42195 dihord10 42200 dihord11b 42199 dihord11c 42201 dihord2 42204 dihord2a 42196 dihord2b 42197 dihord2cN 42198 dihord2pre 42202 dihord2pre2 42203 dihordlem6 42190 dihordlem7 42191 dihordlem7b 42192 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42207 dihfval 42208 dihval 42209 |
| [Diestel] p. 3 | Definition | df-gric 48901 df-grim 48898 isuspgrim 48916 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29927 df-nbgr 29848 |
| [Diestel] p. 3 | Definition by | df-grisom 48897 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48881 df-subgr 29783 uhgrspan1 29818 uhgrspansubgr 29806 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 30069 vtxdgoddnumeven 30068 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29571 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34430 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34442 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34434 zarcls1 34435 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34445 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34448 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34451 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3901 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9626 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8827 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9634 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10033 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10611 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5258 |
| [Enderton] p. 19 | Definition | df-tp 4588 |
| [Enderton] p. 26 | Exercise 5 | unissb 4900 |
| [Enderton] p. 26 | Exercise 10 | pwel 5342 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5540 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5038 iinin2 5037 iinun2 5030 iunin1 5029 iunin1f 33086 iunin2 5028 uniin1 5032 uniin2 5033 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5036 iundif2 5031 |
| [Enderton] p. 32 | Exercise 20 | unineq 4233 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5057 |
| [Enderton] p. 33 | Exercise 25 | iununi 5058 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5065 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7768 iunpwss 5066 |
| [Enderton] p. 36 | Definition | opthwiener 5483 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5417 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4905 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5438 rnex 7905 rnexg 7897 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5892 rnuni 6134 |
| [Enderton] p. 42 | Definition of a function | dffun7 6555 dffun8 6556 |
| [Enderton] p. 43 | Definition of function value | funfv2 6961 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6597 |
| [Enderton] p. 44 | Definition (d) | dfima2 6052 dfima3 6053 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6970 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10523 ac7g 10524 df-ac 10167 dfac2 10182 dfac2a 10180 dfac2b 10181 dfac3 10172 dfac7 10183 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7238 |
| [Enderton] p. 52 | Definition | df-map 8827 |
| [Enderton] p. 53 | Exercise 21 | coass 6256 |
| [Enderton] p. 53 | Exercise 27 | dmco 6245 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6604 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6092 |
| [Enderton] p. 54 | Remark | ixpf 8926 ixpssmap 8938 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8904 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10533 ac9s 10543 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39546 erref 8716 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39549 erthi 8752 |
| [Enderton] p. 57 | Definition | df-ec 8697 |
| [Enderton] p. 58 | Definition | df-qs 8701 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8697 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5888 |
| [Enderton] p. 68 | Definition of successor | df-suc 6357 |
| [Enderton] p. 71 | Definition | df-tr 5212 dftr4 5217 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6433 unisucg 6432 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6433 unisucg 6432 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5227 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5229 trintALT 45807 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8591 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8593 onasuc 8514 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7411 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8592 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8594 onmsuc 8515 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8609 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8596 nnacom 8604 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8610 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8611 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8613 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8597 nnmsucr 8612 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8625 |
| [Enderton] p. 129 | Definition | df-en 8952 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7362 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10066 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16349 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9200 |
| [Enderton] p. 135 | Corollary 6C | php3 9202 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9199 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9231 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9233 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9162 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9166 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9138 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10230 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10231 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10226 dju1en 10222 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9310 unifi 9311 unifi2 9312 |
| [Enderton] p. 144 | Corollary 6K | undif2 4430 unfi 9164 unfi2 9280 |
| [Enderton] p. 145 | Figure 38 | ffoss 7941 |
| [Enderton] p. 145 | Definition | df-dom 8953 |
| [Enderton] p. 146 | Example 1 | domen 8966 domeng 8967 |
| [Enderton] p. 146 | Example 3 | nndomo 9211 nnsdom 9633 nnsdomg 9269 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10234 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9139 xpdom1 9073 xpdom1g 9071 xpdom2g 9070 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9145 |
| [Enderton] p. 151 | Theorem 6M | zorn 10557 zorng 10554 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10542 dfac5 10179 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10632 |
| [Enderton] p. 164 | Example | infdif 10258 |
| [Enderton] p. 168 | Definition | df-po 5555 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6467 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6399 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6466 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6407 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7833 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7778 |
| [Enderton] p. 194 | Remark | onprc 7775 |
| [Enderton] p. 194 | Exercise 16 | suc11 6461 |
| [Enderton] p. 197 | Definition | df-card 9992 |
| [Enderton] p. 197 | Theorem 7P | carden 10607 |
| [Enderton] p. 200 | Exercise 25 | tfis 7849 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9758 |
| [Enderton] p. 202 | Definition | df-r1 9746 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9768 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9857 rankval4b 9853 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9585 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9844 rankprb 9838 rankpw 9829 rankpwi 9805 rankuniss 9856 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9597 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9598 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10161 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10127 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10141 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8327 |
| [Enderton] p. 222 | Definition | df-kard 35743 |
| [Enderton] p. 222 | Definition of kard | karden 9931 kardex 9929 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8584 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8586 |
| [Enderton] p. 240 | Exercise 25 | oarec 8548 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10299 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17778 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17720 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18689 mrieqv2d 17775 mrieqvd 17774 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17779 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17784 mreexexlem2d 17781 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18695 mreexfidimd 17786 |
| [Frege1879] p. 11 | Statement | df3or2 44712 |
| [Frege1879] p. 12 | Statement | df3an2 44713 dfxor4 44710 dfxor5 44711 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44734 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44735 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44739 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44743 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44744 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44750 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44752 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44753 axfrege8 44751 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38288 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44756 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44764 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44758 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44757 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44766 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44767 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44770 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44760 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44765 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44762 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44768 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44772 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44771 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44763 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44769 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44759 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44761 rp-frege25 44749 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44754 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44774 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44755 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44775 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44778 axfrege31 44777 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44776 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44779 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44780 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44781 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44782 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44783 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44784 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44785 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44786 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44787 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44789 axfrege41 44788 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44790 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44791 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44792 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44793 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44794 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44795 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44796 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44797 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44798 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44801 ax-frege52c 44832 frege52aid 44802 frege52b 44833 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44806 ax-frege54c 44836 frege54b 44837 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44799 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3740 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44804 frege53aid 44803 frege53b 44834 frege53c 44858 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2760 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44812 frege55aid 44809 frege55b 44841 frege55c 44862 frege55cor1a 44813 frege55lem2a 44811 frege55lem2b 44840 frege55lem2c 44861 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44815 frege56aid 44814 frege56b 44842 frege56c 44863 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44819 ax-frege58b 44845 frege58bid 44846 frege58c 44865 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44817 frege57aid 44816 frege57b 44843 frege57c 44864 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3751 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44821 frege59b 44848 frege59c 44866 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44822 frege60b 44849 frege60c 44867 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44823 frege61b 44850 frege61c 44868 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44824 frege62b 44851 frege62c 44869 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44825 frege63b 44852 frege63c 44870 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44826 frege64b 44853 frege64c 44871 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44827 frege65b 44854 frege65c 44872 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44828 frege66b 44855 frege66c 44873 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44829 frege67b 44856 frege67c 44874 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44830 frege68b 44857 frege68c 44875 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44876 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44877 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44878 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44879 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44880 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44883 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44881 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44882 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44884 frege77d 44690 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44885 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44886 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44887 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44888 frege81d 44691 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44889 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44890 frege83d 44692 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44891 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44892 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44893 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44894 frege87d 44694 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44895 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44896 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44897 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44898 frege91d 44695 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44899 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44900 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44901 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44902 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44906 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44903 frege96d 44693 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44904 frege97d 44696 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44905 frege98d 44697 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44907 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44908 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44909 frege102d 44698 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44910 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44911 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44912 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44913 frege106d 44699 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44914 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44915 frege108d 44700 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44916 frege109d 44701 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44917 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44918 frege111d 44703 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44919 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44920 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44921 frege114d 44702 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44922 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44923 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44924 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44925 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44926 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44927 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44928 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44929 frege122d 44704 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44930 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44931 frege124d 44705 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44932 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44933 frege126d 44706 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44934 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44935 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44936 frege129d 44707 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44937 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44938 frege131d 44708 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44939 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44940 frege133d 44709 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47245 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47568 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47268 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47383 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47403 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47394 meadjunre 47408 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47395 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47396 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47392 meaiunle 47401 meaiunlelem 47400 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47413 meaiuninc2 47414 meaiuninc3 47417 meaiuninc3v 47416 meaiunincf 47415 meaiuninclem 47412 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47419 meaiininc2 47420 meaiininclem 47418 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47438 caragendifcl 47446 caratheodory 47460 omelesplit 47450 |
| [Fremlin1] p. 19 | Definition 113A | isome 47426 isomennd 47463 isomenndlem 47462 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47448 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47467 voncmpl 47553 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47430 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47455 carageniuncllem1 47453 carageniuncllem2 47454 caragenuncl 47445 caragenuncllem 47444 caragenunicl 47456 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47464 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47458 caratheodorylem2 47459 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47467 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47526 hoidmv1lelem1 47523 hoidmv1lelem2 47524 hoidmv1lelem3 47525 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47570 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47526 hoidmvle 47532 hoidmvlelem1 47527 hoidmvlelem2 47528 hoidmvlelem3 47529 hoidmvlelem4 47530 hoidmvlelem5 47531 hsphoidmvle2 47517 hsphoif 47508 hsphoival 47511 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47480 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47488 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47515 hoidmvn0val 47516 hoidmvval 47509 hoidmvval0 47519 hoidmvval0b 47522 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47520 hsphoidmvle 47518 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47469 df-voln 47471 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47536 ovn0 47498 ovn0lem 47497 ovnf 47495 ovnome 47505 ovnssle 47493 ovnsslelem 47492 ovnsupge0 47489 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47535 ovnhoilem1 47533 ovnhoilem2 47534 vonhoi 47599 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47552 hoidifhspf 47550 hoidifhspval 47540 hoidifhspval2 47547 hoidifhspval3 47551 hspmbl 47561 hspmbllem1 47558 hspmbllem2 47559 hspmbllem3 47560 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47553 vonmea 47506 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47504 ovnsubadd2 47578 ovnsubadd2lem 47577 ovnsubaddlem1 47502 ovnsubaddlem2 47503 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47563 hoimbl2 47597 hoimbllem 47562 hspdifhsp 47548 opnvonmbl 47566 opnvonmbllem2 47565 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47568 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47611 iccvonmbllem 47610 ioovonmbl 47609 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47617 vonicclem2 47616 vonioo 47614 vonioolem2 47613 vonn0icc 47620 vonn0icc2 47624 vonn0ioo 47619 vonn0ioo2 47622 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47621 snvonmbl 47618 vonct 47625 vonsn 47623 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47291 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47290 subsaliuncllem 47289 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47657 salpreimalegt 47641 salpreimaltle 47658 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47660 issmff 47666 issmflem 47659 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47677 issmflelem 47676 smfpreimale 47686 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47688 issmfgtlem 47687 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47628 issmf 47660 issmff 47666 issmfge 47702 issmfgelem 47701 issmfgt 47688 issmfgtlem 47687 issmfle 47677 issmflelem 47676 issmflem 47659 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47639 salpreimagtlt 47662 salpreimalelt 47661 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47702 issmfgelem 47701 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47685 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47683 cnfsmf 47672 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47699 decsmflem 47698 incsmf 47674 incsmflem 47673 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47633 pimconstlt1 47634 smfconst 47681 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47697 smfaddlem1 47695 smfaddlem2 47696 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47728 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47727 smfmullem1 47723 smfmullem2 47724 smfmullem3 47725 smfmullem4 47726 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47729 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47732 smfpimbor1lem2 47731 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47734 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47722 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47721 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47730 smfresal 47720 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47709 smflim2 47738 smflimlem1 47703 smflimlem2 47704 smflimlem3 47705 smflimlem4 47706 smflimlem5 47707 smflimlem6 47708 smflimmpt 47742 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47746 smfsuplem1 47743 smfsuplem2 47744 smfsuplem3 47745 smfsupmpt 47747 smfsupxr 47748 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47750 smfinflem 47749 smfinfmpt 47751 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47709 smflim2 47738 smflimmpt 47742 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47740 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47770 smfdivdmmbl2 47773 smfinfdmmbl 47781 smfinfdmmbllem 47780 smfsupdmmbl 47777 smfsupdmmbllem 47776 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47760 smflimsuplem2 47753 smflimsuplem6 47757 smflimsuplem7 47758 smflimsuplem8 47759 smflimsupmpt 47761 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47763 smfliminflem 47762 smfliminfmpt 47764 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47628 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47774 fsupdm2 47775 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47765 adddmmbl2 47766 finfdm 47778 finfdm2 47779 fsupdm 47774 fsupdm2 47775 muldmmbl 47767 muldmmbl2 47768 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47778 finfdm2 47779 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25819 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25862 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25872 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38536 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38539 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9617 inf1 9601 inf2 9602 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10968 enqer 10978 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10973 df-nq 10969 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10965 df-plq 10971 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7646 df-mpq 10966 df-mq 10972 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10974 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11032 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11033 ltbtwnnq 11035 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11028 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11029 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11036 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11038 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11050 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11052 |
| [Gleason] p. 122 | Definition | df-1p 11039 |
| [Gleason] p. 122 | Remark (1) | prub 11051 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11090 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11042 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11089 psslinpr 11088 supexpr 11111 suplem1pr 11109 suplem2pr 11110 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11075 addclprlem1 11073 addclprlem2 11074 df-plp 11040 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11079 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11078 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11091 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11100 ltexprlem1 11093 ltexprlem2 11094 ltexprlem3 11095 ltexprlem4 11096 ltexprlem5 11097 ltexprlem6 11098 ltexprlem7 11099 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11102 ltaprlem 11101 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11103 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11104 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11041 mulclpr 11077 mulclprlem 11076 reclem2pr 11105 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11086 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11081 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11080 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11085 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11108 reclem3pr 11106 reclem4pr 11107 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11112 enrer 11120 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11117 df-1r 11118 df-nr 11113 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11115 df-plr 11114 negexsr 11159 recexsr 11164 recexsrlem 11160 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11116 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12285 creur 12284 cru 12282 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11245 axcnre 11221 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15250 crimd 15367 crimi 15328 crre 15249 crred 15366 crrei 15327 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15252 remimd 15333 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15419 absval2d 15583 absval2i 15533 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15276 cjaddd 15355 cjaddi 15323 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15277 cjmuld 15356 cjmuli 15324 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15275 cjcjd 15334 cjcji 15306 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15274 cjreb 15258 cjrebd 15337 cjrebi 15309 cjred 15361 rere 15257 rereb 15255 rerebd 15336 rerebi 15308 rered 15359 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15283 addcjd 15347 addcji 15318 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15373 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15414 abscjd 15588 abscji 15537 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15424 abs00d 15584 abs00i 15534 absne0d 15585 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15457 releabsd 15589 releabsi 15538 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15429 absmuld 15592 absmuli 15540 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15417 sqabsaddi 15541 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15466 abstrid 15594 abstrii 15544 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14174 exp0 14177 expp1 14180 expp1d 14259 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26971 cxpaddd 27009 expadd 14216 expaddd 14260 expaddz 14218 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26980 cxpmuld 27029 expmul 14219 expmuld 14261 expmulz 14220 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26977 mulcxpd 27020 mulexp 14213 mulexpd 14273 mulexpz 14214 |
| [Gleason] p. 140 | Exercise 1 | znnen 16348 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13611 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15767 rlimadd 15778 rlimdiv 15781 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15769 rlimsub 15779 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15768 rlimmul 15780 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15772 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15718 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15739 climcj 15740 climim 15742 climre 15741 rlimabs 15744 rlimcj 15745 rlimim 15747 rlimre 15746 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11320 df-xr 11319 ltxr 13214 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15606 limsupval 15609 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15805 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15814 caucvgb 15815 caucvgbf 46421 caucvgr 15811 climcau 15806 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15951 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 16020 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15471 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13937 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21634 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24624 xmet0 24623 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24640 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24631 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24633 mstri 24750 xmettri 24632 xmstri 24749 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24663 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23929 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25593 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24821 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25147 addcn2 15729 mulcn 25149 mulcn2 15731 subcn 25148 subcn2 15730 |
| [Gleason] p. 295 | Remark | bcval3 14418 bcval4 14419 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14433 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14416 df-bc 14415 |
| [Gleason] p. 296 | Remark | bcn0 14422 bcnn 14424 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15967 |
| [Gleason] p. 308 | Equation 2 | ef0 16225 |
| [Gleason] p. 308 | Equation 3 | efcj 16226 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16232 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16237 |
| [Gleason] p. 310 | Equation 14 | sinadd 16300 |
| [Gleason] p. 310 | Equation 15 | cosadd 16301 |
| [Gleason] p. 311 | Equation 17 | sincossq 16312 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16317 sinbnd 16316 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14328 sqeqori 14326 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16206 |
| [Godowski] p. 730 | Equation SF | goeqi 32809 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32204 |
| [Golan] p. 1 | Remark | srgisid 20397 |
| [Golan] p. 1 | Definition | df-srg 20375 |
| [Golan] p. 149 | Definition | df-slmd 33696 |
| [Gonshor] p. 7 | Definition | df-cuts 28080 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28119 lesrecd 28120 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28240 cofcut1d 28241 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28242 cofcut2d 28243 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28244 cofcutr1d 28245 cofcutr2d 28246 |
| [Gonshor] p. 13 | Definition | df-adds 28280 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28296 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28322 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28450 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28470 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28778 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28780 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28779 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28815 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28338 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36846 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17718 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17720 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 49207 df-cllaw 49205 df-comlaw 49206 |
| [Hall] p. 2 | Section 1.2 | df-clintop 49219 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49240 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39720 dfmembpart2 39725 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32601 riesz2 32602 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32477 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32709 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32721 elpjidm 32720 pjnmopi 32684 |
| [Halmos] p. 44 | Remark | pjinormi 32223 pjinormii 32212 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32725 pjrn 32243 pjrni 32238 pjvec 32232 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32263 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32690 hmopidmpji 32688 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32727 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32716 pjocvec 32233 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32705 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32708 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32711 pjssdif2i 32710 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32391 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1828 |
| [Hatcher] p. 25 | Definition | df-phtpc 25275 df-phtpy 25254 |
| [Hatcher] p. 26 | Definition | df-pco 25288 df-pi1 25291 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25278 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25333 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22767 df-dmatalt 49432 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48837 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48822 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48834 bgoldbtbnd 48829 bgoldbtbnd 48829 tgblthelfgott 48835 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35206 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35207 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35221 hgt750lemb 35220 hgt750leme 35222 hgt750lemf 35217 hgt750lemg 35218 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48831 tgoldbachgt 35227 tgoldbachgtALTV 48832 tgoldbachgtd 35226 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35208 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 31029 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19117 grpoideu 31045 mndideu 18896 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19147 grpoinveu 31055 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19178 grpo2inv 31067 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19190 grpoinvop 31069 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19212 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1801 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1802 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1804 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32956 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32969 cdj3i 32977 cdj3lem1 32970 cdjreui 32968 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32967 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42938 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42868 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42890 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42891 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42888 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42894 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42813 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42908 |
| [Holland95] p. 204 | Definition of involution | df-srng 21059 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40480 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42505 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42458 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40910 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42354 poml4N 40930 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42445 pexmidALTN 40955 pexmidN 40946 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42510 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 40101 ldualset 40102 |
| [Holland95] p. 222 | Item 1 | df-lines 40478 df-pointsN 40479 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40880 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40924 omllaw4 40223 pol1N 40887 polcon3N 40894 |
| [Holland95] p. 223 | Definition | df-psubclN 40912 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40883 |
| [Holmes] p. 40 | Definition | df-xrn 39232 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31620 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32718 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32499 eigre 32371 eigrei 32370 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32500 eigorth 32374 eigorthi 32373 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32372 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30844 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30840 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30841 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30842 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30860 frgrregorufr0 30859 frgrregorufrg 30861 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30867 frrusgrord 30876 frrusgrord0 30875 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30613 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30850 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30853 frgrwopreg2 30854 frgrwopregasn 30851 frgrwopregbsn 30852 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30856 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30870 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30873 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30611 numclwlk1 30906 numclwlk1lem1 30904 numclwlk1lem2 30905 numclwwlk1 30896 numclwwlk8 30927 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30847 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30292 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30882 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30908 numclwwlkovh0 30907 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30916 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30503 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30920 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30923 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30926 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30938 natded 30938 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30938 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30938 natded 30938 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30938 |
| [Jech] p. 4 | Definition of class | cv 1569 cvjust 2754 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10636 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10634 alephmul 10635 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10633 infmap2 10267 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9796 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9901 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9857 rankval4b 9853 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9926 |
| [Jech] p. 78 | Note | opthprc 5711 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43860 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43948 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43949 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43872 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43876 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43877 rmyp1 43878 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43879 rmym1 43880 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43870 rmx1 43871 rmxluc 43881 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43874 rmy1 43875 rmyluc 43882 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43884 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43885 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43905 jm2.17b 43906 jm2.17c 43907 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43938 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43942 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43933 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43908 jm2.24nn 43904 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43947 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43953 rmygeid 43909 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43965 |
| [Juillerat] p. 11 | Section *5 | etransc 47215 etransclem47 47213 etransclem48 47214 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47210 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47212 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47198 |
| [Juillerat] p. 13 | Proof | etransclem35 47201 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47204 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47190 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47207 |
| [Juillerat] p. 14 | Proof | etransclem23 47189 |
| [KalishMontague] p. 81 | Note 1 | ax-6 2000 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2045 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2050 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2040 cbvaliw 2039 wl-cbvmotv 38365 wl-motae 38367 wl-moteq 38366 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2019 spimw 2003 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2066 spw 2067 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 32052 chabs1i 32054 chabs2 32053 chabs2i 32055 chjass 32069 chjassi 32022 latabs1 18611 latabs2 18612 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32874 ela 32875 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32819 cvrval2 40251 |
| [Kalmbach] p. 16 | Definition | df-ol 40155 df-oml 40156 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 32120 cmbri 32126 cmtvalN 40188 df-cm 32119 df-cmtN 40154 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40224 pjoml5 32149 pjoml5i 32124 |
| [Kalmbach] p. 22 | Definition | pjoml2 32147 pjoml2i 32121 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 32150 cmcmi 32128 cmcmii 32133 cmtcomN 40226 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40222 omlsi 31940 pjoml 31972 pjomli 31971 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40221 |
| [Kalmbach] p. 23 | Remark | cmbr2i 32132 cmcm3 32151 cmcm3i 32130 cmcm3ii 32135 cmcm4i 32131 cmt3N 40228 cmt4N 40229 cmtbr2N 40230 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 32144 cmbr3i 32136 cmtbr3N 40231 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 32154 fh1i 32157 fh2 32155 fh2i 32158 omlfh1N 40235 |
| [Kalmbach] p. 65 | Remark | chjatom 32893 chslej 32034 chsleji 31994 shslej 31916 shsleji 31906 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 32031 chocini 31990 chsupcl 31876 chsupval2 31946 h0elch 31791 helch 31779 hsupval2 31945 ocin 31832 ococss 31829 shococss 31830 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31848 |
| [Kalmbach] p. 66 | Remark | df-pjh 31931 pjssmi 32701 pjssmii 32217 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32181 osumi 32178 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32736 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32936 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32846 |
| [Kalmbach] p. 140 | Remark | hatomic 32896 hatomici 32895 hatomistici 32898 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40296 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32917 lsatexch 40020 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32891 cvlcvr1 40316 cvr1 40387 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32910 cvexchi 32905 cvrexch 40397 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32900 hlrelat 40379 hlrelat5N 40378 lrelat 39991 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21381 lsmsatcv 39987 spansncv 32189 spansncvi 32188 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 40006 spansncv2 32829 |
| [Kalmbach] p. 266 | Definition | df-st 32747 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32385 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10703 fpwwe2 10700 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10704 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10711 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10706 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10708 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10721 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10725 gchxpidm 10726 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10737 gchhar 10736 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10265 unxpwdom 9561 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10727 |
| [Kreyszig] p. 3 | Property M1 | metcl 24613 xmetcl 24612 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24620 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24853 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 12004 muleqadd 11930 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24719 |
| [Kreyszig] p. 19 | Remark | mopntopon 24720 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24779 mopnm 24725 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24777 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24782 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24823 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23538 lmmbr 25541 lmmbr2 25542 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23660 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25596 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25559 iscmet2 25577 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25599 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23742 metelcls 25588 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25589 metcld2 25590 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25382 lmodvneg1 21142 nvinv 31175 vcm 31112 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25378 lmod0vs 21132 slmd0vs 33719 vc0 31110 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21133 slmdvs0 33720 vcz 31111 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31227 ngpmet 24884 nrmmetd 24855 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31222 imsdval2 31223 ncvspds 25444 ngpds 24885 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24870 nvnd 31224 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24899 nmge0 24898 nvge0 31209 nvz 31205 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24905 nvabs 31208 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31337 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31281 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31343 blocni 31341 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31342 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25487 ipeq0 21906 ipz 31255 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25499 pythi 31386 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31390 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25521 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15993 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25719 minveco 31420 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31286 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25612 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31409 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32659 leopg 32658 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32677 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31454 |
| [Kulpa] p. 547 | Theorem | poimir 38491 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38490 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38489 |
| [Kulpa] p. 548 | Theorem | broucube 38492 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38484 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38485 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2412 axnul 5258 |
| [Kunen] p. 11 | Axiom 3 | axnul 5258 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5241 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8836 mapvalg 8834 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10572 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7935 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9746 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9788 r1elssi 9787 |
| [Kunen] p. 107 | Exercise 4 | rankop 9845 rankopb 9839 rankuni 9852 rankxplim 9869 rankxpsuc 9872 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45881 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45889 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45888 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45890 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45895 rexabso 45896 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45902 n0abso 45903 ssabso 45901 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45904 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45914 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45909 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45912 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45913 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45908 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45920 wfaxpr 45925 wfaxreg 45927 wfaxrep 45921 wfaxsep 45922 wfaxun 45926 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45911 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45924 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45920 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45919 omelaxinf2 45916 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45929 wfaxinf2 45928 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45942 permaxext 45932 permaxinf2 45940 permaxnul 45935 permaxpow 45936 permaxpr 45937 permaxrep 45933 permaxsep 45934 permaxun 45938 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45930 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45941 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4963 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34231 |
| [Lang] p. | Definition | df-rn 5658 |
| [Lang] p. 3 | Statement | lidrideqd 18812 mndbn0 18902 |
| [Lang] p. 3 | Definition | df-mnd 18886 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18838 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18999 |
| [Lang] p. 5 | Equation | gsumreidx 20093 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 49201 |
| [Lang] p. 6 | Example | nn0mnd 49198 |
| [Lang] p. 6 | Equation | gsumxp2 20156 |
| [Lang] p. 6 | Statement | cycsubm 19379 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19252 |
| [Lang] p. 6 | Observation | mndlsmidm 19846 |
| [Lang] p. 7 | Definition | dfgrp2e 19136 |
| [Lang] p. 30 | Definition | df-tocyc 33602 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33647 |
| [Lang] p. 32 | Property (b) | cyc3conja 33652 cycpmconjv 33637 |
| [Lang] p. 53 | Definition | df-cat 17804 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18234 cat1lem 18233 |
| [Lang] p. 54 | Definition | df-iso 17886 |
| [Lang] p. 57 | Definition | df-inito 18121 df-termo 18122 |
| [Lang] p. 58 | Example | irinitoringc 21747 |
| [Lang] p. 58 | Statement | initoeu1 18148 termoeu1 18155 |
| [Lang] p. 62 | Definition | df-func 17995 |
| [Lang] p. 65 | Definition | df-nat 18083 |
| [Lang] p. 83 | Definition of "ring with unit" | dfring2 20479 |
| [Lang] p. 91 | Note | df-ringc 20860 |
| [Lang] p. 92 | Statement | mxidlprm 33929 |
| [Lang] p. 92 | Definition | isprmidlc 21590 |
| [Lang] p. 128 | Remark | dsmmlmod 22013 |
| [Lang] p. 129 | Proof | lincscm 49464 lincscmcl 49466 lincsum 49463 lincsumcl 49465 |
| [Lang] p. 129 | Statement | lincolss 49468 |
| [Lang] p. 129 | Observation | dsmmfi 22006 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34193 qusdimsum 34194 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34174 |
| [Lang] p. 147 | Definition | snlindsntor 49505 |
| [Lang] p. 504 | Statement | mat1 22724 matring 22720 |
| [Lang] p. 504 | Definition | df-mamu 22668 |
| [Lang] p. 505 | Statement | mamuass 22679 mamutpos 22735 matassa 22721 mattposvs 22732 tposmap 22734 |
| [Lang] p. 513 | Definition | mdet1 22878 mdetf 22872 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22971 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22864 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22888 |
| [Lang] p. 515 | Definition | df-minmar1 22912 smadiadetr 22952 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22887 mdetralt 22885 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22900 |
| [Lang] p. 518 | Definition | df-madu 22911 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22922 madurid 22921 matinv 22954 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23170 |
| [Lang], p. 190 | Chapter 6 | vieta 34146 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34260 finextalg 34264 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34229 fedgmul 34197 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34291 |
| [Lang], p. 561 | Remark | chpmatply1 23112 |
| [Lang], p. 561 | Definition | df-chpmat 23107 |
| [Lang2] p. 3 | Notations | df-ind 12291 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45262 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45257 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45263 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5258 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2739 wl-df.clab 38350 |
| [Levy] p. 59 | Definition | df-ttrcl 9687 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9733 |
| [Levy] p. 338 | Axiom | df-clel 2835 df-cleq 2752 wl-df.cleq 38351 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38354 |
| [Levy] p. 357 | Definition extends to class variables a relation already valid for set variables, and is therefore conservative. This only sketches the conservativity arguement; for details see Appendix | wl-df.clel 38354 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2835 df-cleq 2752 wl-df.cleq 38351 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2739 wl-df.clab 38350 |
| [Levy] p. 358 | Axiom | df-clab 2739 wl-df.clab 38350 |
| [Levy58] p. 2 | Definition I | isfin1-3 10436 |
| [Levy58] p. 2 | Definition II | df-fin2 10336 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10335 |
| [Levy58] p. 2 | Definition III | df-fin3 10338 |
| [Levy58] p. 3 | Definition V | df-fin5 10339 |
| [Levy58] p. 3 | Definition IV | df-fin4 10337 |
| [Levy58] p. 4 | Definition VI | df-fin6 10340 |
| [Levy58] p. 4 | Definition VII | df-fin7 10341 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10465 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27977 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27988 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 28020 nosupbnd1 28005 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 28022 nosupbnd2 28007 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 28026 noetasuplem4 28027 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 28023 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1801 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1802 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1804 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32944 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32948 mdsymi 32947 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32942 mdsymlem6 32944 mdsymlem7 32945 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32946 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32849 ssdmd2 32850 ssmd1 32847 ssmd2 32848 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32845 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32817 df-md 32816 mdbr 32830 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32867 mdslj1i 32855 mdslj2i 32856 mdslle1i 32853 mdslle2i 32854 mdslmd1i 32865 mdslmd2i 32866 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32857 mdsl2bi 32859 mdsl2i 32858 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32871 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32868 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32869 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32846 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32851 mdsl3 32852 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32870 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32965 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40298 hlrelat1 40377 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 40016 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32872 cvmdi 32860 cvnbtwn4 32825 cvrnbtwn4 40256 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32873 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40317 cvp 32911 cvrp 40393 lcvp 40017 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32935 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32934 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40310 hlexch4N 40369 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32937 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40420 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40726 atpsubN 40730 df-pointsN 40479 pointpsubN 40728 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40481 pmap11 40739 pmaple 40738 pmapsub 40745 pmapval 40734 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40742 pmap1N 40744 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40747 pmapglb2N 40748 pmapglb2xN 40749 pmapglbx 40746 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40829 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40454 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40773 paddclN 40819 paddidm 40818 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40455 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40815 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40454 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40455 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19851 lsmmod2 19852 lssats 39989 shatomici 32894 shatomistici 32897 shmodi 31926 shmodsi 31925 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32836 mdsymlem7 32945 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 32125 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 32029 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32951 |
| [Margaris] p. 40 | Rule C | exlimiv 1963 |
| [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 402 df-ex 1813 df-or 862 dfbi2 480 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 30935 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45841 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45842 |
| [Margaris] p. 79 | Rule C | exinst01 45552 exinst11 45553 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2009 19.2g 2224 r19.2z 4454 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2238 rr19.3v 3620 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2196 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1859 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1814 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2217 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2241 19.9h 2319 exlimd 2254 exlimdh 2323 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2199 excomim 2200 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2357 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30936 conventions-labels 30936 conventions-labels 30936 conventions-labels 30936 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1860 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45306 albi 1851 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2261 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2262 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45308 exbi 1880 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2265 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45305 2alimdv 1951 alimd 2248 alimdh 1850 alimdv 1949 ax-4 1842 ralimdaa 3263 ralimdv 3176 ralimdva 3174 ralimdvva 3209 sbcimdv 3806 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2243 19.21h 2320 19.21t 2242 19.21vv 45304 alrimd 2251 alrimdd 2250 alrimdh 1896 alrimdv 1962 alrimi 2249 alrimih 1857 alrimiv 1960 alrimivv 1961 bj-alrimdh 37416 hbralrimi 3152 r19.21be 3255 r19.21bi 3254 ralrimd 3267 ralrimdv 3160 ralrimdva 3162 ralrimdvv 3206 ralrimdvva 3217 ralrimi 3260 ralrimia 3261 ralrimiv 3153 ralrimiva 3154 ralrimivv 3203 ralrimivva 3205 ralrimivvva 3208 ralrimivw 3158 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45307 2eximdv 1952 bj-exim 37431 exim 1867 eximd 2252 eximdh 1897 eximdv 1950 rexim 3103 reximd2a 3272 reximdai 3264 reximdd 46084 reximddv 3178 reximddv2 3221 reximddv3 3179 reximdv 3177 reximdv2 3172 reximdva 3175 reximdvai 3173 reximdvva 3210 reximi2 3095 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2247 19.23bi 2227 19.23h 2321 19.23t 2246 exlimdv 1966 exlimdvv 1967 exlimexi 45451 exlimiv 1963 exlimivv 1965 rexlimd3 46080 rexlimdv 3161 rexlimdv3a 3167 rexlimdva 3163 rexlimdva2 3165 rexlimdvaa 3164 rexlimdvv 3218 rexlimdvva 3219 rexlimdvvva 3220 rexlimdvw 3168 rexlimiv 3156 rexlimiva 3155 rexlimivv 3204 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2024 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1913 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1903 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2263 r19.27z 4465 r19.27zv 4466 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2264 19.28vv 45314 r19.28z 4457 r19.28zf 46095 r19.28zv 4461 rr19.28v 3621 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1906 r19.29d2r 3149 r19.29imd 3127 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1914 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2270 19.31vv 45312 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2269 r19.32 48090 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45310 19.33 1917 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2025 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1910 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2266 19.36vv 45311 r19.36zv 4467 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2268 19.37vv 45313 r19.37zv 4462 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1872 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2023 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1920 19.40 1919 r19.40 3128 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2271 19.41rg 45477 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2272 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1915 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2273 r19.44zv 4464 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2274 r19.45zv 4463 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2635 |
| [Mayet] p. 370 | Remark | jpi 32806 largei 32803 stri 32793 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32748 ishst 32750 |
| [Mayet3] p. 10 | Theorem | hstrbi 32802 hstri 32801 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32264 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32265 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32814 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31868 chsupcl 31876 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32896 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32890 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32917 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40960 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18623 latj32 18621 latjass 18619 |
| [Megill] p. 444 | Axiom C5 | ax-5 1943 ax5ALT 39884 |
| [Megill] p. 444 | Section 7 | conventions 30935 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39878 ax-c11n 39865 axc11n 2455 |
| [Megill] p. 446 | Lemma L17 | equtrr 2055 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39873 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39905 hbnae 2461 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2510 sbid 2290 sbidd-misc 50734 sbidd 50733 |
| [Megill] p. 448 | Remark 9.6 | axc14 2492 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39861 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39860 sp 2219 |
| [Megill] p. 448 | Scheme C6' | ax-11 2194 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39862 |
| [Megill] p. 448 | Scheme C8' | ax-7 2041 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39867 |
| [Megill] p. 448 | Scheme C10' | ax-6 2000 ax-c10 39863 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39864 |
| [Megill] p. 448 | Scheme C12' | ax-8 2147 |
| [Megill] p. 448 | Scheme C13' | ax-9 2155 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39868 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39866 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39869 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39881 dral1 2468 dral2-o 39907 dral2 2467 drex1 2470 drex2 2471 drsb1 2524 drsb2 2300 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2209 sbequ 2120 sbid2v 2538 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39874 hba1 2326 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47884 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3825 rspsbca 3826 stdpc4 2105 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39861 ra4 3832 stdpc5 2244 |
| [Mendelson] p. 81 | Rule C | exlimiv 1963 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2061 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2285 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3737 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5483 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4347 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4348 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4222 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4279 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4223 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4087 |
| [Mendelson] p. 231 | Definition of union | dfun3 4221 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5418 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4863 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5538 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4574 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5539 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4890 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5800 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6260 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7772 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6357 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8582 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9137 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9058 xpsneng 9059 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9065 xpcomeng 9066 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9068 |
| [Mendelson] p. 255 | Definition | brsdom 8979 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9061 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8829 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9043 mapsnend 9042 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9143 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9142 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8888 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9046 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9062 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10229 djucomen 10228 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10233 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10227 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8517 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8544 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10615 |
| [Mendelson] p. 281 | Definition | df-r1 9746 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9795 |
| [Mendelson] p. 287 | Axiom system MK | ru 3737 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30794 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30829 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30831 vdgn1frgrv3 30832 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30833 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30826 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30819 2pthfrgrrn 30817 2pthfrgrrn2 30818 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31788 |
| [Monk1] p. 22 | Remark | conventions 30935 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30935 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4183 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5755 ssrelf 33143 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5756 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5167 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6253 coi2 6254 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5898 rn0 5904 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5859 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5665 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5907 rnxp 6157 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5746 xp0 5747 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6067 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6064 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7909 imaexg 7908 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6061 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7063 funfvop 7037 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6927 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6938 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6574 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7246 dff13f 7247 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7213 funrnex 7949 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7239 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6217 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4923 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8001 df-1st 7984 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8002 df-2nd 7985 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9841 ranksnb 9810 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9842 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9843 rankunb 9837 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9823 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9746 r1val2 9822 |
| [Monk1] p. 117 | Lemma | zorn2 10556 zorn2g 10553 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10039 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10617 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10034 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1842 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2041 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2213 ax-c15 39866 ax12v2 2215 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39861 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2194 |
| [Monk2] p. 109 | Lemma 15 | equvini 2484 equvinv 2062 eqvinop 5455 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1943 ax5ALT 39884 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2178 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2194 |
| [Monk2] p. 114 | Lemma 21 | sp 2219 |
| [Monk2] p. 114 | Lemma 22 | axc4 2351 hba1-o 39874 hba1 2326 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2190 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2210 nfra2 3361 nfra2w 3298 |
| [Moore] p. 53 | Part I | df-mre 17718 |
| [Munkres] p. 77 | Example 2 | distop 23275 indistop 23282 indistopon 23281 |
| [Munkres] p. 77 | Example 3 | fctop 23284 fctop2 23285 |
| [Munkres] p. 77 | Example 4 | cctop 23286 |
| [Munkres] p. 78 | Definition of basis | df-bases 23226 isbasis3g 23229 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17576 tgval2 23236 |
| [Munkres] p. 79 | Remark | tgcl 23249 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23243 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23267 tgss3 23266 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23268 basgen2 23269 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38192 topdifinfeq 38193 topdifinffin 38191 topdifinfindis 38189 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23440 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23318 topcld 23315 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23319 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23321 |
| [Munkres] p. 94 | Definition of closure | clsval 23317 |
| [Munkres] p. 94 | Definition of interior | ntrval 23316 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23355 elcls 23353 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23363 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23428 neindisj 23397 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23430 |
| [Munkres] p. 97 | Definition of limit point | islp2 23425 lpval 23419 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23595 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23507 iscn 23515 iscn2 23518 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23560 cncnp2 23561 cncnpi 23558 df-cnp 23508 iscnp 23517 iscnp2 23519 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24824 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25594 |
| [Nathanson] p. 123 | Remark | reprgt 35185 reprinfz1 35186 reprlt 35183 |
| [Nathanson] p. 123 | Definition | df-repr 35173 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35205 |
| [Nathanson] p. 123 | Proposition | breprexp 35197 breprexpnat 35198 itgexpif 35170 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32640 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48830 |
| [Pfenning] p. 17 | Definition XM | natded 30938 |
| [Pfenning] p. 17 | Definition NNC | natded 30938 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 30938 |
| [Pfenning] p. 18 | Rule" | natded 30938 |
| [Pfenning] p. 18 | Definition /\I | natded 30938 |
| [Pfenning] p. 18 | Definition ` `E | natded 30938 natded 30938 natded 30938 natded 30938 natded 30938 |
| [Pfenning] p. 18 | Definition ` `I | natded 30938 natded 30938 natded 30938 natded 30938 natded 30938 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30938 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30938 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30938 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30938 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30938 |
| [Pfenning] p. 127 | Definition =E | natded 30938 |
| [Pfenning] p. 127 | Definition =I | natded 30938 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25485 df-dip 31237 dip0l 31254 ip0l 21904 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25526 ipval 31239 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31250 ipcj 21902 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25488 dipdir 31378 ipdir 21907 ipdiri 31366 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31246 nmsq 25477 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31361 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31363 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31364 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25494 dipass 31381 ipass 21913 ipassi 31377 |
| [Prugovecki] p. 186 | Definition of bra | braval 32480 df-bra 32386 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32387 kbval 32490 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32918 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40865 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32932 atcvat4i 32933 cvrat3 40419 cvrat4 40420 lsatcvat3 40029 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32818 cvrval 40246 df-cv 32815 df-lcv 39996 lspsncv0 21386 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40877 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40878 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2739 rabid 3432 rabidd 46091 wl-df.clab 38350 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2312 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2752 wl-df.cleq 38351 |
| [Quine] p. 19 | Definition 2.9 | conventions 30935 df-v 3452 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2899 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2896 abid2f 2952 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2309 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2122 sbalex 2278 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2835 wl-df.clel 38354 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2760 eqid1 31002 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2767 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3739 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3740 dfsbcq2 3741 |
| [Quine] p. 43 | Theorem 6.8 | vex 3454 |
| [Quine] p. 43 | Theorem 6.9 | isset 3464 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3545 spcgv 3550 spcimgf 3513 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3751 spsbcd 3752 |
| [Quine] p. 44 | Theorem 6.12 | elex 3471 |
| [Quine] p. 44 | Theorem 6.13 | elab 3632 elabg 3629 elabgf 3627 |
| [Quine] p. 44 | Theorem 6.14 | noel 4283 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4677 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4586 df-sn 4584 |
| [Quine] p. 49 | Theorem 7.4 | snss 4744 snssg 4743 |
| [Quine] p. 49 | Theorem 7.5 | prss 4780 prssg 4779 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4722 prid1g 4720 prid2 4723 prid2g 4721 snid 4622 snidg 4620 |
| [Quine] p. 51 | Theorem 7.12 | snex 5396 |
| [Quine] p. 51 | Theorem 7.13 | prex 5395 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4885 unisnALT 45852 unisng 4884 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4889 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4898 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4895 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6497 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 48078 dfiota2 6484 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 48087 iotaval 6501 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6507 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6503 |
| [Quine] p. 58 | Definition 9.1 | df-op 4590 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5495 opabidw 5494 opelopab 5513 opelopaba 5506 opelopabaf 5515 opelopabf 5516 opelopabg 5509 opelopabga 5503 opelopabgf 5511 oprabid 7440 oprabidw 7439 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5653 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5655 |
| [Quine] p. 64 | Definition 9.15 | df-id 5542 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6593 |
| [Quine] p. 65 | Theorem 10.4 | funi 6560 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6581 funsng 6579 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6529 |
| [Quine] p. 65 | Definition 10.2 | args 6082 dffv4 6870 |
| [Quine] p. 68 | Definition 10.11 | conventions 30935 df-fv 6535 fv2 6868 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14384 nn0opth2i 14383 nn0opthi 14382 omopthi 8648 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8396 |
| [Quine] p. 232 | Equation i | carddom 10610 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6615 funimaexg 6614 |
| [Quine] p. 331 | Axiom system NF | ru 3737 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31620 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31237 polid 31695 polid2i 31693 polidi 31694 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31349 |
| [ReedSimon] p. 195 | Remark | lnophm 32555 lnophmi 32554 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32668 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32670 leopmuli 32669 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32673 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32388 leoppos 32662 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32672 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32661 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48631 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48639 |
| [Roman] p. 4 | Definition | df-dmat 22767 df-dmatalt 49432 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20337 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20423 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49519 |
| [Roman] p. 112 | Note | isldepslvec2 49519 ldepsnlinc 49542 zlmodzxznm 49531 |
| [Roman] p. 112 | Example | zlmodzxzequa 49530 zlmodzxzequap 49533 zlmodzxzldep 49538 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23170 |
| [Rosenlicht] p. 80 | Theorem | heicant 38493 |
| [Rosser] p. 281 | Definition | df-op 4590 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35209 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35210 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49400 pmtr3ncom 19651 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19647 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19590 cayleyth 19591 |
| [Rudin] p. 164 | Equation 27 | efcan 16230 |
| [Rudin] p. 164 | Equation 30 | efzval 16238 |
| [Rudin] p. 167 | Equation 48 | absefi 16332 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 50854 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1804 |
| [Sanford] p. 39 | Rule 4 | mptxor 1802 |
| [Sanford] p. 40 | Rule 1 | mptnan 1801 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6103 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6106 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6102 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6100 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17718 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17719 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17719 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17721 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10187 |
| [Schechter] p. 141 | Definition (MC) | dfac11 44007 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10496 axdc3 10504 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20425 isrngo 38751 |
| [Schechter] p. 276 | Remark 11.6.e | span0 32078 |
| [Schechter] p. 276 | Definition of span | df-span 31845 spanval 31869 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23273 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6376 onelond 36870 onelord 44196 ordelon 6375 ordelord 6373 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44197 sucidg 6435 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6407 onsuc 7807 ord0 6406 ordsuci 7805 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44198 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5215 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43973 elon2 6362 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6357 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5550 epelg 5548 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9572 epirron 44199 ordirr 6369 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44201 oneptr 44200 ontr1 6399 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6395 oneptri 44202 ordtri3or 6384 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8487 ord0eln0 6408 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6421 onsucss 44211 trsucss 6442 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7812 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6448 ordnbtwn 6447 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44213 ordnexbtwnsuc 44212 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10451 onsucf1lem 44214 onsucf1o 44217 onsucf1olem 44215 onsucrn 44216 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44218 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7839 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44207 ordne0gt0 44206 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44209 limnsuc 44210 onsucelab 44208 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9622 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7854 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9625 ordom 7870 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9626 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8627 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7777 ssorduni 7776 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8517 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9629 limom 7876 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8454 df1o2 8461 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8502 oa0suclim 44220 oalim 8518 oasuc 8510 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8503 om0suclim 44221 omlim 8519 omsuc 8512 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8508 oe0m1 8507 oe0suclim 44222 oelim 8520 oesuc 8513 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 44174 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44224 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44225 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44226 limexissupab 44228 limiun 44227 limuni 6414 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8524 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8528 om1om1r 44229 om1r 8529 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8521 oaomoecl 44223 oecl 8523 omcl 8522 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 44176 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8530 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8531 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44230 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44231 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8598 nnamecl 44232 nnecl 8600 nnmcl 8599 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44233 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8538 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8539 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8546 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44235 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44236 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44238 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8545 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44242 omword1 8559 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44241 oaordnrex 44240 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44237 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44243 omword2 8560 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44244 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44245 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44246 omordi 8552 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8554 omord2com 44247 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44248 df-2o 8455 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44251 oewordi 8578 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44252 oeworde 8580 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44253 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44254 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44250 omnord1ex 44249 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44255 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44257 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44261 oenord1ex 44260 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44262 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8547 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44256 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8565 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8566 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44264 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8584 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44265 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44266 cantnfub2 44267 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44270 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29426 axtgcgrrflx 28858 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29427 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29428 axtgcgrid 28859 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28844 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29439 axtgsegcon 28860 df-trkgcb 28846 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29450 axtg5seg 28861 df-trkgcb 28846 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29451 axtgbtwnid 28862 df-trkgb 28845 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29453 axtgpasch 28863 df-trkgb 28845 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29472 df-trkg2d 35229 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28866 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28867 df-trkg2d 35229 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29475 axtgeucl 28868 df-trkge 28847 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29488 axtgcont 28865 axtgcont1 28864 df-trkgb 28845 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29366 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36674 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36676 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36679 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36683 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36684 tgcgrcomimp 28873 tgcgrcoml 28875 tgcgrcomr 28874 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36689 tgcgrtriv 28880 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36693 tg5segofs 35240 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35237 df-ofs 36670 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36695 tgcgrextend 28881 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36697 tgsegconeq 28882 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36709 btwntriv2 36699 tgbtwntriv2 28884 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36700 tgbtwncom 28885 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36703 tgbtwntriv1 28888 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36704 tgbtwnswapid 28889 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36710 btwnintr 36706 tgbtwnexch2 28893 tgbtwnintr 28890 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36712 btwnexch3 36707 tgbtwnexch 28895 tgbtwnexch3 28891 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36711 tgbtwnouttr 28894 tgbtwnouttr2 28892 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29471 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36714 tgbtwndiff 28903 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28896 trisegint 36715 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36731 tgifscgr 28905 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28955 colrot1 28956 colrot2 28957 lncom 29024 lnrot1 29025 lnrot2 29026 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36727 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36732 tgcgrsub 28906 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36742 tgcgrxfr 28915 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28914 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36728 df-cgrg 28908 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28908 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36743 tgbtwnxfr 28927 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36749 colinearperm2 36751 colinearperm3 36750 colinearperm4 36752 colinearperm5 36753 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28930 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36726 tgellng 28950 tglng 28943 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36754 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36762 lnxfr 28963 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36763 lnext 28964 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36767 tgfscgr 28965 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36768 lncgr 28966 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36729 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36770 lnid 28967 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36771 tgidinside 28968 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36788 tgbtwnconn1 28972 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36789 tgbtwnconn2 28973 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36790 tgbtwnconn3 28974 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36796 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36794 legov 28982 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28983 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28996 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36797 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36799 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36801 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36802 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36803 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36800 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36805 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28984 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28986 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28987 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28988 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28989 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36812 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36813 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36808 df-outsideof 36807 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36809 ishlg 29002 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 29007 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 29009 outsideofrflx 36814 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 29003 hlcomd 29004 outsideofcom 36815 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 29010 outsideoftr 36816 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 29019 hlcgreu 29018 outsideofeu 36818 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36825 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36826 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36819 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36834 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36835 tglineelsb2 29034 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36837 linerflx1 36836 linerflx2 36838 tglinecom 29037 tglinerflx1 29035 tglinerflx2 29036 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36840 tglinethru 29038 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36824 tglng 28943 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28991 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36843 tglinethrueu 29041 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36844 tglineineq 29045 tglineinsn 29046 tglineinteq 29048 tglineintmo 29044 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 29052 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 29053 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 29054 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 29072 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 29068 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 29060 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 29059 ismir 29065 mirbtwn 29064 mircgr 29063 mirfv 29062 mirval 29061 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 29070 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 29071 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 29072 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 29075 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 29076 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 29081 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 29078 mirbtwni 29077 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 29079 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 29091 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 29095 symquadmid 29238 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 29092 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 29093 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 29094 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 29097 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 29098 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 29107 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 29103 israg 29106 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 29108 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 29109 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 29111 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 29112 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 29113 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 29114 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 29115 ragncol 29118 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 29116 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29122 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29126 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29123 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 29105 isperp 29121 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29124 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29131 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29140 colperpexlem2 29141 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29143 colperpexlem3 29142 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29148 midex 29147 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29145 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29154 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29149 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29158 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29161 opphllem6 29162 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29164 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28863 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29167 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29175 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29170 hpgbr 29172 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29177 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29176 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29178 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29179 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29180 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29181 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29182 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29196 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29198 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29202 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29186 elplng 29192 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29204 lnssplng1 29205 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29209 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29223 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29213 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29227 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29228 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29229 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29230 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29231 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29234 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29236 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29214 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29237 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29241 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29242 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29243 lnperpexs 29244 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29245 trgcopyeu 29247 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29272 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29250 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29259 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29257 cgrahl2 29258 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29260 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29261 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29263 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29264 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29268 cgrahl 29269 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29273 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29274 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29275 acopyeu 29276 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29277 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29278 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29279 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29280 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29282 |
| [Schwabhauser] p. 99 | Theorem 11.22 | tgaaddcpbl 29286 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29294 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29298 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29291 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29306 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29299 isleag 29300 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29334 tgsas1 29333 tgsas2 29335 tgsas3 29336 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29338 tgasa1 29337 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29339 tgsss2 29340 tgsss3 29341 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29349 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29352 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29353 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29358 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29359 dfprlng3 29360 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29362 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29363 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29366 prlngmo2 29368 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29367 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29370 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29371 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29372 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29373 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29374 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29376 prlngsymquadopp 29377 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29378 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29379 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27562 dchrsum 27560 dchrsum2 27559 sumdchr 27563 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27564 sum2dchr 27565 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20244 ablfacrp2 20245 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27507 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27508 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27515 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27773 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27776 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27830 vmalogdivsum2 27829 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27820 dirith2 27819 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27818 rpvmasum 27817 rpvmasum2 27803 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27778 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27816 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27783 dchrisumlem1 27780 dchrisumlem2 27781 dchrisumlem3 27782 dchrisumlema 27779 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27786 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27815 dchrmusumlem 27813 dchrvmasumlem 27814 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27785 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27787 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27811 dchrisum0re 27804 dchrisumn0 27812 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27797 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27801 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27802 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27857 pntrsumbnd2 27858 pntrsumo1 27856 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27821 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27823 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27825 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27828 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27833 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27834 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27839 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27841 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27842 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27850 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27851 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27848 selberg3lem2 27849 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27852 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27846 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27859 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27860 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27861 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27875 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27887 pntlemb 27888 pntlemc 27886 pntlemd 27885 pntlemg 27889 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27887 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27879 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27884 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27887 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27900 pntleml 27902 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34309 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34296 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34328 constrinvcl 34339 constrmulcl 34337 constrnegcl 34329 constrsqrtcl 34345 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34315 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34325 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34347 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34357 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4251 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4355 dif0 4326 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4446 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4428 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4242 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4243 |
| [Stoll] p. 20 | Remark | invdif 4224 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4592 |
| [Stoll] p. 43 | Definition | uniiun 5016 |
| [Stoll] p. 44 | Definition | intiin 5017 |
| [Stoll] p. 45 | Definition | df-iin 4953 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4952 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 407 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4251 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45263 |
| [Suppes] p. 22 | Theorem 2 | eq0 4296 eq0f 4293 |
| [Suppes] p. 22 | Theorem 4 | eqss 3945 eqssd 3947 eqssi 3946 |
| [Suppes] p. 23 | Theorem 5 | ss0 4351 ss0b 4350 |
| [Suppes] p. 23 | Theorem 6 | sstr 3938 sstrALT2 45761 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4050 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4052 |
| [Suppes] p. 23 | Theorem 9 | psstr 4055 |
| [Suppes] p. 23 | Theorem 10 | pssss 4045 |
| [Suppes] p. 25 | Theorem 12 | elin 3914 elun 4099 |
| [Suppes] p. 26 | Theorem 15 | inidm 4171 |
| [Suppes] p. 26 | Theorem 16 | in0 4344 |
| [Suppes] p. 27 | Theorem 23 | unidm 4103 |
| [Suppes] p. 27 | Theorem 24 | un0 4343 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4123 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4131 |
| [Suppes] p. 27 | Theorem 27 | unss 4135 |
| [Suppes] p. 27 | Theorem 28 | indir 4231 |
| [Suppes] p. 27 | Theorem 29 | undir 4232 |
| [Suppes] p. 28 | Theorem 32 | difid 4324 |
| [Suppes] p. 29 | Theorem 33 | difin 4217 |
| [Suppes] p. 29 | Theorem 34 | indif 4225 |
| [Suppes] p. 29 | Theorem 35 | undif1 4429 |
| [Suppes] p. 29 | Theorem 36 | difun2 4436 |
| [Suppes] p. 29 | Theorem 37 | difin0 4427 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4425 |
| [Suppes] p. 29 | Theorem 39 | difundi 4235 |
| [Suppes] p. 29 | Theorem 40 | difindi 4237 |
| [Suppes] p. 30 | Theorem 41 | nalset 5267 |
| [Suppes] p. 39 | Theorem 61 | uniss 4874 |
| [Suppes] p. 39 | Theorem 65 | uniop 5484 |
| [Suppes] p. 41 | Theorem 70 | intsn 4943 |
| [Suppes] p. 42 | Theorem 71 | intpr 4941 intprg 4940 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5439 |
| [Suppes] p. 42 | Theorem 78 | intun 4939 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4989 dfiun2g 4987 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4990 |
| [Suppes] p. 47 | Theorem 86 | elpw 4560 elpw2 5295 elpw2g 5294 elpwg 4559 elpwgdedVD 45843 |
| [Suppes] p. 47 | Theorem 87 | pwid 4579 |
| [Suppes] p. 47 | Theorem 89 | pw0 4772 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4773 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5662 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5806 xpindir 5807 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5716 xpundir 5717 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9569 |
| [Suppes] p. 58 | Theorem 2 | relss 5754 |
| [Suppes] p. 59 | Theorem 4 | eldm 5878 eldm2 5879 eldm2g 5877 eldmg 5876 |
| [Suppes] p. 59 | Definition 3 | df-dm 5657 |
| [Suppes] p. 60 | Theorem 6 | dmin 5889 |
| [Suppes] p. 60 | Theorem 8 | rnun 6130 |
| [Suppes] p. 60 | Theorem 9 | rnin 6131 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5866 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5856 brcnvg 5853 |
| [Suppes] p. 62 | Equation 5 | elcnv 5850 elcnv2 5851 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6094 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6129 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6127 |
| [Suppes] p. 63 | Definition | dftrrels2 39511 |
| [Suppes] p. 63 | Theorem 20 | co02 6251 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5953 |
| [Suppes] p. 63 | Definition 7 | df-co 5656 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5863 |
| [Suppes] p. 64 | Theorem 27 | coass 6256 |
| [Suppes] p. 65 | Theorem 31 | resundi 5980 |
| [Suppes] p. 65 | Theorem 34 | elima 6055 elima2 6056 elima3 6057 elimag 6054 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6135 |
| [Suppes] p. 66 | Theorem 40 | dminss 6138 |
| [Suppes] p. 66 | Theorem 41 | imainss 6139 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6142 |
| [Suppes] p. 81 | Definition 34 | dfec2 8698 |
| [Suppes] p. 82 | Theorem 72 | elec 8742 elecALTV 39123 elecg 8740 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39547 erth 8750 erth2 8751 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39550 erdisj 8753 |
| [Suppes] p. 83 | Definition 35, | df-parts 39720 dfmembpart2 39725 |
| [Suppes] p. 89 | Theorem 96 | map0b 8889 |
| [Suppes] p. 89 | Theorem 97 | map0 8893 map0g 8890 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8894 mapsnd 8892 |
| [Suppes] p. 89 | Theorem 99 | mapss 8895 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10119 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10118 |
| [Suppes] p. 92 | Theorem 1 | enref 8990 enrefg 8989 |
| [Suppes] p. 92 | Theorem 2 | ensym 9008 ensymb 9007 ensymi 9009 |
| [Suppes] p. 92 | Theorem 3 | entr 9011 |
| [Suppes] p. 92 | Theorem 4 | unen 9051 |
| [Suppes] p. 94 | Theorem 15 | endom 8984 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9005 |
| [Suppes] p. 94 | Theorem 17 | domtr 9012 |
| [Suppes] p. 95 | Theorem 18 | sbth 9094 |
| [Suppes] p. 97 | Theorem 23 | canth2 9127 canth2g 9128 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9098 df-sdom 8954 dfsdom2 9097 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9111 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9100 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9099 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9109 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8987 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9112 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9107 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9037 fundmeng 9038 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9072 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9108 |
| [Suppes] p. 104 | Theorem 37 | fofi 9283 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9288 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9288 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10607 |
| [Suppes] p. 130 | Definition 3 | df-tr 5212 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7777 |
| [Suppes] p. 134 | Definition 6 | df-suc 6357 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7895 finds 7891 finds1 7894 finds2 7893 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9631 isfinite2 9268 isfiniteg 9270 unbnn 9266 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10975 df-ltpq 10967 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7857 tfinds 7854 tfinds2 7858 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8537 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8539 |
| [Suppes] p. 211 | Theorem 25 | oaass 8547 |
| [Suppes] p. 225 | Definition 8 | iscard2 10029 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10619 |
| [Suppes] p. 228 | Theorem 59 | harcard 10031 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10117 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6404 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7790 onminsb 7791 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10629 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10121 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10128 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10122 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9993 |
| [Suppes] p. 242 | Theorem 6 | weth 10545 |
| [Suppes] p. 242 | Theorem 8 | entric 10613 |
| [Suppes] p. 242 | Theorem 9 | carden 10607 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36382 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36386 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2732 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2752 wl-df.cleq 38351 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2835 wl-df.clel 38354 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2754 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2780 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7412 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3737 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5382 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4608 elpr2 4610 elpr2g 4609 elprg 4606 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4598 elsn2 4625 elsn2g 4624 elsng 4597 velsn 4599 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5435 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4593 sneqr 4799 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4604 dfsn2 4596 dfsn2ALT 4605 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7741 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5444 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5431 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5415 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7744 unexg 7743 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4651 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4867 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3905 df-un 3903 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4883 uniprg 4882 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5338 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4649 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6424 elsucg 6422 sstr2 3937 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4104 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4154 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4117 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4172 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4229 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4230 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3918 df-ss 3915 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4558 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4132 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3916 sseqin2 4168 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3952 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4181 inss2 4182 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3994 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4877 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5416 sspwimp 45844 sspwimpALT 45851 sspwimpALT2 45854 sspwimpcf 45846 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5423 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5231 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3413 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5260 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3901 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37362 dfnul2 4281 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4324 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4299 n0f 4295 neq0 4298 neq0f 4294 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9568 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9711 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9726 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3452 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5273 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4349 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5281 ssexg 5280 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5276 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9580 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9572 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4313 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4081 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4245 undif3VD 45808 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4082 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4089 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3077 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3087 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7750 xpexg 7747 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5654 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6599 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6777 fun11 6602 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6540 svrelfun 6600 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5865 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5867 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5659 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5660 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5656 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6181 dfrel2 6176 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5663 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5785 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5792 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5805 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5992 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5972 opelresi 5974 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5999 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5988 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5993 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6570 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6098 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6568 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6779 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2634 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30935 df-fv 6535 fv3 6891 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7920 cnvexg 7919 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7904 dmexg 7896 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7905 rnexg 7897 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45380 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7915 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6886 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 48166 tz6.12-1-afv2 48233 tz6.12-1 6896 tz6.12-afv 48165 tz6.12-afv2 48232 tz6.12 6897 tz6.12c-afv2 48234 tz6.12c 6895 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48229 tz6.12-2 6860 tz6.12i-afv2 48235 tz6.12i 6899 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6530 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6531 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6533 wfo 6525 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6532 wf1 6524 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6534 wf1o 6526 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7017 eqfnfv2 7018 eqfnfv2f 7021 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6971 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7211 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7209 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6615 funimaexg 6614 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5103 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5556 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5608 dffr3 6089 eliniseg 6084 iniseg 6087 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5547 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5624 fr3nr 7769 frirr 5623 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5600 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7771 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5611 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5633 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6339 tz6.26i 6340 wefrc 5641 wereu2 5644 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6341 wfii 6342 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6536 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7325 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7326 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7332 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7333 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7338 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7345 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7347 |
| [TakeutiZaring] p. 35 | Notation | wtr 5211 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45381 tz7.2 5630 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5216 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6364 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6372 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6373 ordelordALT 45464 ordelordALTVD 45793 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6379 ordelssne 6378 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6377 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6382 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7779 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7780 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6355 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6384 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45476 ordon 7774 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7775 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7847 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6400 ontr2d 36871 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5213 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7789 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7825 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6458 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6457 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7776 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4898 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6357 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6434 sucidg 6435 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7807 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6448 ordnbtwn 6447 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7822 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6356 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7875 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7880 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7835 ordelsuc 7814 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7816 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7845 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7862 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7883 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7884 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7885 |
| [TakeutiZaring] p. 43 | Remark | omon 7872 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9614 omex 9622 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7870 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7890 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7887 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7888 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7865 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4921 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5230 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4922 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5304 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7792 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6403 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4907 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9639 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7787 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8361 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8383 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8384 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8385 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8392 tz7.44-2 8393 tz7.44-3 8394 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8353 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8348 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8332 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8433 tz7.49c 8434 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8431 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8430 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8432 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2680 |
| [TakeutiZaring] p. 54 | Definition 7.55 | df-lexo 35797 |
| [TakeutiZaring] p. 54 | Definition 7.57 | df-r0 35798 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10062 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10063 |
| [TakeutiZaring] p. 55 | Definition 7.59 | df-j0 35799 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8518 oasuc 8510 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7855 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8521 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8502 oa0r 8524 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8522 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8534 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8606 nnaordi 8605 oaord 8533 oaordi 8532 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5007 uniss2 4901 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8536 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8541 oawordex 8543 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8598 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8635 |
| [TakeutiZaring] p. 60 | Remark | oancom 9630 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8546 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8603 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8538 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8505 omlim 8519 omsuc 8512 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8503 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8600 nnmcl 8599 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8619 nnmordi 8618 omord 8554 omordi 8552 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8555 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8623 omwordri 8558 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8525 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8528 om1r 8529 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8561 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8563 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8564 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8565 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8566 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8595 oe0 8508 oelim 8520 oesuc 8513 onesuc 8516 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8506 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8573 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8574 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8507 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8531 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8575 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8581 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8579 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8580 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8584 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8586 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9707 tz9.1 9708 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9746 r10 9750 r1lim 9754 r1limg 9753 r1suc 9752 r1sucg 9751 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9762 r1ord2 9763 r1ordg 9760 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9772 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9797 tz9.13 9773 tz9.13g 9774 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9747 rankval 9798 rankvalb 9779 rankvalg 9799 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9824 rankelb 9806 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9840 rankval3 9826 rankval3b 9809 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9812 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9777 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9819 rankr1c 9803 rankr1g 9817 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9820 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9836 rankssb 9835 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9828 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9827 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10525 dfac3 10172 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10081 numth 10522 numth2 10521 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10602 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10603 cardid2 10006 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10013 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10607 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 10012 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9997 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10018 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 10010 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9147 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9023 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9152 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9076 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10016 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10149 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9199 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9207 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10150 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9204 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10139 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10117 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10025 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10266 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9292 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8955 isfi 8980 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9208 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10585 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9069 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10577 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10236 unxpdom 9228 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10027 cardsdomelir 10026 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9230 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10065 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8827 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10618 infxpidm2 10068 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10257 infxp 10264 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9081 pw2f1o 9079 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9140 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10537 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10532 ac6s5 10541 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10599 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10600 uniimadomf 10601 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10324 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10319 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10303 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10300 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10307 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10314 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10323 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10639 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10301 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10326 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10148 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10147 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10159 alephfp2 10160 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10756 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10163 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10626 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10640 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10641 |
| [TakeutiZaring] p. 143 | Definition 14.1(1) | df-cnv2 35777 |
| [TakeutiZaring] p. 143 | Definition 14.1(2) | df-cnv3 35778 |
| [TakeutiZaring] p. 144 | Definition 14.2 | df-gdlop1 35779 df-gdlop2 35780 df-gdlop3 35781 df-gdlop4 35782 df-gdlop5 35783 df-gdlop6 35784 df-gdlop7 35785 df-gdlop8 35786 df-gdlopc 35787 |
| [TakeutiZaring] p. 155 | Definition 15.2 | df-j 35800 |
| [TakeutiZaring] p. 156 | Definition 15.7 | df-k1 35801 df-k2 35802 df-k3 35803 |
| [TakeutiZaring] p. 158 | Definition 15.13 | df-fnl 35804 |
| [TakeutiZaring] p. 158 | Definition 15.15 | df-l 35805 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39860 |
| [Tarski] p. 67 | Scheme B5 | sp 2219 |
| [Tarski] p. 68 | Lemma 6 | avril1 30998 equid 2045 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2050 |
| [Tarski] p. 70 | Lemma 14 | spim 2416 spime 2418 spimew 2004 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2213 ax-c15 39866 ax12i 1999 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2122 |
| [Tarski] p. 75 | Axiom B7 | ax6v 2001 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1943 ax5ALT 39884 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2041 ax-8 2147 ax-9 2155 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28860 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28861 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28863 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28863 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28864 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16379 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38497 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38499 |
| [Weierstrass] p. 272 | Definition | df-mdet 22862 mdetuni 22899 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 917 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 883 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 933 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38288 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44744 imim2 59 wl-luk-imim2 38283 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 48011 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 910 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2687 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 916 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38286 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 908 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 911 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45853 wl-luk-notnotr 38287 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44774 axfrege28 44773 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 881 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 938 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38280 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 903 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30936 pm2.27 43 wl-luk-pm2.27 38278 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 936 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 39223 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 937 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1104 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 921 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 895 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 866 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 902 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 904 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 913 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 905 pm2.67 906 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 912 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 914 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 947 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 475 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 477 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 465 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 408 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 815 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 455 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 488 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 490 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 778 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 820 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 634 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 822 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 499 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 479 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 819 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 846 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 818 bitr 817 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 574 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 918 pm4.25 919 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 466 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1025 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 884 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 474 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 935 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 645 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 931 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 649 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1105 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1023 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1069 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1040 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 841 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 867 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 555 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 870 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 411 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 864 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 567 pm4.71d 571 pm4.71i 569 pm4.71r 568 pm4.71rd 572 pm4.71ri 570 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 537 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 950 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 527 pm4.76 528 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 948 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1021 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 399 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1041 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1042 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 392 impexp 456 pm4.87 857 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 836 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1031 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 391 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 837 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1032 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1065 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1066 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 915 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 393 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 844 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 584 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 849 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 838 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 847 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 394 pm5.41 395 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 553 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1036 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1037 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1045 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1046 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37413 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45286 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45287 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1903 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45288 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45289 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45290 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1926 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45291 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45292 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45293 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45294 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45295 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45297 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45298 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45299 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45296 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2127 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45302 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45303 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2107 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2197 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1862 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1863 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45304 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45305 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45306 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45307 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45309 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45308 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1920 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45311 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45312 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45310 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1861 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45313 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45314 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1879 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45315 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2375 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1893 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45320 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45316 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45317 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45318 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45319 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45324 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45321 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45322 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45323 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45325 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2594 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45335 pm13.13b 45336 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45337 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3036 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3037 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3619 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45343 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45344 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45338 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45479 pm13.193 45339 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45340 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45341 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45342 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45349 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45348 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45347 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3800 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45350 pm14.122b 45351 pm14.122c 45352 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45353 pm14.123b 45354 pm14.123c 45355 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45357 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45356 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45358 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6508 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45359 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6509 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45360 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45362 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2658 eupickbi 2661 sbaniota 45363 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45361 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2609 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45364 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30935 df-fv 6535 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10054 pm54.43lem 10053 |
| [Young] p. 141 | Definition of operator ordering | leop2 32660 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32666 idleop 32667 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43773 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43780 pellexlem1 43774 |