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 17629 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17629 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18038 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17650 0funcg 49074 df-termc 49462 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 49539 prsthinc 49453 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 49567 df-mndtc 49567 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 49563 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17673 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 49555 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 49580 oppgoppchom 49579 oppgoppcid 49581 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17743 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17731 invisoinvl 17752 |
| [Adamek] p. 28 | Example 3.13 | idinv 17751 idiso 17750 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17736 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17710 df-iso 17711 dfiso2 17734 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17717 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17768 cicerALT 49035 |
| [Adamek] p. 29 | Definition 3.15 | cic 17761 df-cic 17758 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17820 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17732 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17733 isoco 17739 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17820 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17843 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49293 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17836 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 49563 discthing 49450 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49407 prsthinc 49453 thincciso 49442 thincciso2 49444 thincciso3 49445 thinccisod 49443 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 49567 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17850 cofucla 49085 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49151 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18073 catcisoi 49389 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18128 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17869 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17868 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18128 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17893 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17899 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17898 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18113 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18113 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49121 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49112 funcoppc 17837 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18061 elcatchom 49386 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17887 fthoppf 49153 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17886 fulloppf 49152 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18070 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49074 df-catc 18061 |
| [Adamek] p. 45 | Exercise 3G | incat 49590 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 49593 nelsubc3 49060 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49140 imasubc2 49141 imasubc3 49145 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17800 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17801 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49060 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17812 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17774 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49149 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49148 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49150 ressffth 17902 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 49591 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17908 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17929 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17933 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17909 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17935 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49074 df-inito 17946 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49074 df-termc 49462 initc 49080 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21389 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17947 oppctermo 49225 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17974 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17978 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49226 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17948 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21390 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17981 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17709 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49458 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49457 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49422 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17744 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17746 |
| [Adamek] p. 185 | Section 10.67 | updjud 9887 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 49634 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 49634 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 49634 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 49635 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 49635 |
| [Adamek] p. 478 | Item Rng | df-ringc 20555 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 48537 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 48559 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14536 df-pfx 14636 df-substr 14606 df-word 14479 lencl 14498 wrd0 14504 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24596 df-nmoo 30674 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32082 hmopidmchi 32080 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32130 pjcmul2i 32131 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31847 unoplin 31849 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31848 unopadj2 31867 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 31942 lnopunii 31941 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32015 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27835 |
| [Alling] p. 184 | Axiom B | bdayfo 27589 |
| [Alling] p. 184 | Axiom O | sltso 27588 |
| [Alling] p. 184 | Axiom SD | nodense 27604 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27690 |
| [Alling] p. 185 | Theorem | conway 27711 |
| [Alling] p. 185 | Axiom FE | noeta 27655 |
| [Alling] p. 186 | Theorem 4 | slerec 27731 |
| [Alling], p. 2 | Definition | rp-brsslt 43412 |
| [Alling], p. 3 | Note | nla0001 43415 nla0002 43413 nla0003 43414 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11358 addcan2d 11378 addcan2i 11368 addcand 11377 addcani 11367 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11411 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11470 negsubd 11539 negsubi 11500 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11472 negnegd 11524 negnegi 11492 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11611 subdid 11634 subdii 11627 subdir 11612 subdird 11635 subdiri 11628 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11353 mul01d 11373 mul01i 11364 mul02 11352 mul02d 11372 mul02i 11363 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11815 mulcan2d 11812 mulcand 11811 mulcani 11817 |
| [Apostol] p. 18 | Theorem I.8 | receu 11823 xreceu 32842 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11853 divrecd 11961 divreci 11927 divreczi 11920 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11879 recreci 11914 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11818 mul0ord 11826 mul0ori 11825 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11617 mul2negd 11633 mul2negi 11626 mulneg1 11614 mulneg1d 11631 mulneg1i 11624 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11897 divadddivd 12002 divadddivi 11944 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11882 divmuldivd 11999 divmuldivi 11942 rdivmuldivd 20322 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11883 divdivdivd 12005 divdivdivi 11945 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12975 rpaddcld 13010 rpmulcl 12976 rpmulcld 13011 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12985 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12988 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11300 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11771 ltadd1dd 11789 ltadd1i 11732 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12032 ltmul1a 12031 ltmul1i 12101 ltmul1ii 12111 ltmul2 12033 ltmul2d 13037 ltmul2dd 13051 ltmul2i 12104 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11698 msqgt0d 11745 msqgt0i 11715 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11700 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11684 lt0neg1d 11747 ltneg 11678 ltnegd 11756 ltnegi 11722 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11663 lt2addd 11801 lt2addi 11740 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12952 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12028 recgt0d 12117 recgt0i 12088 recgt0ii 12089 |
| [Apostol] p. 22 | Definition of integers | df-z 12530 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12200 |
| [Apostol] p. 22 | Definition of rationals | df-q 12908 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9405 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12438 |
| [Apostol] p. 26 | Theorem I.29 | arch 12439 archd 45156 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12637 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12440 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12906 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12905 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13159 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16309 zneo 12617 zneoALTV 47670 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26639 msqsqrtd 15409 resqrtth 15221 sqrtth 15331 sqrtthi 15337 sqsqrtd 15408 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12189 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12872 |
| [Apostol] p. 361 | Remark | crreczi 14193 |
| [Apostol] p. 363 | Remark | absgt0i 15366 |
| [Apostol] p. 363 | Example | abssubd 15422 abssubi 15370 |
| [ApostolNT] p. 7 | Remark | fmtno0 47541 fmtno1 47542 fmtno2 47551 fmtno3 47552 fmtno4 47553 fmtno5fac 47583 fmtnofz04prm 47578 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47529 |
| [ApostolNT] p. 8 | Definition | df-ppi 27010 |
| [ApostolNT] p. 14 | Definition | df-dvds 16223 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16239 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16264 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16259 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16252 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16254 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16240 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16241 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16246 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16281 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16283 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16285 |
| [ApostolNT] p. 15 | Definition | df-gcd 16465 dfgcd2 16516 |
| [ApostolNT] p. 16 | Definition | isprm2 16652 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16623 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16886 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16483 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16517 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16519 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16498 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16490 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16681 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16683 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16899 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16893 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16373 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16557 |
| [ApostolNT] p. 24 | Definition | df-mu 27011 |
| [ApostolNT] p. 25 | Definition | df-phi 16736 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27101 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16761 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16746 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16750 |
| [ApostolNT] p. 32 | Definition | df-vma 27008 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27103 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27127 |
| [ApostolNT] p. 38 | Remark | df-sgm 27012 |
| [ApostolNT] p. 38 | Definition | df-sgm 27012 |
| [ApostolNT] p. 75 | Definition | df-chp 27009 df-cht 27007 |
| [ApostolNT] p. 104 | Definition | congr 16634 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16226 |
| [ApostolNT] p. 106 | Definition | moddvds 16233 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16316 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16317 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13850 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13890 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14203 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16258 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16637 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17045 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16639 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16753 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16772 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16754 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26982 |
| [ApostolNT] p. 179 | Definition | df-lgs 27206 lgsprme0 27250 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27251 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27227 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27242 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27299 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27318 2lgsoddprm 27327 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27285 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27294 |
| [ApostolNT] p. 188 | Definition | df-lgs 27206 lgs1 27252 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27243 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27245 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27253 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27254 |
| [Baer] p. 40 | Property (b) | mapdord 41632 |
| [Baer] p. 40 | Property (c) | mapd11 41633 |
| [Baer] p. 40 | Property (e) | mapdin 41656 mapdlsm 41658 |
| [Baer] p. 40 | Property (f) | mapd0 41659 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 41619 mapd1o 41642 |
| [Baer] p. 41 | Property (g) | mapdat 41661 |
| [Baer] p. 44 | Part (1) | mapdpg 41700 |
| [Baer] p. 45 | Part (2) | hdmap1eq 41795 mapdheq 41722 mapdheq2 41723 mapdheq2biN 41724 |
| [Baer] p. 45 | Part (3) | baerlem3 41707 |
| [Baer] p. 46 | Part (4) | mapdheq4 41726 mapdheq4lem 41725 |
| [Baer] p. 46 | Part (5) | baerlem5a 41708 baerlem5abmN 41712 baerlem5amN 41710 baerlem5b 41709 baerlem5bmN 41711 |
| [Baer] p. 47 | Part (6) | hdmap1l6 41815 hdmap1l6a 41803 hdmap1l6e 41808 hdmap1l6f 41809 hdmap1l6g 41810 hdmap1l6lem1 41801 hdmap1l6lem2 41802 mapdh6N 41741 mapdh6aN 41729 mapdh6eN 41734 mapdh6fN 41735 mapdh6gN 41736 mapdh6lem1N 41727 mapdh6lem2N 41728 |
| [Baer] p. 48 | Part 9 | hdmapval 41822 |
| [Baer] p. 48 | Part 10 | hdmap10 41834 |
| [Baer] p. 48 | Part 11 | hdmapadd 41837 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 41811 mapdh6hN 41737 |
| [Baer] p. 48 | Part (7) | mapdh75cN 41747 mapdh75d 41748 mapdh75e 41746 mapdh75fN 41749 mapdh7cN 41743 mapdh7dN 41744 mapdh7eN 41742 mapdh7fN 41745 |
| [Baer] p. 48 | Part (8) | mapdh8 41782 mapdh8a 41769 mapdh8aa 41770 mapdh8ab 41771 mapdh8ac 41772 mapdh8ad 41773 mapdh8b 41774 mapdh8c 41775 mapdh8d 41777 mapdh8d0N 41776 mapdh8e 41778 mapdh8g 41779 mapdh8i 41780 mapdh8j 41781 |
| [Baer] p. 48 | Part (9) | mapdh9a 41783 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 41763 |
| [Baer] p. 49 | Part 12 | hdmap11 41842 hdmapeq0 41838 hdmapf1oN 41859 hdmapneg 41840 hdmaprnN 41858 hdmaprnlem1N 41843 hdmaprnlem3N 41844 hdmaprnlem3uN 41845 hdmaprnlem4N 41847 hdmaprnlem6N 41848 hdmaprnlem7N 41849 hdmaprnlem8N 41850 hdmaprnlem9N 41851 hdmapsub 41841 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 41862 hdmap14lem10 41871 hdmap14lem1a 41860 hdmap14lem2N 41863 hdmap14lem2a 41861 hdmap14lem3 41864 hdmap14lem8 41869 hdmap14lem9 41870 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 41872 hdmap14lem12 41873 hdmap14lem13 41874 hdmap14lem14 41875 hdmap14lem15 41876 hgmapval 41881 |
| [Baer] p. 50 | Part 15 | hgmapadd 41888 hgmapmul 41889 hgmaprnlem2N 41891 hgmapvs 41885 |
| [Baer] p. 50 | Part 16 | hgmaprnN 41895 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 41911 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 41912 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 41913 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 41914 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 41916 hgmapvv 41920 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 41915 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 41917 |
| [Baer] p. 111 | Line 15 | hdmapg 41924 hdmapglem7 41923 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26640 2irrexpqALT 26710 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2562 |
| [BellMachover] p. 460 | Notation | df-mo 2533 |
| [BellMachover] p. 460 | Definition | mo3 2557 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2701 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2705 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5242 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5251 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37052 sepex 5255 |
| [BellMachover] p. 466 | Problem | axpow2 5322 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5323 |
| [BellMachover] p. 466 | Axiom Union | axun2 7713 |
| [BellMachover] p. 468 | Definition | df-ord 6335 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6350 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6357 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6352 |
| [BellMachover] p. 471 | Definition of N | df-om 7843 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7777 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6337 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9595 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7858 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9717 |
| [BellMachover] p. 478 | Definition | rankval2 9771 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9735 r1ord3g 9732 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9548 |
| [BellMachover] p. 488 | Axiom AC | ac5 10430 dfac4 10075 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10063 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39312 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32282 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32324 chirredi 32323 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32312 |
| [Beran] p. 3 | Definition of join | sshjval3 31283 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31545 cmcm2i 31522 cmcm2ii 31527 cmt2N 39243 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31546 lecmi 31531 lecmii 31532 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31520 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31549 cm2ji 31554 cm2mi 31555 |
| [Beran] p. 95 | Definition | df-sh 31136 issh2 31138 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31015 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31028 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31019 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31757 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31759 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31758 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31760 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31011 his1i 31029 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31012 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31013 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31014 |
| [Beran] p. 96 | Definition of norm | df-hnorm 30897 dfhnorm2 31051 normval 31053 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31113 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 30902 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31170 |
| [Beran] p. 96 | Definition of converge | df-hlim 30901 hlimi 31117 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31062 norm-i 31058 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31066 norm-ii 31067 normlem0 31038 normlem1 31039 normlem2 31040 normlem3 31041 normlem4 31042 normlem5 31043 normlem6 31044 normlem7 31045 normlem7tALT 31048 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31068 norm-iii 31069 |
| [Beran] p. 98 | Remark 3.4 | bcs 31110 bcsiALT 31108 bcsiHIL 31109 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31050 normpar 31084 normpari 31083 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31075 normpyth 31074 normpythi 31071 |
| [Beran] p. 99 | Remark | lnfn0 31976 lnfn0i 31971 lnop0 31895 lnop0i 31899 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 31955 nmcfnex 31982 nmcfnexi 31980 nmcopex 31958 nmcopexi 31956 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 31983 nmcfnlbi 31981 nmcoplb 31959 nmcoplbi 31957 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 31985 lnfnconi 31984 lnopcon 31964 lnopconi 31963 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31085 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31082 norm3adifii 31077 norm3dif 31079 norm3difi 31076 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31230 pjhth 31322 pjhtheu 31323 pjpjhth 31354 pjpjhthi 31355 pjth 25339 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31335 ococi 31334 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31990 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31991 riesz4 31993 riesz4i 31992 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32008 cnlnadjeu 32007 cnlnadjeui 32006 cnlnadji 32005 cnlnadjlem1 31996 nmopadjlei 32017 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32020 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32019 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32021 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 31865 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32031 nmopcoadji 32030 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32022 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32032 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32029 pjadj2coi 32133 pjadjcoi 32090 |
| [Beran] p. 107 | Definition | df-ch 31150 isch2 31152 |
| [Beran] p. 107 | Remark 3.12 | choccl 31235 isch3 31170 occl 31233 ocsh 31212 shoccl 31234 shocsh 31213 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31337 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31261 |
| [Beran] p. 109 | Property (i) | pjadj2 32116 pjadj3 32117 pjadji 31614 pjadjii 31603 |
| [Beran] p. 109 | Property (ii) | pjidmco 32110 pjidmcoi 32106 pjidmi 31602 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32102 |
| [Beran] p. 111 | Remark | ho0val 31679 pjch1 31599 |
| [Beran] p. 111 | Definition | df-hfmul 31663 df-hfsum 31662 df-hodif 31661 df-homul 31660 df-hosum 31659 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31600 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31623 pjchi 31361 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31368 pjoc2i 31367 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31609 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32094 pjssmii 31610 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32093 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32092 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32097 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32095 pjssge0ii 31611 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32096 pjdifnormii 31612 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1776 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1774 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1777 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1772 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34283 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34291 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34289 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34293 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34313 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34344 df-sitm 34322 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34344 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34321 |
| [Bollobas] p. 1 | Section I.1 | df-edg 28975 isuhgrop 28997 isusgrop 29089 isuspgrop 29088 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 47861 df-subgr 29195 uhgrspan1 29230 uhgrspansubgr 29218 |
| [Bollobas] p. 3 | Definition | df-gric 47881 gricuspgr 47918 isuspgrim 47896 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29382 df-clnbgr 47820 df-cusgr 29339 df-nbgr 29260 fusgrmaxsize 29392 |
| [Bollobas] p. 4 | Definition | df-upwlks 48122 df-wlks 29527 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29478 finsumvtxdgeven 29480 fusgr1th 29479 fusgrvtxdgonume 29482 vtxdgoddnumeven 29481 |
| [Bollobas] p. 5 | Notation | df-pths 29644 |
| [Bollobas] p. 5 | Definition | df-crcts 29716 df-cycls 29717 df-trls 29620 df-wlkson 29528 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28986 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48188 df-cllaw 48174 df-mgm 18567 df-mgm2 48207 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48189 df-asslaw 48176 df-sgrp 18646 df-sgrp2 48209 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48208 df-comlaw 48175 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18662 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 32967 mndlactf1o 32971 mndractf1 32969 mndractf1o 32972 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20144 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20062 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33629 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33633 assarrginv 33632 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33673 fldextrspunfld 33671 fldextrspunlem1 33670 fldextrspunlem2 33672 fldextrspunlsp 33669 fldextrspunlsplem 33668 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33508 dfufd2 33521 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7262 fcofo 7263 |
| [BourbakiTop1] p. | Remark | xnegmnf 13170 xnegpnf 13169 |
| [BourbakiTop1] p. | Remark | rexneg 13171 |
| [BourbakiTop1] p. | Remark 3 | ust0 24107 ustfilxp 24100 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23977 |
| [BourbakiTop1] p. | Criterion | ishmeo 23646 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24171 iducn 24170 snfil 23751 |
| [BourbakiTop1] p. | Example 2 | neifil 23767 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23954 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24191 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 33947 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23750 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24163 df-ust 24088 filintn0 23748 filn0 23749 istgp 23964 ucnprima 24169 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24174 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24185 df-usp 24145 df-utop 24119 trust 24117 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 33846 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23003 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23156 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24093 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24096 |
| [BourbakiTop1] p. | Property V_ii | innei 23012 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23020 neissex 23014 |
| [BourbakiTop1] p. | Proposition 1 | neips 23000 neiss 22996 ucncn 24172 ustund 24109 ustuqtop 24134 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23154 neiptopreu 23020 utop2nei 24138 utop3cls 24139 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24179 uspreg 24161 utopreg 24140 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23578 imasncls 23579 imasnopn 23577 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23887 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24095 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24097 |
| [BourbakiTop1] p. | Property V_iii | elnei 22998 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24190 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24094 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24098 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23274 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23733 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22781 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33843 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46060 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46062 stoweid 46061 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 45999 stoweidlem10 46008 stoweidlem14 46012 stoweidlem15 46013 stoweidlem35 46033 stoweidlem36 46034 stoweidlem37 46035 stoweidlem38 46036 stoweidlem40 46038 stoweidlem41 46039 stoweidlem43 46041 stoweidlem44 46042 stoweidlem46 46044 stoweidlem5 46003 stoweidlem50 46048 stoweidlem52 46050 stoweidlem53 46051 stoweidlem55 46053 stoweidlem56 46054 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46021 stoweidlem24 46022 stoweidlem27 46025 stoweidlem28 46026 stoweidlem30 46028 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46032 stoweidlem59 46057 stoweidlem60 46058 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46043 stoweidlem49 46047 stoweidlem7 46005 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46029 stoweidlem39 46037 stoweidlem42 46040 stoweidlem48 46046 stoweidlem51 46049 stoweidlem54 46052 stoweidlem57 46055 stoweidlem58 46056 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46023 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46015 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46009 stoweidlem13 46011 stoweidlem26 46024 stoweidlem61 46059 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46016 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48188 df-mgm 18567 df-mgm2 48207 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18646 df-sgrp2 48209 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18971 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5189 |
| [Church] p. 129 | Section II.24 | df-ifp 1063 dfifp2 1064 |
| [Clemente] p. 10 | Definition IT | natded 30332 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30332 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30332 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30332 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30332 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30332 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30332 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30332 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30332 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30332 |
| [Clemente] p. 14 | Proof 5.11 | natded 30332 |
| [Clemente] p. 14 | Definition E` `n | natded 30332 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30334 ex-natded5.2 30333 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30337 ex-natded5.3 30336 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30339 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30341 ex-natded5.7 30340 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30343 ex-natded5.8 30342 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30345 ex-natded5.13 30344 |
| [Clemente] p. 32 | Definition I` `n | natded 30332 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30332 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30332 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30332 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30346 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30347 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30349 ex-natded9.26 30348 |
| [Cohen] p. 301 | Remark | relogoprlem 26500 |
| [Cohen] p. 301 | Property 2 | relogmul 26501 relogmuld 26534 |
| [Cohen] p. 301 | Property 3 | relogdiv 26502 relogdivd 26535 |
| [Cohen] p. 301 | Property 4 | relogexp 26505 |
| [Cohen] p. 301 | Property 1a | log1 26494 |
| [Cohen] p. 301 | Property 1b | loge 26495 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26697 |
| [Cohen4] p. 349 | Property | relogbf 26701 |
| [Cohen4] p. 352 | Definition | elogb 26680 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26687 |
| [Cohen4] p. 361 | Property 3 | logbrec 26692 relogbdiv 26689 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26685 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26690 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26678 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26679 |
| [Cohen4] p. 367 | Property | logbchbase 26681 |
| [Cohen4] p. 377 | Property 2 | logblt 26694 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34276 sxbrsigalem4 34278 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18516 acsinfd 18515 acsinfdimd 18517 acsmap2d 18514 acsmapd 18513 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34281 |
| [Connell] p. 57 | Definition | df-scmat 22378 df-scmatalt 48388 |
| [Conway] p. 4 | Definition | slerec 27731 |
| [Conway] p. 5 | Definition | addsval 27869 addsval2 27870 df-adds 27867 df-muls 28010 df-negs 27927 |
| [Conway] p. 7 | Theorem | 0slt1s 27741 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27783 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27782 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27675 |
| [Conway] p. 17 | Theorem 3 | addsass 27912 addsassd 27913 addscom 27873 addscomd 27874 addsrid 27871 addsridd 27872 |
| [Conway] p. 17 | Definition | df-0s 27736 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27950 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27947 negsidd 27948 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27896 sleadd1d 27902 |
| [Conway] p. 18 | Definition | df-1s 27737 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27942 negscld 27943 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27887 |
| [Conway] p. 19 | Note | mulsunif2 28073 |
| [Conway] p. 19 | Theorem 7 | addsdi 28058 addsdid 28059 addsdird 28060 mulnegs1d 28063 mulnegs2d 28064 mulsass 28069 mulsassd 28070 mulscom 28042 mulscomd 28043 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28037 mulscld 28038 |
| [Conway] p. 19 | Theorem 8(iii) | slemuld 28041 sltmul 28039 sltmuld 28040 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28047 mulsgt0d 28048 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28120 |
| [Conway] p. 24 | Definition | df-reno 28345 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28350 remulscl 28353 renegscl 28349 |
| [Conway] p. 27 | Definition | df-ons 28153 elons2 28159 |
| [Conway] p. 27 | Theorem 14 | sltonex 28163 |
| [Conway] p. 28 | Theorem 15 | onscutlt 28165 onswe 28170 |
| [Conway] p. 29 | Remark | madebday 27811 newbday 27813 oldbday 27812 |
| [Conway] p. 29 | Definition | df-made 27755 df-new 27757 df-old 27756 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13823 |
| [Crawley] p. 1 | Definition of poset | df-poset 18274 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39380 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40184 dalaw 39880 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 41955 |
| [Crawley] p. 111 | Definition of set W | df-watsN 39984 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40100 df-ldil 40098 isldil 40104 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40099 df-trnN 40101 isltrn 40113 ltrnu 40115 |
| [Crawley] p. 112 | Lemma A | cdlema1N 39785 cdlema2N 39786 exatleN 39398 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39470 cdlemb 39788 cdlemb2 40035 cdlemb3 40600 idltrn 40144 l1cvat 39048 lhpat 40037 lhpat2 40039 lshpat 39049 ltrnel 40133 ltrnmw 40145 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40185 cdlemc2 40186 ltrnnidn 40168 trlat 40163 trljat1 40160 trljat2 40161 trljat3 40162 trlne 40179 trlnidat 40167 trlnle 40180 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 39985 |
| [Crawley] p. 113 | Lemma C | cdlemc 40191 cdlemc3 40187 cdlemc4 40188 |
| [Crawley] p. 113 | Lemma D | cdlemd 40201 cdlemd1 40192 cdlemd2 40193 cdlemd3 40194 cdlemd4 40195 cdlemd5 40196 cdlemd6 40197 cdlemd7 40198 cdlemd8 40199 cdlemd9 40200 cdleme31sde 40379 cdleme31se 40376 cdleme31se2 40377 cdleme31snd 40380 cdleme32a 40435 cdleme32b 40436 cdleme32c 40437 cdleme32d 40438 cdleme32e 40439 cdleme32f 40440 cdleme32fva 40431 cdleme32fva1 40432 cdleme32fvcl 40434 cdleme32le 40441 cdleme48fv 40493 cdleme4gfv 40501 cdleme50eq 40535 cdleme50f 40536 cdleme50f1 40537 cdleme50f1o 40540 cdleme50laut 40541 cdleme50ldil 40542 cdleme50lebi 40534 cdleme50rn 40539 cdleme50rnlem 40538 cdlemeg49le 40505 cdlemeg49lebilem 40533 |
| [Crawley] p. 113 | Lemma E | cdleme 40554 cdleme00a 40203 cdleme01N 40215 cdleme02N 40216 cdleme0a 40205 cdleme0aa 40204 cdleme0b 40206 cdleme0c 40207 cdleme0cp 40208 cdleme0cq 40209 cdleme0dN 40210 cdleme0e 40211 cdleme0ex1N 40217 cdleme0ex2N 40218 cdleme0fN 40212 cdleme0gN 40213 cdleme0moN 40219 cdleme1 40221 cdleme10 40248 cdleme10tN 40252 cdleme11 40264 cdleme11a 40254 cdleme11c 40255 cdleme11dN 40256 cdleme11e 40257 cdleme11fN 40258 cdleme11g 40259 cdleme11h 40260 cdleme11j 40261 cdleme11k 40262 cdleme11l 40263 cdleme12 40265 cdleme13 40266 cdleme14 40267 cdleme15 40272 cdleme15a 40268 cdleme15b 40269 cdleme15c 40270 cdleme15d 40271 cdleme16 40279 cdleme16aN 40253 cdleme16b 40273 cdleme16c 40274 cdleme16d 40275 cdleme16e 40276 cdleme16f 40277 cdleme16g 40278 cdleme19a 40297 cdleme19b 40298 cdleme19c 40299 cdleme19d 40300 cdleme19e 40301 cdleme19f 40302 cdleme1b 40220 cdleme2 40222 cdleme20aN 40303 cdleme20bN 40304 cdleme20c 40305 cdleme20d 40306 cdleme20e 40307 cdleme20f 40308 cdleme20g 40309 cdleme20h 40310 cdleme20i 40311 cdleme20j 40312 cdleme20k 40313 cdleme20l 40316 cdleme20l1 40314 cdleme20l2 40315 cdleme20m 40317 cdleme20y 40296 cdleme20zN 40295 cdleme21 40331 cdleme21d 40324 cdleme21e 40325 cdleme22a 40334 cdleme22aa 40333 cdleme22b 40335 cdleme22cN 40336 cdleme22d 40337 cdleme22e 40338 cdleme22eALTN 40339 cdleme22f 40340 cdleme22f2 40341 cdleme22g 40342 cdleme23a 40343 cdleme23b 40344 cdleme23c 40345 cdleme26e 40353 cdleme26eALTN 40355 cdleme26ee 40354 cdleme26f 40357 cdleme26f2 40359 cdleme26f2ALTN 40358 cdleme26fALTN 40356 cdleme27N 40363 cdleme27a 40361 cdleme27cl 40360 cdleme28c 40366 cdleme3 40231 cdleme30a 40372 cdleme31fv 40384 cdleme31fv1 40385 cdleme31fv1s 40386 cdleme31fv2 40387 cdleme31id 40388 cdleme31sc 40378 cdleme31sdnN 40381 cdleme31sn 40374 cdleme31sn1 40375 cdleme31sn1c 40382 cdleme31sn2 40383 cdleme31so 40373 cdleme35a 40442 cdleme35b 40444 cdleme35c 40445 cdleme35d 40446 cdleme35e 40447 cdleme35f 40448 cdleme35fnpq 40443 cdleme35g 40449 cdleme35h 40450 cdleme35h2 40451 cdleme35sn2aw 40452 cdleme35sn3a 40453 cdleme36a 40454 cdleme36m 40455 cdleme37m 40456 cdleme38m 40457 cdleme38n 40458 cdleme39a 40459 cdleme39n 40460 cdleme3b 40223 cdleme3c 40224 cdleme3d 40225 cdleme3e 40226 cdleme3fN 40227 cdleme3fa 40230 cdleme3g 40228 cdleme3h 40229 cdleme4 40232 cdleme40m 40461 cdleme40n 40462 cdleme40v 40463 cdleme40w 40464 cdleme41fva11 40471 cdleme41sn3aw 40468 cdleme41sn4aw 40469 cdleme41snaw 40470 cdleme42a 40465 cdleme42b 40472 cdleme42c 40466 cdleme42d 40467 cdleme42e 40473 cdleme42f 40474 cdleme42g 40475 cdleme42h 40476 cdleme42i 40477 cdleme42k 40478 cdleme42ke 40479 cdleme42keg 40480 cdleme42mN 40481 cdleme42mgN 40482 cdleme43aN 40483 cdleme43bN 40484 cdleme43cN 40485 cdleme43dN 40486 cdleme5 40234 cdleme50ex 40553 cdleme50ltrn 40551 cdleme51finvN 40550 cdleme51finvfvN 40549 cdleme51finvtrN 40552 cdleme6 40235 cdleme7 40243 cdleme7a 40237 cdleme7aa 40236 cdleme7b 40238 cdleme7c 40239 cdleme7d 40240 cdleme7e 40241 cdleme7ga 40242 cdleme8 40244 cdleme8tN 40249 cdleme9 40247 cdleme9a 40245 cdleme9b 40246 cdleme9tN 40251 cdleme9taN 40250 cdlemeda 40292 cdlemedb 40291 cdlemednpq 40293 cdlemednuN 40294 cdlemefr27cl 40397 cdlemefr32fva1 40404 cdlemefr32fvaN 40403 cdlemefrs32fva 40394 cdlemefrs32fva1 40395 cdlemefs27cl 40407 cdlemefs32fva1 40417 cdlemefs32fvaN 40416 cdlemesner 40290 cdlemeulpq 40214 |
| [Crawley] p. 114 | Lemma E | 4atex 40070 4atexlem7 40069 cdleme0nex 40284 cdleme17a 40280 cdleme17c 40282 cdleme17d 40492 cdleme17d1 40283 cdleme17d2 40489 cdleme18a 40285 cdleme18b 40286 cdleme18c 40287 cdleme18d 40289 cdleme4a 40233 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40319 cdleme21at 40322 cdleme21b 40320 cdleme21c 40321 cdleme21ct 40323 cdleme21f 40326 cdleme21g 40327 cdleme21h 40328 cdleme21i 40329 cdleme22gb 40288 |
| [Crawley] p. 116 | Lemma F | cdlemf 40557 cdlemf1 40555 cdlemf2 40556 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 40561 cdlemg16 40651 cdlemg28 40698 cdlemg28a 40687 cdlemg28b 40697 cdlemg3a 40591 cdlemg42 40723 cdlemg43 40724 cdlemg44 40727 cdlemg44a 40725 cdlemg46 40729 cdlemg47 40730 cdlemg9 40628 ltrnco 40713 ltrncom 40732 tgrpabl 40745 trlco 40721 |
| [Crawley] p. 116 | Definition of G | df-tgrp 40737 |
| [Crawley] p. 117 | Lemma G | cdlemg17 40671 cdlemg17b 40656 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 40750 df-edring 40751 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 40754 |
| [Crawley] p. 118 | Remark | tendopltp 40774 |
| [Crawley] p. 118 | Lemma H | cdlemh 40811 cdlemh1 40809 cdlemh2 40810 |
| [Crawley] p. 118 | Lemma I | cdlemi 40814 cdlemi1 40812 cdlemi2 40813 |
| [Crawley] p. 118 | Lemma J | cdlemj1 40815 cdlemj2 40816 cdlemj3 40817 tendocan 40818 |
| [Crawley] p. 118 | Lemma K | cdlemk 40968 cdlemk1 40825 cdlemk10 40837 cdlemk11 40843 cdlemk11t 40940 cdlemk11ta 40923 cdlemk11tb 40925 cdlemk11tc 40939 cdlemk11u-2N 40883 cdlemk11u 40865 cdlemk12 40844 cdlemk12u-2N 40884 cdlemk12u 40866 cdlemk13-2N 40870 cdlemk13 40846 cdlemk14-2N 40872 cdlemk14 40848 cdlemk15-2N 40873 cdlemk15 40849 cdlemk16-2N 40874 cdlemk16 40851 cdlemk16a 40850 cdlemk17-2N 40875 cdlemk17 40852 cdlemk18-2N 40880 cdlemk18-3N 40894 cdlemk18 40862 cdlemk19-2N 40881 cdlemk19 40863 cdlemk19u 40964 cdlemk1u 40853 cdlemk2 40826 cdlemk20-2N 40886 cdlemk20 40868 cdlemk21-2N 40885 cdlemk21N 40867 cdlemk22-3 40895 cdlemk22 40887 cdlemk23-3 40896 cdlemk24-3 40897 cdlemk25-3 40898 cdlemk26-3 40900 cdlemk26b-3 40899 cdlemk27-3 40901 cdlemk28-3 40902 cdlemk29-3 40905 cdlemk3 40827 cdlemk30 40888 cdlemk31 40890 cdlemk32 40891 cdlemk33N 40903 cdlemk34 40904 cdlemk35 40906 cdlemk36 40907 cdlemk37 40908 cdlemk38 40909 cdlemk39 40910 cdlemk39u 40962 cdlemk4 40828 cdlemk41 40914 cdlemk42 40935 cdlemk42yN 40938 cdlemk43N 40957 cdlemk45 40941 cdlemk46 40942 cdlemk47 40943 cdlemk48 40944 cdlemk49 40945 cdlemk5 40830 cdlemk50 40946 cdlemk51 40947 cdlemk52 40948 cdlemk53 40951 cdlemk54 40952 cdlemk55 40955 cdlemk55u 40960 cdlemk56 40965 cdlemk5a 40829 cdlemk5auN 40854 cdlemk5u 40855 cdlemk6 40831 cdlemk6u 40856 cdlemk7 40842 cdlemk7u-2N 40882 cdlemk7u 40864 cdlemk8 40832 cdlemk9 40833 cdlemk9bN 40834 cdlemki 40835 cdlemkid 40930 cdlemkj-2N 40876 cdlemkj 40857 cdlemksat 40840 cdlemksel 40839 cdlemksv 40838 cdlemksv2 40841 cdlemkuat 40860 cdlemkuel-2N 40878 cdlemkuel-3 40892 cdlemkuel 40859 cdlemkuv-2N 40877 cdlemkuv2-2 40879 cdlemkuv2-3N 40893 cdlemkuv2 40861 cdlemkuvN 40858 cdlemkvcl 40836 cdlemky 40920 cdlemkyyN 40956 tendoex 40969 |
| [Crawley] p. 120 | Remark | dva1dim 40979 |
| [Crawley] p. 120 | Lemma L | cdleml1N 40970 cdleml2N 40971 cdleml3N 40972 cdleml4N 40973 cdleml5N 40974 cdleml6 40975 cdleml7 40976 cdleml8 40977 cdleml9 40978 dia1dim 41055 |
| [Crawley] p. 120 | Lemma M | dia11N 41042 diaf11N 41043 dialss 41040 diaord 41041 dibf11N 41155 djajN 41131 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41026 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41112 dia2dimlem1 41058 dia2dimlem2 41059 dia2dimlem3 41060 dia2dimlem4 41061 dia2dimlem5 41062 diaf1oN 41124 diarnN 41123 dvheveccl 41106 dvhopN 41110 |
| [Crawley] p. 121 | Lemma N | cdlemn 41206 cdlemn10 41200 cdlemn11 41205 cdlemn11a 41201 cdlemn11b 41202 cdlemn11c 41203 cdlemn11pre 41204 cdlemn2 41189 cdlemn2a 41190 cdlemn3 41191 cdlemn4 41192 cdlemn4a 41193 cdlemn5 41195 cdlemn5pre 41194 cdlemn6 41196 cdlemn7 41197 cdlemn8 41198 cdlemn9 41199 diclspsn 41188 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41167 |
| [Crawley] p. 122 | Lemma N | dih11 41259 dihf11 41261 dihjust 41211 dihjustlem 41210 dihord 41258 dihord1 41212 dihord10 41217 dihord11b 41216 dihord11c 41218 dihord2 41221 dihord2a 41213 dihord2b 41214 dihord2cN 41215 dihord2pre 41219 dihord2pre2 41220 dihordlem6 41207 dihordlem7 41208 dihordlem7b 41209 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41224 dihfval 41225 dihval 41226 |
| [Diestel] p. 3 | Definition | df-gric 47881 df-grim 47878 isuspgrim 47896 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29339 df-nbgr 29260 |
| [Diestel] p. 3 | Definition by | df-grisom 47877 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 47861 df-subgr 29195 uhgrspan1 29230 uhgrspansubgr 29218 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29482 vtxdgoddnumeven 29481 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28986 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 33854 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 33866 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 33858 zarcls1 33859 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 33869 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 33872 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 33875 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3917 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9600 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8801 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9608 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9933 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10508 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5260 |
| [Enderton] p. 19 | Definition | df-tp 4594 |
| [Enderton] p. 26 | Exercise 5 | unissb 4903 |
| [Enderton] p. 26 | Exercise 10 | pwel 5336 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5531 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5043 iinin2 5042 iinun2 5037 iunin1 5036 iunin1f 32486 iunin2 5035 uniin1 32480 uniin2 32481 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5041 iundif2 5038 |
| [Enderton] p. 32 | Exercise 20 | unineq 4251 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5062 |
| [Enderton] p. 33 | Exercise 25 | iununi 5063 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5070 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7747 iunpwss 5071 |
| [Enderton] p. 36 | Definition | opthwiener 5474 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5410 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4909 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5430 rnex 7886 rnexg 7878 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5878 rnuni 6121 |
| [Enderton] p. 42 | Definition of a function | dffun7 6543 dffun8 6544 |
| [Enderton] p. 43 | Definition of function value | funfv2 6949 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6585 |
| [Enderton] p. 44 | Definition (d) | dfima2 6033 dfima3 6034 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6958 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10426 ac7g 10427 df-ac 10069 dfac2 10085 dfac2a 10083 dfac2b 10084 dfac3 10074 dfac7 10086 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7220 |
| [Enderton] p. 52 | Definition | df-map 8801 |
| [Enderton] p. 53 | Exercise 21 | coass 6238 |
| [Enderton] p. 53 | Exercise 27 | dmco 6227 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6592 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6073 |
| [Enderton] p. 54 | Remark | ixpf 8893 ixpssmap 8905 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8871 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10436 ac9s 10446 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 38601 erref 8691 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 38604 erthi 8727 |
| [Enderton] p. 57 | Definition | df-ec 8673 |
| [Enderton] p. 58 | Definition | df-qs 8677 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8673 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5874 |
| [Enderton] p. 68 | Definition of successor | df-suc 6338 |
| [Enderton] p. 71 | Definition | df-tr 5215 dftr4 5221 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6413 unisucg 6412 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6413 unisucg 6412 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5230 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5232 trintALT 44870 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8568 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8570 onasuc 8492 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7390 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8569 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8571 onmsuc 8493 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8586 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8573 nnacom 8581 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8587 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8588 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8590 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8574 nnmsucr 8589 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8602 |
| [Enderton] p. 129 | Definition | df-en 8919 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7341 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9968 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16181 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9171 |
| [Enderton] p. 135 | Corollary 6C | php3 9173 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9170 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9203 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9205 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9132 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9137 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9105 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10133 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10134 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10129 dju1en 10125 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9294 unifi 9295 unifi2 9296 |
| [Enderton] p. 144 | Corollary 6K | undif2 4440 unfi 9135 unfi2 9259 |
| [Enderton] p. 145 | Figure 38 | ffoss 7924 |
| [Enderton] p. 145 | Definition | df-dom 8920 |
| [Enderton] p. 146 | Example 1 | domen 8933 domeng 8934 |
| [Enderton] p. 146 | Example 3 | nndomo 9181 nnsdom 9607 nnsdomg 9246 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10137 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9106 xpdom1 9040 xpdom1g 9038 xpdom2g 9037 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9112 |
| [Enderton] p. 151 | Theorem 6M | zorn 10460 zorng 10457 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10445 dfac5 10082 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10528 |
| [Enderton] p. 164 | Example | infdif 10161 |
| [Enderton] p. 168 | Definition | df-po 5546 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6448 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6379 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6447 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6387 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7814 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7757 |
| [Enderton] p. 194 | Remark | onprc 7754 |
| [Enderton] p. 194 | Exercise 16 | suc11 6441 |
| [Enderton] p. 197 | Definition | df-card 9892 |
| [Enderton] p. 197 | Theorem 7P | carden 10504 |
| [Enderton] p. 200 | Exercise 25 | tfis 7831 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9729 |
| [Enderton] p. 202 | Definition | df-r1 9717 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9739 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9820 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9559 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9810 rankprb 9804 rankpw 9796 rankpwi 9776 rankuniss 9819 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9571 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9572 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10063 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10029 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10043 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8310 |
| [Enderton] p. 222 | Definition of kard | karden 9848 kardex 9847 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8561 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8563 |
| [Enderton] p. 240 | Exercise 25 | oarec 8526 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10203 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17603 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17549 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18512 mrieqv2d 17600 mrieqvd 17599 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17604 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17609 mreexexlem2d 17606 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18518 mreexfidimd 17611 |
| [Frege1879] p. 11 | Statement | df3or2 43757 |
| [Frege1879] p. 12 | Statement | df3an2 43758 dfxor4 43755 dfxor5 43756 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 43779 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 43780 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 43784 |
| [Frege1879] p. 31 | Proposition 4 | frege4 43788 |
| [Frege1879] p. 32 | Proposition 5 | frege5 43789 |
| [Frege1879] p. 33 | Proposition 6 | frege6 43795 |
| [Frege1879] p. 34 | Proposition 7 | frege7 43797 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 43798 axfrege8 43796 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37433 |
| [Frege1879] p. 35 | Proposition 9 | frege9 43801 |
| [Frege1879] p. 36 | Proposition 10 | frege10 43809 |
| [Frege1879] p. 36 | Proposition 11 | frege11 43803 |
| [Frege1879] p. 37 | Proposition 12 | frege12 43802 |
| [Frege1879] p. 37 | Proposition 13 | frege13 43811 |
| [Frege1879] p. 37 | Proposition 14 | frege14 43812 |
| [Frege1879] p. 38 | Proposition 15 | frege15 43815 |
| [Frege1879] p. 38 | Proposition 16 | frege16 43805 |
| [Frege1879] p. 39 | Proposition 17 | frege17 43810 |
| [Frege1879] p. 39 | Proposition 18 | frege18 43807 |
| [Frege1879] p. 39 | Proposition 19 | frege19 43813 |
| [Frege1879] p. 40 | Proposition 20 | frege20 43817 |
| [Frege1879] p. 40 | Proposition 21 | frege21 43816 |
| [Frege1879] p. 41 | Proposition 22 | frege22 43808 |
| [Frege1879] p. 42 | Proposition 23 | frege23 43814 |
| [Frege1879] p. 42 | Proposition 24 | frege24 43804 |
| [Frege1879] p. 42 | Proposition 25 | frege25 43806 rp-frege25 43794 |
| [Frege1879] p. 42 | Proposition 26 | frege26 43799 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 43819 |
| [Frege1879] p. 43 | Proposition 27 | frege27 43800 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 43820 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 43823 axfrege31 43822 |
| [Frege1879] p. 44 | Proposition 30 | frege30 43821 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 43824 |
| [Frege1879] p. 44 | Proposition 33 | frege33 43825 |
| [Frege1879] p. 45 | Proposition 34 | frege34 43826 |
| [Frege1879] p. 45 | Proposition 35 | frege35 43827 |
| [Frege1879] p. 45 | Proposition 36 | frege36 43828 |
| [Frege1879] p. 46 | Proposition 37 | frege37 43829 |
| [Frege1879] p. 46 | Proposition 38 | frege38 43830 |
| [Frege1879] p. 46 | Proposition 39 | frege39 43831 |
| [Frege1879] p. 46 | Proposition 40 | frege40 43832 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 43834 axfrege41 43833 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 43835 |
| [Frege1879] p. 47 | Proposition 43 | frege43 43836 |
| [Frege1879] p. 47 | Proposition 44 | frege44 43837 |
| [Frege1879] p. 47 | Proposition 45 | frege45 43838 |
| [Frege1879] p. 48 | Proposition 46 | frege46 43839 |
| [Frege1879] p. 48 | Proposition 47 | frege47 43840 |
| [Frege1879] p. 49 | Proposition 48 | frege48 43841 |
| [Frege1879] p. 49 | Proposition 49 | frege49 43842 |
| [Frege1879] p. 49 | Proposition 50 | frege50 43843 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 43846 ax-frege52c 43877 frege52aid 43847 frege52b 43878 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 43851 ax-frege54c 43881 frege54b 43882 |
| [Frege1879] p. 50 | Proposition 51 | frege51 43844 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3755 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 43849 frege53aid 43848 frege53b 43879 frege53c 43903 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2729 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 43857 frege55aid 43854 frege55b 43886 frege55c 43907 frege55cor1a 43858 frege55lem2a 43856 frege55lem2b 43885 frege55lem2c 43906 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 43860 frege56aid 43859 frege56b 43887 frege56c 43908 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 43864 ax-frege58b 43890 frege58bid 43891 frege58c 43910 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 43862 frege57aid 43861 frege57b 43888 frege57c 43909 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3766 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 43866 frege59b 43893 frege59c 43911 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 43867 frege60b 43894 frege60c 43912 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 43868 frege61b 43895 frege61c 43913 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 43869 frege62b 43896 frege62c 43914 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 43870 frege63b 43897 frege63c 43915 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 43871 frege64b 43898 frege64c 43916 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 43872 frege65b 43899 frege65c 43917 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 43873 frege66b 43900 frege66c 43918 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 43874 frege67b 43901 frege67c 43919 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 43875 frege68b 43902 frege68c 43920 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 43921 |
| [Frege1879] p. 58 | Proposition 70 | frege70 43922 |
| [Frege1879] p. 59 | Proposition 71 | frege71 43923 |
| [Frege1879] p. 59 | Proposition 72 | frege72 43924 |
| [Frege1879] p. 59 | Proposition 73 | frege73 43925 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 43928 |
| [Frege1879] p. 60 | Proposition 74 | frege74 43926 |
| [Frege1879] p. 60 | Proposition 75 | frege75 43927 |
| [Frege1879] p. 62 | Proposition 77 | frege77 43929 frege77d 43735 |
| [Frege1879] p. 63 | Proposition 78 | frege78 43930 |
| [Frege1879] p. 63 | Proposition 79 | frege79 43931 |
| [Frege1879] p. 63 | Proposition 80 | frege80 43932 |
| [Frege1879] p. 63 | Proposition 81 | frege81 43933 frege81d 43736 |
| [Frege1879] p. 64 | Proposition 82 | frege82 43934 |
| [Frege1879] p. 65 | Proposition 83 | frege83 43935 frege83d 43737 |
| [Frege1879] p. 65 | Proposition 84 | frege84 43936 |
| [Frege1879] p. 66 | Proposition 85 | frege85 43937 |
| [Frege1879] p. 66 | Proposition 86 | frege86 43938 |
| [Frege1879] p. 66 | Proposition 87 | frege87 43939 frege87d 43739 |
| [Frege1879] p. 67 | Proposition 88 | frege88 43940 |
| [Frege1879] p. 68 | Proposition 89 | frege89 43941 |
| [Frege1879] p. 68 | Proposition 90 | frege90 43942 |
| [Frege1879] p. 68 | Proposition 91 | frege91 43943 frege91d 43740 |
| [Frege1879] p. 69 | Proposition 92 | frege92 43944 |
| [Frege1879] p. 70 | Proposition 93 | frege93 43945 |
| [Frege1879] p. 70 | Proposition 94 | frege94 43946 |
| [Frege1879] p. 70 | Proposition 95 | frege95 43947 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 43951 |
| [Frege1879] p. 71 | Proposition 96 | frege96 43948 frege96d 43738 |
| [Frege1879] p. 71 | Proposition 97 | frege97 43949 frege97d 43741 |
| [Frege1879] p. 71 | Proposition 98 | frege98 43950 frege98d 43742 |
| [Frege1879] p. 72 | Proposition 100 | frege100 43952 |
| [Frege1879] p. 72 | Proposition 101 | frege101 43953 |
| [Frege1879] p. 72 | Proposition 102 | frege102 43954 frege102d 43743 |
| [Frege1879] p. 73 | Proposition 103 | frege103 43955 |
| [Frege1879] p. 73 | Proposition 104 | frege104 43956 |
| [Frege1879] p. 73 | Proposition 105 | frege105 43957 |
| [Frege1879] p. 73 | Proposition 106 | frege106 43958 frege106d 43744 |
| [Frege1879] p. 74 | Proposition 107 | frege107 43959 |
| [Frege1879] p. 74 | Proposition 108 | frege108 43960 frege108d 43745 |
| [Frege1879] p. 74 | Proposition 109 | frege109 43961 frege109d 43746 |
| [Frege1879] p. 75 | Proposition 110 | frege110 43962 |
| [Frege1879] p. 75 | Proposition 111 | frege111 43963 frege111d 43748 |
| [Frege1879] p. 76 | Proposition 112 | frege112 43964 |
| [Frege1879] p. 76 | Proposition 113 | frege113 43965 |
| [Frege1879] p. 76 | Proposition 114 | frege114 43966 frege114d 43747 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 43967 |
| [Frege1879] p. 77 | Proposition 116 | frege116 43968 |
| [Frege1879] p. 78 | Proposition 117 | frege117 43969 |
| [Frege1879] p. 78 | Proposition 118 | frege118 43970 |
| [Frege1879] p. 78 | Proposition 119 | frege119 43971 |
| [Frege1879] p. 78 | Proposition 120 | frege120 43972 |
| [Frege1879] p. 79 | Proposition 121 | frege121 43973 |
| [Frege1879] p. 79 | Proposition 122 | frege122 43974 frege122d 43749 |
| [Frege1879] p. 79 | Proposition 123 | frege123 43975 |
| [Frege1879] p. 80 | Proposition 124 | frege124 43976 frege124d 43750 |
| [Frege1879] p. 81 | Proposition 125 | frege125 43977 |
| [Frege1879] p. 81 | Proposition 126 | frege126 43978 frege126d 43751 |
| [Frege1879] p. 82 | Proposition 127 | frege127 43979 |
| [Frege1879] p. 83 | Proposition 128 | frege128 43980 |
| [Frege1879] p. 83 | Proposition 129 | frege129 43981 frege129d 43752 |
| [Frege1879] p. 84 | Proposition 130 | frege130 43982 |
| [Frege1879] p. 85 | Proposition 131 | frege131 43983 frege131d 43753 |
| [Frege1879] p. 86 | Proposition 132 | frege132 43984 |
| [Frege1879] p. 86 | Proposition 133 | frege133 43985 frege133d 43754 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46311 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 46634 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46334 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46449 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46469 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46460 meadjunre 46474 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46461 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46462 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46458 meaiunle 46467 meaiunlelem 46466 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46479 meaiuninc2 46480 meaiuninc3 46483 meaiuninc3v 46482 meaiunincf 46481 meaiuninclem 46478 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46485 meaiininc2 46486 meaiininclem 46484 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46504 caragendifcl 46512 caratheodory 46526 omelesplit 46516 |
| [Fremlin1] p. 19 | Definition 113A | isome 46492 isomennd 46529 isomenndlem 46528 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46514 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46533 voncmpl 46619 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46496 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46521 carageniuncllem1 46519 carageniuncllem2 46520 caragenuncl 46511 caragenuncllem 46510 caragenunicl 46522 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46530 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46524 caratheodorylem2 46525 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46533 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 46592 hoidmv1lelem1 46589 hoidmv1lelem2 46590 hoidmv1lelem3 46591 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 46636 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 46592 hoidmvle 46598 hoidmvlelem1 46593 hoidmvlelem2 46594 hoidmvlelem3 46595 hoidmvlelem4 46596 hoidmvlelem5 46597 hsphoidmvle2 46583 hsphoif 46574 hsphoival 46577 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46546 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46554 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 46581 hoidmvn0val 46582 hoidmvval 46575 hoidmvval0 46585 hoidmvval0b 46588 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 46586 hsphoidmvle 46584 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46535 df-voln 46537 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 46602 ovn0 46564 ovn0lem 46563 ovnf 46561 ovnome 46571 ovnssle 46559 ovnsslelem 46558 ovnsupge0 46555 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 46601 ovnhoilem1 46599 ovnhoilem2 46600 vonhoi 46665 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 46618 hoidifhspf 46616 hoidifhspval 46606 hoidifhspval2 46613 hoidifhspval3 46617 hspmbl 46627 hspmbllem1 46624 hspmbllem2 46625 hspmbllem3 46626 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 46619 vonmea 46572 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 46570 ovnsubadd2 46644 ovnsubadd2lem 46643 ovnsubaddlem1 46568 ovnsubaddlem2 46569 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 46629 hoimbl2 46663 hoimbllem 46628 hspdifhsp 46614 opnvonmbl 46632 opnvonmbllem2 46631 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 46634 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 46677 iccvonmbllem 46676 ioovonmbl 46675 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 46683 vonicclem2 46682 vonioo 46680 vonioolem2 46679 vonn0icc 46686 vonn0icc2 46690 vonn0ioo 46685 vonn0ioo2 46688 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 46687 snvonmbl 46684 vonct 46691 vonsn 46689 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46357 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46356 subsaliuncllem 46355 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 46723 salpreimalegt 46707 salpreimaltle 46724 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 46726 issmff 46732 issmflem 46725 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 46743 issmflelem 46742 smfpreimale 46752 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 46754 issmfgtlem 46753 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 46694 issmf 46726 issmff 46732 issmfge 46768 issmfgelem 46767 issmfgt 46754 issmfgtlem 46753 issmfle 46743 issmflelem 46742 issmflem 46725 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 46705 salpreimagtlt 46728 salpreimalelt 46727 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 46768 issmfgelem 46767 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 46751 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 46749 cnfsmf 46738 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 46765 decsmflem 46764 incsmf 46740 incsmflem 46739 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 46699 pimconstlt1 46700 smfconst 46747 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 46763 smfaddlem1 46761 smfaddlem2 46762 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 46794 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 46793 smfmullem1 46789 smfmullem2 46790 smfmullem3 46791 smfmullem4 46792 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 46795 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 46798 smfpimbor1lem2 46797 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 46800 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 46788 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 46787 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 46796 smfresal 46786 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 46775 smflim2 46804 smflimlem1 46769 smflimlem2 46770 smflimlem3 46771 smflimlem4 46772 smflimlem5 46773 smflimlem6 46774 smflimmpt 46808 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 46812 smfsuplem1 46809 smfsuplem2 46810 smfsuplem3 46811 smfsupmpt 46813 smfsupxr 46814 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 46816 smfinflem 46815 smfinfmpt 46817 |
| [Fremlin1] p. 39 | Remark 121G | smflim 46775 smflim2 46804 smflimmpt 46808 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 46806 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 46836 smfdivdmmbl2 46839 smfinfdmmbl 46847 smfinfdmmbllem 46846 smfsupdmmbl 46843 smfsupdmmbllem 46842 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 46826 smflimsuplem2 46819 smflimsuplem6 46823 smflimsuplem7 46824 smflimsuplem8 46825 smflimsupmpt 46827 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 46829 smfliminflem 46828 smfliminfmpt 46830 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 46694 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 46840 fsupdm2 46841 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 46831 adddmmbl2 46832 finfdm 46844 finfdm2 46845 fsupdm 46840 fsupdm2 46841 muldmmbl 46833 muldmmbl2 46834 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 46844 finfdm2 46845 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25437 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25480 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25490 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 37692 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 37695 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9591 inf1 9575 inf2 9576 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10864 enqer 10874 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10869 df-nq 10865 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10861 df-plq 10867 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7626 df-mpq 10862 df-mq 10868 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10870 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10928 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10929 ltbtwnnq 10931 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10924 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10925 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10932 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10934 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10946 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10948 |
| [Gleason] p. 122 | Definition | df-1p 10935 |
| [Gleason] p. 122 | Remark (1) | prub 10947 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10986 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10938 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10985 psslinpr 10984 supexpr 11007 suplem1pr 11005 suplem2pr 11006 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10971 addclprlem1 10969 addclprlem2 10970 df-plp 10936 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10975 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10974 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10987 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10996 ltexprlem1 10989 ltexprlem2 10990 ltexprlem3 10991 ltexprlem4 10992 ltexprlem5 10993 ltexprlem6 10994 ltexprlem7 10995 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10998 ltaprlem 10997 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10999 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11000 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10937 mulclpr 10973 mulclprlem 10972 reclem2pr 11001 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10982 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10977 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10976 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10981 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11004 reclem3pr 11002 reclem4pr 11003 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11008 enrer 11016 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11013 df-1r 11014 df-nr 11009 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11011 df-plr 11010 negexsr 11055 recexsr 11060 recexsrlem 11056 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11012 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12181 creur 12180 cru 12178 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11141 axcnre 11117 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15081 crimd 15198 crimi 15159 crre 15080 crred 15197 crrei 15158 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15083 remimd 15164 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15250 absval2d 15414 absval2i 15364 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15107 cjaddd 15186 cjaddi 15154 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15108 cjmuld 15187 cjmuli 15155 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15106 cjcjd 15165 cjcji 15137 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15105 cjreb 15089 cjrebd 15168 cjrebi 15140 cjred 15192 rere 15088 rereb 15086 rerebd 15167 rerebi 15139 rered 15190 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15114 addcjd 15178 addcji 15149 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15204 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15245 abscjd 15419 abscji 15368 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15255 abs00d 15415 abs00i 15365 absne0d 15416 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15288 releabsd 15420 releabsi 15369 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15260 absmuld 15423 absmuli 15371 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15248 sqabsaddi 15372 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15297 abstrid 15425 abstrii 15375 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14027 exp0 14030 expp1 14033 expp1d 14112 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26588 cxpaddd 26626 expadd 14069 expaddd 14113 expaddz 14071 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26597 cxpmuld 26646 expmul 14072 expmuld 14114 expmulz 14073 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26594 mulcxpd 26637 mulexp 14066 mulexpd 14126 mulexpz 14067 |
| [Gleason] p. 140 | Exercise 1 | znnen 16180 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13470 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15598 rlimadd 15609 rlimdiv 15612 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15600 rlimsub 15610 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15599 rlimmul 15611 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15603 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15549 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15570 climcj 15571 climim 15573 climre 15572 rlimabs 15575 rlimcj 15576 rlimim 15578 rlimre 15577 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11213 df-xr 11212 ltxr 13075 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15437 limsupval 15440 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15636 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15645 caucvgb 15646 caucvgbf 45485 caucvgr 15642 climcau 15637 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15782 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15849 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15302 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13790 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21258 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24231 xmet0 24230 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24247 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24238 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24240 mstri 24357 xmettri 24239 xmstri 24356 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24270 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23535 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25210 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24428 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24754 addcn2 15560 mulcn 24756 mulcn2 15562 subcn 24755 subcn2 15561 |
| [Gleason] p. 295 | Remark | bcval3 14271 bcval4 14272 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14286 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14269 df-bc 14268 |
| [Gleason] p. 296 | Remark | bcn0 14275 bcnn 14277 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15796 |
| [Gleason] p. 308 | Equation 2 | ef0 16057 |
| [Gleason] p. 308 | Equation 3 | efcj 16058 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16064 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16069 |
| [Gleason] p. 310 | Equation 14 | sinadd 16132 |
| [Gleason] p. 310 | Equation 15 | cosadd 16133 |
| [Gleason] p. 311 | Equation 17 | sincossq 16144 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16149 sinbnd 16148 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14181 sqeqori 14179 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16038 |
| [Godowski] p. 730 | Equation SF | goeqi 32202 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31597 |
| [Golan] p. 1 | Remark | srgisid 20118 |
| [Golan] p. 1 | Definition | df-srg 20096 |
| [Golan] p. 149 | Definition | df-slmd 33154 |
| [Gonshor] p. 7 | Definition | df-scut 27695 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27731 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27828 cofcut1d 27829 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27830 cofcut2d 27831 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27832 cofcutr1d 27833 cofcutr2d 27834 |
| [Gonshor] p. 13 | Definition | df-adds 27867 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27883 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27909 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28033 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28053 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28333 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28335 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28334 |
| [Gonshor] p. 95 | Theorem 6.1 | addsbday 27924 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36147 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17547 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17549 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48176 df-cllaw 48174 df-comlaw 48175 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48188 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48209 |
| [Halmos] p. 28 | Partition ` ` | df-parts 38757 dfmembpart2 38762 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 31994 riesz2 31995 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 31870 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32102 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32114 elpjidm 32113 pjnmopi 32077 |
| [Halmos] p. 44 | Remark | pjinormi 31616 pjinormii 31605 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32118 pjrn 31636 pjrni 31631 pjvec 31625 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31656 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32083 hmopidmpji 32081 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32120 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32109 pjocvec 31626 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32098 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32101 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32104 pjssdif2i 32103 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31784 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1795 |
| [Hatcher] p. 25 | Definition | df-phtpc 24891 df-phtpy 24870 |
| [Hatcher] p. 26 | Definition | df-pco 24905 df-pi1 24908 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24894 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24950 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22377 df-dmatalt 48387 |
| [Helfgott] p. 2 | Theorem | tgoldbach 47818 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 47803 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 47815 bgoldbtbnd 47810 bgoldbtbnd 47810 tgblthelfgott 47816 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34633 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34634 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34648 hgt750lemb 34647 hgt750leme 34649 hgt750lemf 34644 hgt750lemg 34645 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 47812 tgoldbachgt 34654 tgoldbachgtALTV 47813 tgoldbachgtd 34653 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34635 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30422 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18876 grpoideu 30438 mndideu 18672 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18906 grpoinveu 30448 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18937 grpo2inv 30460 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18950 grpoinvop 30462 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18972 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1768 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1769 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1771 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32349 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32362 cdj3i 32370 cdj3lem1 32363 cdjreui 32361 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32360 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 41955 |
| [Holland95] p. 14 | Line 15 | hgmapvs 41885 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 41907 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 41908 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 41905 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 41911 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 41830 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 41925 |
| [Holland95] p. 204 | Definition of involution | df-srng 20749 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39497 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41522 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41475 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 39927 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41371 poml4N 39947 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41462 pexmidALTN 39972 pexmidN 39963 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41527 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39117 ldualset 39118 |
| [Holland95] p. 222 | Item 1 | df-lines 39495 df-pointsN 39496 |
| [Holland95] p. 222 | Item 2 | df-polarityN 39897 |
| [Holland95] p. 223 | Remark | ispsubcl2N 39941 omllaw4 39239 pol1N 39904 polcon3N 39911 |
| [Holland95] p. 223 | Definition | df-psubclN 39929 |
| [Holland95] p. 223 | Equation for polarity | polval2N 39900 |
| [Holmes] p. 40 | Definition | df-xrn 38353 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31013 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32111 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 31892 eigre 31764 eigrei 31763 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 31893 eigorth 31767 eigorthi 31766 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31765 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30238 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30234 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30235 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30236 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30254 frgrregorufr0 30253 frgrregorufrg 30255 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30261 frrusgrord 30270 frrusgrord0 30269 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30017 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30244 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30247 frgrwopreg2 30248 frgrwopregasn 30245 frgrwopregbsn 30246 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30250 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30264 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30267 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30015 numclwlk1 30300 numclwlk1lem1 30298 numclwlk1lem2 30299 numclwwlk1 30290 numclwwlk8 30321 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30241 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29701 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30276 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30302 numclwwlkovh0 30301 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30310 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 29907 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30314 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30317 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30320 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30332 natded 30332 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30332 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30332 natded 30332 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30332 |
| [Jech] p. 4 | Definition of class | cv 1539 cvjust 2723 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10532 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10530 alephmul 10531 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10529 infmap2 10170 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9767 |
| [Jech] p. 72 | Equation 9.3 | scott0 9839 scottex 9838 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9820 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9844 |
| [Jech] p. 78 | Note | opthprc 5702 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 42904 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 42992 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 42993 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 42916 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 42920 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 42921 rmyp1 42922 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 42923 rmym1 42924 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 42914 rmx1 42915 rmxluc 42925 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 42918 rmy1 42919 rmyluc 42926 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 42928 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 42929 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 42949 jm2.17b 42950 jm2.17c 42951 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 42982 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 42986 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 42977 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 42952 jm2.24nn 42948 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 42991 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 42997 rmygeid 42953 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43009 |
| [Juillerat] p. 11 | Section *5 | etransc 46281 etransclem47 46279 etransclem48 46280 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46276 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46278 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46264 |
| [Juillerat] p. 13 | Proof | etransclem35 46267 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46270 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46256 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46273 |
| [Juillerat] p. 14 | Proof | etransclem23 46255 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1967 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2012 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2017 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2007 cbvaliw 2006 wl-cbvmotv 37501 wl-motae 37503 wl-moteq 37502 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1986 spimw 1970 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2033 spw 2034 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31445 chabs1i 31447 chabs2 31446 chabs2i 31448 chjass 31462 chjassi 31415 latabs1 18434 latabs2 18435 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32267 ela 32268 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32212 cvrval2 39267 |
| [Kalmbach] p. 16 | Definition | df-ol 39171 df-oml 39172 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31513 cmbri 31519 cmtvalN 39204 df-cm 31512 df-cmtN 39170 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39240 pjoml5 31542 pjoml5i 31517 |
| [Kalmbach] p. 22 | Definition | pjoml2 31540 pjoml2i 31514 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31543 cmcmi 31521 cmcmii 31526 cmtcomN 39242 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39238 omlsi 31333 pjoml 31365 pjomli 31364 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39237 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31525 cmcm3 31544 cmcm3i 31523 cmcm3ii 31528 cmcm4i 31524 cmt3N 39244 cmt4N 39245 cmtbr2N 39246 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31537 cmbr3i 31529 cmtbr3N 39247 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31547 fh1i 31550 fh2 31548 fh2i 31551 omlfh1N 39251 |
| [Kalmbach] p. 65 | Remark | chjatom 32286 chslej 31427 chsleji 31387 shslej 31309 shsleji 31299 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31424 chocini 31383 chsupcl 31269 chsupval2 31339 h0elch 31184 helch 31172 hsupval2 31338 ocin 31225 ococss 31222 shococss 31223 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31241 |
| [Kalmbach] p. 66 | Remark | df-pjh 31324 pjssmi 32094 pjssmii 31610 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31574 osumi 31571 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32129 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32329 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32239 |
| [Kalmbach] p. 140 | Remark | hatomic 32289 hatomici 32288 hatomistici 32291 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39312 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32310 lsatexch 39036 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32284 cvlcvr1 39332 cvr1 39404 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32303 cvexchi 32298 cvrexch 39414 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32293 hlrelat 39396 hlrelat5N 39395 lrelat 39007 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21051 lsmsatcv 39003 spansncv 31582 spansncvi 31581 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39022 spansncv2 32222 |
| [Kalmbach] p. 266 | Definition | df-st 32140 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31778 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10599 fpwwe2 10596 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10600 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10607 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10602 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10604 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10617 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10621 gchxpidm 10622 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10633 gchhar 10632 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10168 unxpwdom 9542 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10623 |
| [Kreyszig] p. 3 | Property M1 | metcl 24220 xmetcl 24219 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24227 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24460 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11899 muleqadd 11822 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24326 |
| [Kreyszig] p. 19 | Remark | mopntopon 24327 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24386 mopnm 24332 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24384 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24389 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24430 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23145 lmmbr 25158 lmmbr2 25159 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23267 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25213 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25176 iscmet2 25194 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25216 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23348 metelcls 25205 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25206 metcld2 25207 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 24999 lmodvneg1 20811 nvinv 30568 vcm 30505 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 24995 lmod0vs 20801 slmd0vs 33177 vc0 30503 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20802 slmdvs0 33178 vcz 30504 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30620 ngpmet 24491 nrmmetd 24462 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30615 imsdval2 30616 ncvspds 25061 ngpds 24492 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24477 nvnd 30617 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24506 nmge0 24505 nvge0 30602 nvz 30598 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24512 nvabs 30601 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30730 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30674 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30736 blocni 30734 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30735 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25104 ipeq0 21547 ipz 30648 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25116 pythi 30779 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30783 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25138 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15822 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25336 minveco 30813 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30679 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25229 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30802 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32052 leopg 32051 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32070 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30847 |
| [Kulpa] p. 547 | Theorem | poimir 37647 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37646 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37645 |
| [Kulpa] p. 548 | Theorem | broucube 37648 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37640 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37641 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2381 axnul 5260 |
| [Kunen] p. 11 | Axiom 3 | axnul 5260 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7933 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8811 mapvalg 8809 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10475 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7917 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9717 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9759 r1elssi 9758 |
| [Kunen] p. 107 | Exercise 4 | rankop 9811 rankopb 9805 rankuni 9816 rankxplim 9832 rankxpsuc 9835 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 44944 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 44952 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 44951 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 44953 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 44958 rexabso 44959 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 44965 n0abso 44966 ssabso 44964 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 44967 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 44977 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 44972 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 44975 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 44976 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 44971 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 44983 wfaxpr 44988 wfaxreg 44990 wfaxrep 44984 wfaxsep 44985 wfaxun 44989 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 44974 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 44987 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 44983 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 44982 omelaxinf2 44979 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 44992 wfaxinf2 44991 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45005 permaxext 44995 permaxinf2 45003 permaxnul 44998 permaxpow 44999 permaxpr 45000 permaxrep 44996 permaxsep 44997 permaxun 45001 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 44993 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45004 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4968 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33660 |
| [Lang] p. | Definition | df-rn 5649 |
| [Lang] p. 3 | Statement | lidrideqd 18596 mndbn0 18677 |
| [Lang] p. 3 | Definition | df-mnd 18662 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18614 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18768 |
| [Lang] p. 5 | Equation | gsumreidx 19847 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48170 |
| [Lang] p. 6 | Example | nn0mnd 48167 |
| [Lang] p. 6 | Equation | gsumxp2 19910 |
| [Lang] p. 6 | Statement | cycsubm 19134 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19012 |
| [Lang] p. 6 | Observation | mndlsmidm 19600 |
| [Lang] p. 7 | Definition | dfgrp2e 18895 |
| [Lang] p. 30 | Definition | df-tocyc 33064 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33109 |
| [Lang] p. 32 | Property (b) | cyc3conja 33114 cycpmconjv 33099 |
| [Lang] p. 53 | Definition | df-cat 17629 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18059 cat1lem 18058 |
| [Lang] p. 54 | Definition | df-iso 17711 |
| [Lang] p. 57 | Definition | df-inito 17946 df-termo 17947 |
| [Lang] p. 58 | Example | irinitoringc 21389 |
| [Lang] p. 58 | Statement | initoeu1 17973 termoeu1 17980 |
| [Lang] p. 62 | Definition | df-func 17820 |
| [Lang] p. 65 | Definition | df-nat 17908 |
| [Lang] p. 91 | Note | df-ringc 20555 |
| [Lang] p. 92 | Statement | mxidlprm 33441 |
| [Lang] p. 92 | Definition | isprmidlc 33418 |
| [Lang] p. 128 | Remark | dsmmlmod 21654 |
| [Lang] p. 129 | Proof | lincscm 48419 lincscmcl 48421 lincsum 48418 lincsumcl 48420 |
| [Lang] p. 129 | Statement | lincolss 48423 |
| [Lang] p. 129 | Observation | dsmmfi 21647 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33623 qusdimsum 33624 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33603 |
| [Lang] p. 147 | Definition | snlindsntor 48460 |
| [Lang] p. 504 | Statement | mat1 22334 matring 22330 |
| [Lang] p. 504 | Definition | df-mamu 22278 |
| [Lang] p. 505 | Statement | mamuass 22289 mamutpos 22345 matassa 22331 mattposvs 22342 tposmap 22344 |
| [Lang] p. 513 | Definition | mdet1 22488 mdetf 22482 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22578 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22474 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22498 |
| [Lang] p. 515 | Definition | df-minmar1 22522 smadiadetr 22562 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22497 mdetralt 22495 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22510 |
| [Lang] p. 518 | Definition | df-madu 22521 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22532 madurid 22531 matinv 22564 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22777 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33659 fedgmul 33627 |
| [Lang], p. 561 | Remark | chpmatply1 22719 |
| [Lang], p. 561 | Definition | df-chpmat 22714 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44323 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44318 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44324 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5260 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2708 |
| [Levy] p. 59 | Definition | df-ttrcl 9661 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9704 |
| [Levy] p. 338 | Axiom | df-clel 2803 df-cleq 2721 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2803 df-cleq 2721 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2708 |
| [Levy] p. 358 | Axiom | df-clab 2708 |
| [Levy58] p. 2 | Definition I | isfin1-3 10339 |
| [Levy58] p. 2 | Definition II | df-fin2 10239 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10238 |
| [Levy58] p. 2 | Definition III | df-fin3 10241 |
| [Levy58] p. 3 | Definition V | df-fin5 10242 |
| [Levy58] p. 3 | Definition IV | df-fin4 10240 |
| [Levy58] p. 4 | Definition VI | df-fin6 10243 |
| [Levy58] p. 4 | Definition VII | df-fin7 10244 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10368 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27598 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27609 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27641 nosupbnd1 27626 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27643 nosupbnd2 27628 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27647 noetasuplem4 27648 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27644 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1768 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1769 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1771 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32337 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32341 mdsymi 32340 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32335 mdsymlem6 32337 mdsymlem7 32338 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32339 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32242 ssdmd2 32243 ssmd1 32240 ssmd2 32241 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32238 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32210 df-md 32209 mdbr 32223 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32260 mdslj1i 32248 mdslj2i 32249 mdslle1i 32246 mdslle2i 32247 mdslmd1i 32258 mdslmd2i 32259 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32250 mdsl2bi 32252 mdsl2i 32251 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32264 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32261 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32262 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32239 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32244 mdsl3 32245 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32263 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32358 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39314 hlrelat1 39394 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39032 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32265 cvmdi 32253 cvnbtwn4 32218 cvrnbtwn4 39272 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32266 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39333 cvp 32304 cvrp 39410 lcvp 39033 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32328 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32327 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39326 hlexch4N 39386 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32330 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39437 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 39743 atpsubN 39747 df-pointsN 39496 pointpsubN 39745 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39498 pmap11 39756 pmaple 39755 pmapsub 39762 pmapval 39751 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 39759 pmap1N 39761 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 39764 pmapglb2N 39765 pmapglb2xN 39766 pmapglbx 39763 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 39846 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39471 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 39790 paddclN 39836 paddidm 39835 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39472 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 39832 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39471 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39472 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19605 lsmmod2 19606 lssats 39005 shatomici 32287 shatomistici 32290 shmodi 31319 shmodsi 31318 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32229 mdsymlem7 32338 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31518 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31422 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32344 |
| [Margaris] p. 40 | Rule C | exlimiv 1930 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1780 df-or 848 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30329 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 44904 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 44905 |
| [Margaris] p. 79 | Rule C | exinst01 44615 exinst11 44616 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1976 19.2g 2189 r19.2z 4458 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2203 rr19.3v 3633 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2160 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1826 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1781 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2182 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2206 19.9h 2286 exlimd 2219 exlimdh 2290 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2163 excomim 2164 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2326 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30330 conventions-labels 30330 conventions-labels 30330 conventions-labels 30330 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1827 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44367 albi 1818 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2226 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2227 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44369 exbi 1847 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2230 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44366 2alimdv 1918 alimd 2213 alimdh 1817 alimdv 1916 ax-4 1809 ralimdaa 3238 ralimdv 3147 ralimdva 3145 ralimdvva 3184 sbcimdv 3822 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2208 19.21h 2287 19.21t 2207 19.21vv 44365 alrimd 2216 alrimdd 2215 alrimdh 1863 alrimdv 1929 alrimi 2214 alrimih 1824 alrimiv 1927 alrimivv 1928 hbralrimi 3123 r19.21be 3230 r19.21bi 3229 ralrimd 3242 ralrimdv 3131 ralrimdva 3133 ralrimdvv 3181 ralrimdvva 3192 ralrimi 3235 ralrimia 3236 ralrimiv 3124 ralrimiva 3125 ralrimivv 3178 ralrimivva 3180 ralrimivvva 3183 ralrimivw 3129 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44368 2eximdv 1919 exim 1834 eximd 2217 eximdh 1864 eximdv 1917 rexim 3070 reximd2a 3247 reximdai 3239 reximdd 45142 reximddv 3149 reximddv2 3196 reximddv3 3150 reximdv 3148 reximdv2 3143 reximdva 3146 reximdvai 3144 reximdvva 3185 reximi2 3062 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2212 19.23bi 2192 19.23h 2288 19.23t 2211 exlimdv 1933 exlimdvv 1934 exlimexi 44514 exlimiv 1930 exlimivv 1932 rexlimd3 45138 rexlimdv 3132 rexlimdv3a 3138 rexlimdva 3134 rexlimdva2 3136 rexlimdvaa 3135 rexlimdvv 3193 rexlimdvva 3194 rexlimdvvva 3195 rexlimdvw 3139 rexlimiv 3127 rexlimiva 3126 rexlimivv 3179 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1991 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1880 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1870 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2228 r19.27z 4468 r19.27zv 4469 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2229 19.28vv 44375 r19.28z 4461 r19.28zf 45153 r19.28zv 4464 rr19.28v 3634 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1873 r19.29d2r 3120 r19.29imd 3098 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1881 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2235 19.31vv 44373 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2234 r19.32 47099 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44371 19.33 1884 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1992 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1877 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2231 19.36vv 44372 r19.36zv 4470 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2233 19.37vv 44374 r19.37zv 4465 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1839 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1990 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1887 19.40 1886 r19.40 3099 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2236 19.41rg 44540 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2237 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1882 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2238 r19.44zv 4467 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2239 r19.45zv 4466 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2603 |
| [Mayet] p. 370 | Remark | jpi 32199 largei 32196 stri 32186 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32141 ishst 32143 |
| [Mayet3] p. 10 | Theorem | hstrbi 32195 hstri 32194 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31657 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31658 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32207 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31261 chsupcl 31269 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32289 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32283 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32310 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 39977 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18446 latj32 18444 latjass 18442 |
| [Megill] p. 444 | Axiom C5 | ax-5 1910 ax5ALT 38900 |
| [Megill] p. 444 | Section 7 | conventions 30329 |
| [Megill] p. 445 | Lemma L12 | aecom-o 38894 ax-c11n 38881 axc11n 2424 |
| [Megill] p. 446 | Lemma L17 | equtrr 2022 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 38889 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 38921 hbnae 2430 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2479 sbid 2256 sbidd-misc 49708 sbidd 49707 |
| [Megill] p. 448 | Remark 9.6 | axc14 2461 |
| [Megill] p. 448 | Scheme C4' | ax-c4 38877 |
| [Megill] p. 448 | Scheme C5' | ax-c5 38876 sp 2184 |
| [Megill] p. 448 | Scheme C6' | ax-11 2158 |
| [Megill] p. 448 | Scheme C7' | ax-c7 38878 |
| [Megill] p. 448 | Scheme C8' | ax-7 2008 |
| [Megill] p. 448 | Scheme C9' | ax-c9 38883 |
| [Megill] p. 448 | Scheme C10' | ax-6 1967 ax-c10 38879 |
| [Megill] p. 448 | Scheme C11' | ax-c11 38880 |
| [Megill] p. 448 | Scheme C12' | ax-8 2111 |
| [Megill] p. 448 | Scheme C13' | ax-9 2119 |
| [Megill] p. 448 | Scheme C14' | ax-c14 38884 |
| [Megill] p. 448 | Scheme C15' | ax-c15 38882 |
| [Megill] p. 448 | Scheme C16' | ax-c16 38885 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 38897 dral1 2437 dral2-o 38923 dral2 2436 drex1 2439 drex2 2440 drsb1 2493 drsb2 2267 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2174 sbequ 2084 sbid2v 2507 |
| [Megill] p. 450 | Example in Appendix | hba1-o 38890 hba1 2293 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 46893 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3842 rspsbca 3843 stdpc4 2069 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 38877 ra4 3849 stdpc5 2209 |
| [Mendelson] p. 81 | Rule C | exlimiv 1930 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2028 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2251 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3751 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5474 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4361 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4362 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4240 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4297 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4241 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4104 |
| [Mendelson] p. 231 | Definition of union | dfun3 4239 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5411 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4868 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5529 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4581 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5530 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4895 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5789 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6241 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7751 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6338 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8559 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9104 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9025 xpsneng 9026 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9032 xpcomeng 9033 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9035 |
| [Mendelson] p. 255 | Definition | brsdom 8946 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9028 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8803 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9008 mapsnend 9007 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9110 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9109 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8855 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9011 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9029 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10132 djucomen 10131 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10136 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10130 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8495 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8522 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10512 |
| [Mendelson] p. 281 | Definition | df-r1 9717 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9766 |
| [Mendelson] p. 287 | Axiom system MK | ru 3751 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30188 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30223 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30225 vdgn1frgrv3 30226 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30227 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30220 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30213 2pthfrgrrn 30211 2pthfrgrrn2 30212 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31181 |
| [Monk1] p. 22 | Remark | conventions 30329 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30329 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4202 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5745 ssrelf 32543 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5747 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5170 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6235 coi2 6236 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5884 rn0 5889 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6114 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5656 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5892 rnxp 6143 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5737 xp0 6131 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6048 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6045 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7890 imaexg 7889 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6042 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7047 funfvop 7022 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6915 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6926 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6562 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7229 dff13f 7230 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7193 funrnex 7932 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7221 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6200 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4928 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7985 df-1st 7968 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7986 df-2nd 7969 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9807 ranksnb 9780 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9808 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9809 rankunb 9803 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9791 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9717 r1val2 9790 |
| [Monk1] p. 117 | Lemma | zorn2 10459 zorn2g 10456 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9939 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10514 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9934 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1809 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2008 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2178 ax-c15 38882 ax12v2 2180 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 38877 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2158 |
| [Monk2] p. 109 | Lemma 15 | equvini 2453 equvinv 2029 eqvinop 5447 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1910 ax5ALT 38900 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2142 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2158 |
| [Monk2] p. 114 | Lemma 21 | sp 2184 |
| [Monk2] p. 114 | Lemma 22 | axc4 2320 hba1-o 38890 hba1 2293 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2154 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2177 nfra2 3350 nfra2w 3274 |
| [Moore] p. 53 | Part I | df-mre 17547 |
| [Munkres] p. 77 | Example 2 | distop 22882 indistop 22889 indistopon 22888 |
| [Munkres] p. 77 | Example 3 | fctop 22891 fctop2 22892 |
| [Munkres] p. 77 | Example 4 | cctop 22893 |
| [Munkres] p. 78 | Definition of basis | df-bases 22833 isbasis3g 22836 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17406 tgval2 22843 |
| [Munkres] p. 79 | Remark | tgcl 22856 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22850 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22874 tgss3 22873 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22875 basgen2 22876 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37337 topdifinfeq 37338 topdifinffin 37336 topdifinfindis 37334 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23047 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22925 topcld 22922 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22926 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22928 |
| [Munkres] p. 94 | Definition of closure | clsval 22924 |
| [Munkres] p. 94 | Definition of interior | ntrval 22923 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22962 elcls 22960 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22970 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23035 neindisj 23004 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23037 |
| [Munkres] p. 97 | Definition of limit point | islp2 23032 lpval 23026 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23202 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23114 iscn 23122 iscn2 23125 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23167 cncnp2 23168 cncnpi 23165 df-cnp 23115 iscnp 23124 iscnp2 23126 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24431 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25211 |
| [Nathanson] p. 123 | Remark | reprgt 34612 reprinfz1 34613 reprlt 34610 |
| [Nathanson] p. 123 | Definition | df-repr 34600 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34632 |
| [Nathanson] p. 123 | Proposition | breprexp 34624 breprexpnat 34625 itgexpif 34597 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32033 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 47811 |
| [Pfenning] p. 17 | Definition XM | natded 30332 |
| [Pfenning] p. 17 | Definition NNC | natded 30332 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30332 |
| [Pfenning] p. 18 | Rule" | natded 30332 |
| [Pfenning] p. 18 | Definition /\I | natded 30332 |
| [Pfenning] p. 18 | Definition ` `E | natded 30332 natded 30332 natded 30332 natded 30332 natded 30332 |
| [Pfenning] p. 18 | Definition ` `I | natded 30332 natded 30332 natded 30332 natded 30332 natded 30332 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30332 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30332 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30332 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30332 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30332 |
| [Pfenning] p. 127 | Definition =E | natded 30332 |
| [Pfenning] p. 127 | Definition =I | natded 30332 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25102 df-dip 30630 dip0l 30647 ip0l 21545 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25143 ipval 30632 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30643 ipcj 21543 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25105 dipdir 30771 ipdir 21548 ipdiri 30759 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30639 nmsq 25094 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30754 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30756 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30757 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25111 dipass 30774 ipass 21554 ipassi 30770 |
| [Prugovecki] p. 186 | Definition of bra | braval 31873 df-bra 31779 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31780 kbval 31883 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32311 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 39882 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32325 atcvat4i 32326 cvrat3 39436 cvrat4 39437 lsatcvat3 39045 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32211 cvrval 39262 df-cv 32208 df-lcv 39012 lspsncv0 21056 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 39894 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 39895 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2708 rabid 3427 rabidd 45149 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2279 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2721 |
| [Quine] p. 19 | Definition 2.9 | conventions 30329 df-v 3449 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2867 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2864 abid2f 2922 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2276 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2086 sbalex 2243 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2803 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2729 eqid1 30396 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2736 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3754 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3755 dfsbcq2 3756 |
| [Quine] p. 43 | Theorem 6.8 | vex 3451 |
| [Quine] p. 43 | Theorem 6.9 | isset 3461 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3557 spcgv 3562 spcimgf 3516 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3766 spsbcd 3767 |
| [Quine] p. 44 | Theorem 6.12 | elex 3468 |
| [Quine] p. 44 | Theorem 6.13 | elab 3646 elabg 3643 elabgf 3641 |
| [Quine] p. 44 | Theorem 6.14 | noel 4301 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4681 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4592 df-sn 4590 |
| [Quine] p. 49 | Theorem 7.4 | snss 4749 snssg 4747 |
| [Quine] p. 49 | Theorem 7.5 | prss 4784 prssg 4783 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4726 prid1g 4724 prid2 4727 prid2g 4725 snid 4626 snidg 4624 |
| [Quine] p. 51 | Theorem 7.12 | snex 5391 |
| [Quine] p. 51 | Theorem 7.13 | prex 5392 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4890 unisnALT 44915 unisng 4889 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4894 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4901 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4899 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6478 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47087 dfiota2 6465 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47096 iotaval 6482 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6489 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6484 |
| [Quine] p. 58 | Definition 9.1 | df-op 4596 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5485 opabidw 5484 opelopab 5502 opelopaba 5496 opelopabaf 5504 opelopabf 5505 opelopabg 5498 opelopabga 5493 opelopabgf 5500 oprabid 7419 oprabidw 7418 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5644 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5646 |
| [Quine] p. 64 | Definition 9.15 | df-id 5533 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6581 |
| [Quine] p. 65 | Theorem 10.4 | funi 6548 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6569 funsng 6567 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6513 |
| [Quine] p. 65 | Definition 10.2 | args 6063 dffv4 6855 |
| [Quine] p. 68 | Definition 10.11 | conventions 30329 df-fv 6519 fv2 6853 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14237 nn0opth2i 14236 nn0opthi 14235 omopthi 8625 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8378 |
| [Quine] p. 232 | Equation i | carddom 10507 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6605 funimaexg 6603 |
| [Quine] p. 331 | Axiom system NF | ru 3751 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31013 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30630 polid 31088 polid2i 31086 polidi 31087 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30742 |
| [ReedSimon] p. 195 | Remark | lnophm 31948 lnophmi 31947 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32061 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32063 leopmuli 32062 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32066 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31781 leoppos 32055 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32065 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32054 |
| [Roman] p. 4 | Definition | df-dmat 22377 df-dmatalt 48387 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20062 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20144 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48474 |
| [Roman] p. 112 | Note | isldepslvec2 48474 ldepsnlinc 48497 zlmodzxznm 48486 |
| [Roman] p. 112 | Example | zlmodzxzequa 48485 zlmodzxzequap 48488 zlmodzxzldep 48493 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22777 |
| [Rosenlicht] p. 80 | Theorem | heicant 37649 |
| [Rosser] p. 281 | Definition | df-op 4596 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34636 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34637 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48354 pmtr3ncom 19405 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19401 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19344 cayleyth 19345 |
| [Rudin] p. 164 | Equation 27 | efcan 16062 |
| [Rudin] p. 164 | Equation 30 | efzval 16070 |
| [Rudin] p. 167 | Equation 48 | absefi 16164 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1771 |
| [Sanford] p. 39 | Rule 4 | mptxor 1769 |
| [Sanford] p. 40 | Rule 1 | mptnan 1768 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6088 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6091 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6085 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6083 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17547 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17548 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17548 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17550 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10090 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43051 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10399 axdc3 10407 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20146 isrngo 37891 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31471 |
| [Schechter] p. 276 | Definition of span | df-span 31238 spanval 31262 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22880 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6357 onelord 43240 ordelon 6356 ordelord 6354 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43241 sucidg 6415 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6387 onsuc 7787 ord0 6386 ordsuci 7784 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43242 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5218 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43017 elon2 6343 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6338 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5541 epelg 5539 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9550 epirron 43243 ordirr 6350 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43245 oneptr 43244 ontr1 6379 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6375 oneptri 43246 ordtri3or 6364 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8465 ord0eln0 6388 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6401 onsucss 43255 trsucss 6422 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7793 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6428 ordnbtwn 6427 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43257 ordnexbtwnsuc 43256 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10354 onsucf1lem 43258 onsucf1o 43261 onsucf1olem 43259 onsucrn 43260 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43262 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7821 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43251 ordne0gt0 43250 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43253 limnsuc 43254 onsucelab 43252 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9596 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7836 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9599 ordom 7852 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9600 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8604 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7756 ssorduni 7755 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8495 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9603 limom 7858 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8434 df1o2 8441 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8480 oa0suclim 43264 oalim 8496 oasuc 8488 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8481 om0suclim 43265 omlim 8497 omsuc 8490 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8486 oe0m1 8485 oe0suclim 43266 oelim 8498 oesuc 8491 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43218 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43268 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43269 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43270 limexissupab 43272 limiun 43271 limuni 6394 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8502 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8506 om1om1r 43273 om1r 8507 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8499 oaomoecl 43267 oecl 8501 omcl 8500 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43220 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8508 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8509 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43274 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43275 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8575 nnamecl 43276 nnecl 8577 nnmcl 8576 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43277 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8516 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8517 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8524 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43279 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43280 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43282 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8523 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43286 omword1 8537 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43285 oaordnrex 43284 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43281 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43287 omword2 8538 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43288 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43289 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43290 omordi 8530 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8532 omord2com 43291 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43292 df-2o 8435 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43295 oewordi 8555 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43296 oeworde 8557 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43297 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43298 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43294 omnord1ex 43293 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43299 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43301 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43305 oenord1ex 43304 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43306 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8525 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43300 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8543 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8544 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43308 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8561 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43309 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43310 cantnfub2 43311 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43314 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28841 axtgcgrrflx 28389 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28842 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28843 axtgcgrid 28390 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28375 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28854 axtgsegcon 28391 df-trkgcb 28377 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 28865 axtg5seg 28392 df-trkgcb 28377 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 28866 axtgbtwnid 28393 df-trkgb 28376 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 28868 axtgpasch 28394 df-trkgb 28376 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 28887 df-trkg2d 34656 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28397 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28398 df-trkg2d 34656 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 28890 axtgeucl 28399 df-trkge 28378 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 28903 axtgcont 28396 axtgcont1 28395 df-trkgb 28376 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 35975 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 35977 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 35980 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 35984 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 35985 tgcgrcomimp 28404 tgcgrcoml 28406 tgcgrcomr 28405 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 35990 tgcgrtriv 28411 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 35994 tg5segofs 34664 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34661 df-ofs 35971 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 35996 tgcgrextend 28412 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 35998 tgsegconeq 28413 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36010 btwntriv2 36000 tgbtwntriv2 28414 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36001 tgbtwncom 28415 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36004 tgbtwntriv1 28418 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36005 tgbtwnswapid 28419 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36011 btwnintr 36007 tgbtwnexch2 28423 tgbtwnintr 28420 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36013 btwnexch3 36008 tgbtwnexch 28425 tgbtwnexch3 28421 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36012 tgbtwnouttr 28424 tgbtwnouttr2 28422 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 28886 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36015 tgbtwndiff 28433 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28426 trisegint 36016 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36032 tgifscgr 28435 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28485 colrot1 28486 colrot2 28487 lncom 28549 lnrot1 28550 lnrot2 28551 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36028 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36033 tgcgrsub 28436 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36043 tgcgrxfr 28445 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28444 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36029 df-cgrg 28438 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28438 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36044 tgbtwnxfr 28457 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36050 colinearperm2 36052 colinearperm3 36051 colinearperm4 36053 colinearperm5 36054 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28460 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36027 tgellng 28480 tglng 28473 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36055 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36063 lnxfr 28493 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36064 lnext 28494 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36068 tgfscgr 28495 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36069 lncgr 28496 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36030 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36071 lnid 28497 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36072 tgidinside 28498 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36089 tgbtwnconn1 28502 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36090 tgbtwnconn2 28503 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36091 tgbtwnconn3 28504 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36097 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36095 legov 28512 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28513 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28526 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36098 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36100 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36102 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36103 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36104 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36101 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36106 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28514 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28516 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28517 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28518 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28519 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36113 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36114 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36109 df-outsideof 36108 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36110 ishlg 28529 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28534 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28536 outsideofrflx 36115 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28530 hlcomd 28531 outsideofcom 36116 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28537 outsideoftr 36117 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28545 outsideofeu 36119 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36126 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36127 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36120 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36135 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36136 tglineelsb2 28559 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36138 linerflx1 36137 linerflx2 36139 tglinecom 28562 tglinerflx1 28560 tglinerflx2 28561 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36141 tglinethru 28563 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36125 tglng 28473 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28521 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36144 tglinethrueu 28566 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36145 tglineineq 28570 tglineinteq 28572 tglineintmo 28569 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28576 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28577 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28578 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28593 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28589 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28581 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28580 ismir 28586 mirbtwn 28585 mircgr 28584 mirfv 28583 mirval 28582 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28591 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28592 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28593 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28596 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28597 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28602 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28599 mirbtwni 28598 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28600 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28612 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28616 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28613 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28614 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28615 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28618 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28619 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28625 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28621 israg 28624 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28626 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28627 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28629 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28630 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28631 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28632 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28633 ragncol 28636 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28634 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28640 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28644 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28641 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28623 isperp 28639 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28642 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28649 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28657 colperpexlem2 28658 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28660 colperpexlem3 28659 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28665 midex 28664 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28662 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28671 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28666 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28675 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28678 opphllem6 28679 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28681 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28394 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28682 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28690 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28685 hpgbr 28687 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28692 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28691 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28693 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28694 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28695 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28696 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28697 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28711 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28701 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28715 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28716 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28717 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28718 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28719 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28722 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28724 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28702 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28725 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28728 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28729 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28730 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28731 trgcopyeu 28733 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28757 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28736 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28745 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28743 cgrahl2 28744 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28746 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28747 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28749 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28750 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28753 cgrahl 28754 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28758 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28759 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28760 acopyeu 28761 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28768 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28772 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28765 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28780 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28773 isleag 28774 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28782 tgsas1 28781 tgsas2 28783 tgsas3 28784 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28786 tgasa1 28785 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28787 tgsss2 28788 tgsss3 28789 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27182 dchrsum 27180 dchrsum2 27179 sumdchr 27183 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27184 sum2dchr 27185 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19998 ablfacrp2 19999 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27127 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27128 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27135 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27393 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27396 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27450 vmalogdivsum2 27449 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27440 dirith2 27439 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27438 rpvmasum 27437 rpvmasum2 27423 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27398 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27436 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27403 dchrisumlem1 27400 dchrisumlem2 27401 dchrisumlem3 27402 dchrisumlema 27399 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27406 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27435 dchrmusumlem 27433 dchrvmasumlem 27434 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27405 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27407 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27431 dchrisum0re 27424 dchrisumn0 27432 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27417 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27421 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27422 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27477 pntrsumbnd2 27478 pntrsumo1 27476 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27441 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27443 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27445 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27448 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27453 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27454 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27459 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27461 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27462 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27470 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27471 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27468 selberg3lem2 27469 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27472 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27466 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27479 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27480 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27481 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27495 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27507 pntlemb 27508 pntlemc 27506 pntlemd 27505 pntlemg 27509 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27507 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27499 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27504 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27507 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27520 pntleml 27522 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33733 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33720 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33752 constrinvcl 33763 constrmulcl 33761 constrnegcl 33753 constrsqrtcl 33769 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33739 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33749 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33771 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33781 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4269 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4368 dif0 4341 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4455 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4438 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4260 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4261 |
| [Stoll] p. 20 | Remark | invdif 4242 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4598 |
| [Stoll] p. 43 | Definition | uniiun 5022 |
| [Stoll] p. 44 | Definition | intiin 5023 |
| [Stoll] p. 45 | Definition | df-iin 4958 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4957 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4269 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44324 |
| [Suppes] p. 22 | Theorem 2 | eq0 4313 eq0f 4310 |
| [Suppes] p. 22 | Theorem 4 | eqss 3962 eqssd 3964 eqssi 3963 |
| [Suppes] p. 23 | Theorem 5 | ss0 4365 ss0b 4364 |
| [Suppes] p. 23 | Theorem 6 | sstr 3955 sstrALT2 44824 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4066 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4067 |
| [Suppes] p. 23 | Theorem 9 | psstr 4070 |
| [Suppes] p. 23 | Theorem 10 | pssss 4061 |
| [Suppes] p. 25 | Theorem 12 | elin 3930 elun 4116 |
| [Suppes] p. 26 | Theorem 15 | inidm 4190 |
| [Suppes] p. 26 | Theorem 16 | in0 4358 |
| [Suppes] p. 27 | Theorem 23 | unidm 4120 |
| [Suppes] p. 27 | Theorem 24 | un0 4357 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4141 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4149 |
| [Suppes] p. 27 | Theorem 27 | unss 4153 |
| [Suppes] p. 27 | Theorem 28 | indir 4249 |
| [Suppes] p. 27 | Theorem 29 | undir 4250 |
| [Suppes] p. 28 | Theorem 32 | difid 4339 |
| [Suppes] p. 29 | Theorem 33 | difin 4235 |
| [Suppes] p. 29 | Theorem 34 | indif 4243 |
| [Suppes] p. 29 | Theorem 35 | undif1 4439 |
| [Suppes] p. 29 | Theorem 36 | difun2 4444 |
| [Suppes] p. 29 | Theorem 37 | difin0 4437 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4435 |
| [Suppes] p. 29 | Theorem 39 | difundi 4253 |
| [Suppes] p. 29 | Theorem 40 | difindi 4255 |
| [Suppes] p. 30 | Theorem 41 | nalset 5268 |
| [Suppes] p. 39 | Theorem 61 | uniss 4879 |
| [Suppes] p. 39 | Theorem 65 | uniop 5475 |
| [Suppes] p. 41 | Theorem 70 | intsn 4948 |
| [Suppes] p. 42 | Theorem 71 | intpr 4946 intprg 4945 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5431 |
| [Suppes] p. 42 | Theorem 78 | intun 4944 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4997 dfiun2g 4994 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4998 |
| [Suppes] p. 47 | Theorem 86 | elpw 4567 elpw2 5289 elpw2g 5288 elpwg 4566 elpwgdedVD 44906 |
| [Suppes] p. 47 | Theorem 87 | pwid 4585 |
| [Suppes] p. 47 | Theorem 89 | pw0 4776 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4777 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5653 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5797 xpindir 5798 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5707 xpundir 5708 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9549 |
| [Suppes] p. 58 | Theorem 2 | relss 5744 |
| [Suppes] p. 59 | Theorem 4 | eldm 5864 eldm2 5865 eldm2g 5863 eldmg 5862 |
| [Suppes] p. 59 | Definition 3 | df-dm 5648 |
| [Suppes] p. 60 | Theorem 6 | dmin 5875 |
| [Suppes] p. 60 | Theorem 8 | rnun 6118 |
| [Suppes] p. 60 | Theorem 9 | rnin 6119 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5852 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5846 brcnvg 5843 |
| [Suppes] p. 62 | Equation 5 | elcnv 5840 elcnv2 5841 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6075 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6117 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6115 |
| [Suppes] p. 63 | Definition | dftrrels2 38566 |
| [Suppes] p. 63 | Theorem 20 | co02 6233 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5938 |
| [Suppes] p. 63 | Definition 7 | df-co 5647 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5849 |
| [Suppes] p. 64 | Theorem 27 | coass 6238 |
| [Suppes] p. 65 | Theorem 31 | resundi 5964 |
| [Suppes] p. 65 | Theorem 34 | elima 6036 elima2 6037 elima3 6038 elimag 6035 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6122 |
| [Suppes] p. 66 | Theorem 40 | dminss 6126 |
| [Suppes] p. 66 | Theorem 41 | imainss 6127 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6130 |
| [Suppes] p. 81 | Definition 34 | dfec2 8674 |
| [Suppes] p. 82 | Theorem 72 | elec 8717 elecALTV 38255 elecg 8715 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 38602 erth 8725 erth2 8726 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 38605 erdisj 8728 |
| [Suppes] p. 83 | Definition 35, | df-parts 38757 dfmembpart2 38762 |
| [Suppes] p. 89 | Theorem 96 | map0b 8856 |
| [Suppes] p. 89 | Theorem 97 | map0 8860 map0g 8857 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8861 mapsnd 8859 |
| [Suppes] p. 89 | Theorem 99 | mapss 8862 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10021 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10020 |
| [Suppes] p. 92 | Theorem 1 | enref 8956 enrefg 8955 |
| [Suppes] p. 92 | Theorem 2 | ensym 8974 ensymb 8973 ensymi 8975 |
| [Suppes] p. 92 | Theorem 3 | entr 8977 |
| [Suppes] p. 92 | Theorem 4 | unen 9017 |
| [Suppes] p. 94 | Theorem 15 | endom 8950 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8971 |
| [Suppes] p. 94 | Theorem 17 | domtr 8978 |
| [Suppes] p. 95 | Theorem 18 | sbth 9061 |
| [Suppes] p. 97 | Theorem 23 | canth2 9094 canth2g 9095 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9065 df-sdom 8921 dfsdom2 9064 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9078 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9067 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9066 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9076 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8953 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9079 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9074 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9002 fundmeng 9003 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9039 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9075 |
| [Suppes] p. 104 | Theorem 37 | fofi 9262 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9268 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9268 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10504 |
| [Suppes] p. 130 | Definition 3 | df-tr 5215 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7756 |
| [Suppes] p. 134 | Definition 6 | df-suc 6338 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7876 finds 7872 finds1 7875 finds2 7874 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9605 isfinite2 9245 isfiniteg 9248 unbnn 9243 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10871 df-ltpq 10863 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7839 tfinds 7836 tfinds2 7840 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8515 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8517 |
| [Suppes] p. 211 | Theorem 25 | oaass 8525 |
| [Suppes] p. 225 | Definition 8 | iscard2 9929 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10516 |
| [Suppes] p. 228 | Theorem 59 | harcard 9931 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10019 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6384 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7769 onminsb 7770 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10525 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10023 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10030 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10024 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9893 |
| [Suppes] p. 242 | Theorem 6 | weth 10448 |
| [Suppes] p. 242 | Theorem 8 | entric 10510 |
| [Suppes] p. 242 | Theorem 9 | carden 10504 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35683 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35687 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2701 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2721 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2803 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2723 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2749 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7391 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3751 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5376 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4614 elpr2 4616 elpr2g 4615 elprg 4612 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4604 elsn2 4629 elsn2g 4628 elsng 4603 velsn 4605 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5427 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4599 sneqr 4804 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4610 dfsn2 4602 dfsn2ALT 4611 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7717 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5436 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5424 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5408 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7720 unexg 7719 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4655 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4872 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3921 df-un 3919 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4888 uniprg 4887 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5332 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4653 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6404 elsucg 6402 sstr2 3953 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4121 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4172 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4135 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4191 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4247 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4248 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3934 df-ss 3931 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4565 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4150 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3932 sseqin2 4186 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3969 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4200 inss2 4201 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4011 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4882 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5409 sspwimp 44907 sspwimpALT 44914 sspwimpALT2 44917 sspwimpcf 44909 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5416 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5234 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3406 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5262 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3917 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4299 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4339 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4316 n0f 4312 neq0 4315 neq0f 4311 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9548 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9685 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9687 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3449 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5270 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4363 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5276 ssexg 5278 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5272 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9555 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9550 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4329 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4098 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4263 undif3VD 44871 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4099 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4106 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3045 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3054 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7729 xpexg 7726 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5645 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6587 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6765 fun11 6590 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6527 svrelfun 6588 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5851 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5853 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5650 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5651 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5647 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6167 dfrel2 6162 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5654 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5774 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5781 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5795 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5976 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5956 opelresi 5958 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5983 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5972 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5977 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6558 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6079 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6556 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6767 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2602 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30329 df-fv 6519 fv3 6876 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7901 cnvexg 7900 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7885 dmexg 7877 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7886 rnexg 7878 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44443 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7896 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6871 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47175 tz6.12-1-afv2 47242 tz6.12-1 6881 tz6.12-afv 47174 tz6.12-afv2 47241 tz6.12 6883 tz6.12c-afv2 47243 tz6.12c 6880 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47238 tz6.12-2 6846 tz6.12i-afv2 47244 tz6.12i 6886 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6514 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6515 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6517 wfo 6509 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6516 wf1 6508 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6518 wf1o 6510 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7003 eqfnfv2 7004 eqfnfv2f 7007 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6959 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7191 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7189 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6605 funimaexg 6603 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5108 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5547 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5599 dffr3 6070 eliniseg 6065 iniseg 6068 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5538 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5615 fr3nr 7748 frirr 5614 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5591 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7750 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5602 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5624 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6320 tz6.26i 6321 wefrc 5632 wereu2 5635 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6322 wfii 6323 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6520 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7304 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7305 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7311 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7312 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7313 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7317 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7324 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7326 |
| [TakeutiZaring] p. 35 | Notation | wtr 5214 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44444 tz7.2 5621 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5220 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6345 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6353 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6354 ordelordALT 44527 ordelordALTVD 44856 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6360 ordelssne 6359 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6358 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6362 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7758 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7759 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6336 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6364 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44539 ordon 7753 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7754 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7829 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6380 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5216 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7768 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7806 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6438 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6437 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7755 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4901 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6338 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6414 sucidg 6415 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7787 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6428 ordnbtwn 6427 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7803 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6337 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7857 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7862 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7817 ordelsuc 7795 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7797 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7827 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7844 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7865 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7866 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7867 |
| [TakeutiZaring] p. 43 | Remark | omon 7854 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9588 omex 9596 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7852 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7871 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7868 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7869 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7847 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4926 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5233 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4927 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5299 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7771 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6383 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4911 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9613 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7766 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8344 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8365 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8366 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8367 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8374 tz7.44-2 8375 tz7.44-3 8376 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8336 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8331 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8315 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8413 tz7.49c 8414 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8411 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8410 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8412 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2649 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9964 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9965 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8496 oasuc 8488 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7837 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8499 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8480 oa0r 8502 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8500 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8512 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8583 nnaordi 8582 oaord 8511 oaordi 8510 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5013 uniss2 4905 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8514 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8519 oawordex 8521 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8575 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8612 |
| [TakeutiZaring] p. 60 | Remark | oancom 9604 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8524 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8580 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8516 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8483 omlim 8497 omsuc 8490 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8481 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8577 nnmcl 8576 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8596 nnmordi 8595 omord 8532 omordi 8530 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8533 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8600 omwordri 8536 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8503 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8506 om1r 8507 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8539 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8541 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8542 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8543 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8544 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8572 oe0 8486 oelim 8498 oesuc 8491 onesuc 8494 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8484 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8550 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8551 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8485 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8509 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8552 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8558 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8556 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8557 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8561 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8563 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9681 tz9.1 9682 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9717 r10 9721 r1lim 9725 r1limg 9724 r1suc 9723 r1sucg 9722 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9733 r1ord2 9734 r1ordg 9731 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9743 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9768 tz9.13 9744 tz9.13g 9745 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9718 rankval 9769 rankvalb 9750 rankvalg 9770 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9792 rankelb 9777 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9806 rankval3 9793 rankval3b 9779 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9782 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9748 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9787 rankr1c 9774 rankr1g 9785 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9788 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9802 rankssb 9801 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9795 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9794 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10428 dfac3 10074 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9983 numth 10425 numth2 10424 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10499 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10500 cardid2 9906 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9913 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10504 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9912 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9897 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9918 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9910 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9114 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8989 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9119 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9043 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9916 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10051 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9170 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9178 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10052 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9175 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10041 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10019 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9925 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10169 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9273 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8922 isfi 8947 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9179 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10487 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9036 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10479 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10139 unxpdom 9200 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9927 cardsdomelir 9926 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9202 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9967 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8801 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10515 infxpidm2 9970 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10160 infxp 10167 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9048 pw2f1o 9046 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9107 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10440 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10435 ac6s5 10444 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10496 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10497 uniimadomf 10498 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10227 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10222 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10207 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10204 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10210 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10217 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10226 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10535 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10205 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10229 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10050 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10049 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10061 alephfp2 10062 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10652 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10065 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10522 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10536 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10537 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 38876 |
| [Tarski] p. 67 | Scheme B5 | sp 2184 |
| [Tarski] p. 68 | Lemma 6 | avril1 30392 equid 2012 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2017 |
| [Tarski] p. 70 | Lemma 14 | spim 2385 spime 2387 spimew 1971 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2178 ax-c15 38882 ax12i 1966 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2086 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1968 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1910 ax5ALT 38900 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2008 ax-8 2111 ax-9 2119 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28391 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28392 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28394 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28394 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28395 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16211 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37653 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37655 |
| [Weierstrass] p. 272 | Definition | df-mdet 22472 mdetuni 22509 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 903 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 868 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 919 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 969 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37433 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 43789 imim2 58 wl-luk-imim2 37428 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47020 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 896 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2656 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 902 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37431 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 894 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 44916 wl-luk-notnotr 37432 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 43819 axfrege28 43818 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 924 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37425 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 889 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 941 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30330 pm2.27 42 wl-luk-pm2.27 37423 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 922 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38345 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 923 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 971 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 970 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1087 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 944 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 881 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 851 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 888 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 890 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 942 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 891 pm2.67 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 898 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 900 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 802 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 807 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 962 pm3.44 961 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 965 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 806 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 832 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 805 bitr 804 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 904 pm4.25 905 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1009 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 870 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 921 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 633 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 917 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 637 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 978 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1088 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1007 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1053 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1024 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 998 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1000 pm4.45 999 pm4.45im 827 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 853 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 985 pm4.56 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 991 pm4.57 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 856 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 849 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 951 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 936 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 963 pm4.77 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 934 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1005 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1025 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 843 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 823 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 946 pm5.11g 945 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 947 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 949 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 948 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1013 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 824 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 901 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 955 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 830 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 835 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 825 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1006 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1019 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 950 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1002 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1029 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1030 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44347 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44348 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1870 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44349 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44350 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44351 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1893 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44352 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44353 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44354 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44355 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44356 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44358 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44359 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44360 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44357 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2091 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44363 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44364 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2071 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2161 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1829 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1830 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44365 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44366 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44367 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44368 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44370 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44369 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1887 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44372 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44373 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44371 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1828 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44374 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44375 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1846 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44376 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2344 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1860 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44381 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44377 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44378 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44379 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44380 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44385 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44382 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44383 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44384 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44386 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2562 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44396 pm13.13b 44397 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44398 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3006 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3007 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3632 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44404 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44405 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44399 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44542 pm13.193 44400 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44401 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44402 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44403 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44410 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44409 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44408 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3816 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44411 pm14.122b 44412 pm14.122c 44413 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44414 pm14.123b 44415 pm14.123c 44416 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44418 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44417 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44419 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6492 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44420 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6493 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44421 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44423 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2626 eupickbi 2629 sbaniota 44424 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44422 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2577 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44426 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30329 df-fv 6519 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9954 pm54.43lem 9953 |
| [Young] p. 141 | Definition of operator ordering | leop2 32053 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32059 idleop 32060 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 42816 |
| [vandenDries] p. 43 | Theorem 62 | pellex 42823 pellexlem1 42817 |