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 17634 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17634 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18043 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17655 0funcg 49554 df-termc 49942 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50019 prsthinc 49933 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50047 df-mndtc 50047 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50043 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17678 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50035 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50060 oppgoppchom 50059 oppgoppcid 50061 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17748 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17736 invisoinvl 17757 |
| [Adamek] p. 28 | Example 3.13 | idinv 17756 idiso 17755 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17741 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17715 df-iso 17716 dfiso2 17739 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17722 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17773 cicerALT 49515 |
| [Adamek] p. 29 | Definition 3.15 | cic 17766 df-cic 17763 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17825 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17737 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17738 isoco 17744 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17825 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17848 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49773 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17841 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50043 discthing 49930 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49887 prsthinc 49933 thincciso 49922 thincciso2 49924 thincciso3 49925 thinccisod 49923 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50047 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17855 cofucla 49565 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49631 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18078 catcisoi 49869 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18133 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17874 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17873 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18133 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17898 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17904 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17903 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18118 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18118 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49601 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49592 funcoppc 17842 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18066 elcatchom 49866 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17892 fthoppf 49633 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17891 fulloppf 49632 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18075 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49554 df-catc 18066 |
| [Adamek] p. 45 | Exercise 3G | incat 50070 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50073 nelsubc3 49540 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49620 imasubc2 49621 imasubc3 49625 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17805 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17806 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49540 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17817 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17779 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49629 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49628 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49630 ressffth 17907 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50071 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17913 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17934 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17938 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17914 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17940 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49554 df-inito 17951 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49554 df-termc 49942 initc 49560 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21459 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17952 oppctermo 49705 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17979 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17983 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49706 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17953 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21460 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17986 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17714 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 49938 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 49937 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 49902 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17749 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17751 |
| [Adamek] p. 185 | Section 10.67 | updjud 9858 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50114 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50114 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50114 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50115 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50115 |
| [Adamek] p. 478 | Item Rng | df-ringc 20623 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49018 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49040 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14533 df-pfx 14634 df-substr 14604 df-word 14476 lencl 14495 wrd0 14501 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24673 df-nmoo 30816 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32224 hmopidmchi 32222 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32272 pjcmul2i 32273 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 31989 unoplin 31991 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 31990 unopadj2 32009 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32084 lnopunii 32083 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32157 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27919 |
| [Alling] p. 184 | Axiom B | bdayfo 27641 |
| [Alling] p. 184 | Axiom O | ltsso 27640 |
| [Alling] p. 184 | Axiom SD | nodense 27656 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27747 |
| [Alling] p. 185 | Theorem | conway 27771 |
| [Alling] p. 185 | Axiom FE | noeta 27707 |
| [Alling] p. 186 | Theorem 4 | lesrec 27791 lesrecd 27792 |
| [Alling], p. 2 | Definition | rp-brsslt 43850 |
| [Alling], p. 3 | Note | nla0001 43853 nla0002 43851 nla0003 43852 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11330 addcan2d 11350 addcan2i 11340 addcand 11349 addcani 11339 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11383 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11442 negsubd 11511 negsubi 11472 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11444 negnegd 11496 negnegi 11464 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11583 subdid 11606 subdii 11599 subdir 11584 subdird 11607 subdiri 11600 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11325 mul01d 11345 mul01i 11336 mul02 11324 mul02d 11344 mul02i 11335 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11787 mulcan2d 11784 mulcand 11783 mulcani 11789 |
| [Apostol] p. 18 | Theorem I.8 | receu 11795 xreceu 32981 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11825 divrecd 11934 divreci 11900 divreczi 11893 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11852 recreci 11887 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11790 mul0ord 11798 mul0ori 11797 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11589 mul2negd 11605 mul2negi 11598 mulneg1 11586 mulneg1d 11603 mulneg1i 11596 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11870 divadddivd 11975 divadddivi 11917 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11855 divmuldivd 11972 divmuldivi 11915 rdivmuldivd 20393 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11856 divdivdivd 11978 divdivdivi 11918 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12966 rpaddcld 13001 rpmulcl 12967 rpmulcld 13002 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12976 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12979 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11272 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11743 ltadd1dd 11761 ltadd1i 11704 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12005 ltmul1a 12004 ltmul1i 12074 ltmul1ii 12084 ltmul2 12006 ltmul2d 13028 ltmul2dd 13042 ltmul2i 12077 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11670 msqgt0d 11717 msqgt0i 11687 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11672 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11656 lt0neg1d 11719 ltneg 11650 ltnegd 11728 ltnegi 11694 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11635 lt2addd 11773 lt2addi 11712 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12943 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12001 recgt0d 12090 recgt0i 12061 recgt0ii 12062 |
| [Apostol] p. 22 | Definition of integers | df-z 12525 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12188 |
| [Apostol] p. 22 | Definition of rationals | df-q 12899 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9367 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12433 |
| [Apostol] p. 26 | Theorem I.29 | arch 12434 archd 45592 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12632 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12435 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12897 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12896 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13151 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16308 zneo 12612 zneoALTV 48139 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26694 msqsqrtd 15405 resqrtth 15217 sqrtth 15327 sqrtthi 15333 sqsqrtd 15404 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12177 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12863 |
| [Apostol] p. 361 | Remark | crreczi 14190 |
| [Apostol] p. 363 | Remark | absgt0i 15362 |
| [Apostol] p. 363 | Example | abssubd 15418 abssubi 15366 |
| [ApostolNT] p. 7 | Remark | fmtno0 47997 fmtno1 47998 fmtno2 48007 fmtno3 48008 fmtno4 48009 fmtno5fac 48039 fmtnofz04prm 48034 |
| [ApostolNT] p. 7 | Definition | df-fmtno 47985 |
| [ApostolNT] p. 8 | Definition | df-ppi 27063 |
| [ApostolNT] p. 14 | Definition | df-dvds 16222 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16238 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16263 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16258 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16251 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16253 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16239 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16240 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16245 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16280 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16282 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16284 |
| [ApostolNT] p. 15 | Definition | df-gcd 16464 dfgcd2 16515 |
| [ApostolNT] p. 16 | Definition | isprm2 16651 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16622 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16886 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16482 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16516 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16518 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16497 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16489 |
| [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 16372 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16556 |
| [ApostolNT] p. 24 | Definition | df-mu 27064 |
| [ApostolNT] p. 25 | Definition | df-phi 16736 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27154 |
| [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 27061 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27156 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27179 |
| [ApostolNT] p. 38 | Remark | df-sgm 27065 |
| [ApostolNT] p. 38 | Definition | df-sgm 27065 |
| [ApostolNT] p. 75 | Definition | df-chp 27062 df-cht 27060 |
| [ApostolNT] p. 104 | Definition | congr 16633 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16225 |
| [ApostolNT] p. 106 | Definition | moddvds 16232 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16315 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16316 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13847 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13887 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14200 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16257 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16636 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17045 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16638 |
| [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 27035 |
| [ApostolNT] p. 179 | Definition | df-lgs 27258 lgsprme0 27302 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27303 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27279 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27294 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27351 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27370 2lgsoddprm 27379 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27337 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27346 |
| [ApostolNT] p. 188 | Definition | df-lgs 27258 lgs1 27304 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27295 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27297 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27305 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27306 |
| [Baer] p. 40 | Property (b) | mapdord 42084 |
| [Baer] p. 40 | Property (c) | mapd11 42085 |
| [Baer] p. 40 | Property (e) | mapdin 42108 mapdlsm 42110 |
| [Baer] p. 40 | Property (f) | mapd0 42111 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42071 mapd1o 42094 |
| [Baer] p. 41 | Property (g) | mapdat 42113 |
| [Baer] p. 44 | Part (1) | mapdpg 42152 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42247 mapdheq 42174 mapdheq2 42175 mapdheq2biN 42176 |
| [Baer] p. 45 | Part (3) | baerlem3 42159 |
| [Baer] p. 46 | Part (4) | mapdheq4 42178 mapdheq4lem 42177 |
| [Baer] p. 46 | Part (5) | baerlem5a 42160 baerlem5abmN 42164 baerlem5amN 42162 baerlem5b 42161 baerlem5bmN 42163 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42267 hdmap1l6a 42255 hdmap1l6e 42260 hdmap1l6f 42261 hdmap1l6g 42262 hdmap1l6lem1 42253 hdmap1l6lem2 42254 mapdh6N 42193 mapdh6aN 42181 mapdh6eN 42186 mapdh6fN 42187 mapdh6gN 42188 mapdh6lem1N 42179 mapdh6lem2N 42180 |
| [Baer] p. 48 | Part 9 | hdmapval 42274 |
| [Baer] p. 48 | Part 10 | hdmap10 42286 |
| [Baer] p. 48 | Part 11 | hdmapadd 42289 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42263 mapdh6hN 42189 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42199 mapdh75d 42200 mapdh75e 42198 mapdh75fN 42201 mapdh7cN 42195 mapdh7dN 42196 mapdh7eN 42194 mapdh7fN 42197 |
| [Baer] p. 48 | Part (8) | mapdh8 42234 mapdh8a 42221 mapdh8aa 42222 mapdh8ab 42223 mapdh8ac 42224 mapdh8ad 42225 mapdh8b 42226 mapdh8c 42227 mapdh8d 42229 mapdh8d0N 42228 mapdh8e 42230 mapdh8g 42231 mapdh8i 42232 mapdh8j 42233 |
| [Baer] p. 48 | Part (9) | mapdh9a 42235 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42215 |
| [Baer] p. 49 | Part 12 | hdmap11 42294 hdmapeq0 42290 hdmapf1oN 42311 hdmapneg 42292 hdmaprnN 42310 hdmaprnlem1N 42295 hdmaprnlem3N 42296 hdmaprnlem3uN 42297 hdmaprnlem4N 42299 hdmaprnlem6N 42300 hdmaprnlem7N 42301 hdmaprnlem8N 42302 hdmaprnlem9N 42303 hdmapsub 42293 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42314 hdmap14lem10 42323 hdmap14lem1a 42312 hdmap14lem2N 42315 hdmap14lem2a 42313 hdmap14lem3 42316 hdmap14lem8 42321 hdmap14lem9 42322 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42324 hdmap14lem12 42325 hdmap14lem13 42326 hdmap14lem14 42327 hdmap14lem15 42328 hgmapval 42333 |
| [Baer] p. 50 | Part 15 | hgmapadd 42340 hgmapmul 42341 hgmaprnlem2N 42343 hgmapvs 42337 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42347 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42363 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42364 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42365 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42366 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42368 hgmapvv 42372 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42367 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42369 |
| [Baer] p. 111 | Line 15 | hdmapg 42376 hdmapglem7 42375 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26695 2irrexpqALT 26764 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2570 |
| [BellMachover] p. 460 | Notation | df-mo 2540 |
| [BellMachover] p. 460 | Definition | mo3 2565 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2709 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2713 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5221 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5232 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37371 sepex 5236 |
| [BellMachover] p. 466 | Problem | axpow2 5310 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5311 |
| [BellMachover] p. 466 | Axiom Union | axun2 7691 |
| [BellMachover] p. 468 | Definition | df-ord 6327 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6342 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6349 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6344 |
| [BellMachover] p. 471 | Definition of N | df-om 7818 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7755 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6329 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9563 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7833 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9688 |
| [BellMachover] p. 478 | Definition | rankval2 9742 rankval2b 35242 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9706 r1ord3g 9703 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9511 |
| [BellMachover] p. 488 | Axiom AC | ac5 10399 dfac4 10044 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10032 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39765 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32424 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32466 chirredi 32465 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32454 |
| [Beran] p. 3 | Definition of join | sshjval3 31425 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31687 cmcm2i 31664 cmcm2ii 31669 cmt2N 39696 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31688 lecmi 31673 lecmii 31674 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31662 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31691 cm2ji 31696 cm2mi 31697 |
| [Beran] p. 95 | Definition | df-sh 31278 issh2 31280 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31157 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31170 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31161 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31899 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31901 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31900 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31902 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31153 his1i 31171 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31154 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31155 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31156 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31039 dfhnorm2 31193 normval 31195 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31255 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31044 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31312 |
| [Beran] p. 96 | Definition of converge | df-hlim 31043 hlimi 31259 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31204 norm-i 31200 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31208 norm-ii 31209 normlem0 31180 normlem1 31181 normlem2 31182 normlem3 31183 normlem4 31184 normlem5 31185 normlem6 31186 normlem7 31187 normlem7tALT 31190 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31210 norm-iii 31211 |
| [Beran] p. 98 | Remark 3.4 | bcs 31252 bcsiALT 31250 bcsiHIL 31251 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31192 normpar 31226 normpari 31225 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31217 normpyth 31216 normpythi 31213 |
| [Beran] p. 99 | Remark | lnfn0 32118 lnfn0i 32113 lnop0 32037 lnop0i 32041 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32097 nmcfnex 32124 nmcfnexi 32122 nmcopex 32100 nmcopexi 32098 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32125 nmcfnlbi 32123 nmcoplb 32101 nmcoplbi 32099 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32127 lnfnconi 32126 lnopcon 32106 lnopconi 32105 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31227 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31224 norm3adifii 31219 norm3dif 31221 norm3difi 31218 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31372 pjhth 31464 pjhtheu 31465 pjpjhth 31496 pjpjhthi 31497 pjth 25406 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31477 ococi 31476 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32132 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32133 riesz4 32135 riesz4i 32134 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32150 cnlnadjeu 32149 cnlnadjeui 32148 cnlnadji 32147 cnlnadjlem1 32138 nmopadjlei 32159 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32162 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32161 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32163 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32007 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32173 nmopcoadji 32172 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32164 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32174 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32171 pjadj2coi 32275 pjadjcoi 32232 |
| [Beran] p. 107 | Definition | df-ch 31292 isch2 31294 |
| [Beran] p. 107 | Remark 3.12 | choccl 31377 isch3 31312 occl 31375 ocsh 31354 shoccl 31376 shocsh 31355 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31479 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31403 |
| [Beran] p. 109 | Property (i) | pjadj2 32258 pjadj3 32259 pjadji 31756 pjadjii 31745 |
| [Beran] p. 109 | Property (ii) | pjidmco 32252 pjidmcoi 32248 pjidmi 31744 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32244 |
| [Beran] p. 111 | Remark | ho0val 31821 pjch1 31741 |
| [Beran] p. 111 | Definition | df-hfmul 31805 df-hfsum 31804 df-hodif 31803 df-homul 31802 df-hosum 31801 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31742 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31765 pjchi 31503 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31510 pjoc2i 31509 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31751 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32236 pjssmii 31752 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32235 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32234 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32239 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32237 pjssge0ii 31753 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32238 pjdifnormii 31754 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1778 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1776 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1779 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1774 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34436 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34444 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34442 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34446 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34466 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34497 df-sitm 34475 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34497 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34474 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29117 isuhgrop 29139 isusgrop 29231 isuspgrop 29230 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48331 df-subgr 29337 uhgrspan1 29372 uhgrspansubgr 29360 |
| [Bollobas] p. 3 | Definition | df-gric 48351 gricuspgr 48388 isuspgrim 48366 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29523 df-clnbgr 48289 df-cusgr 29481 df-nbgr 29402 fusgrmaxsize 29533 |
| [Bollobas] p. 4 | Definition | df-upwlks 48604 df-wlks 29668 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29619 finsumvtxdgeven 29621 fusgr1th 29620 fusgrvtxdgonume 29623 vtxdgoddnumeven 29622 |
| [Bollobas] p. 5 | Notation | df-pths 29782 |
| [Bollobas] p. 5 | Definition | df-crcts 29854 df-cycls 29855 df-trls 29759 df-wlkson 29669 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29128 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48670 df-cllaw 48656 df-mgm 18608 df-mgm2 48689 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48671 df-asslaw 48658 df-sgrp 18687 df-sgrp2 48691 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48690 df-comlaw 48657 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18703 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33086 mndlactf1o 33090 mndractf1 33088 mndractf1o 33091 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20216 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20134 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33777 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33781 assarrginv 33780 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33822 fldextrspunfld 33820 fldextrspunlem1 33819 fldextrspunlem2 33821 fldextrspunlsp 33818 fldextrspunlsplem 33817 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33597 dfufd2 33610 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7242 fcofo 7243 |
| [BourbakiTop1] p. | Remark | xnegmnf 13162 xnegpnf 13161 |
| [BourbakiTop1] p. | Remark | rexneg 13163 |
| [BourbakiTop1] p. | Remark 3 | ust0 24185 ustfilxp 24178 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24055 |
| [BourbakiTop1] p. | Criterion | ishmeo 23724 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24248 iducn 24247 snfil 23829 |
| [BourbakiTop1] p. | Example 2 | neifil 23845 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24032 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24268 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34101 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23828 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24240 df-ust 24166 filintn0 23826 filn0 23827 istgp 24042 ucnprima 24246 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24251 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24262 df-usp 24222 df-utop 24196 trust 24194 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34000 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23081 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23234 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24171 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24174 |
| [BourbakiTop1] p. | Property V_ii | innei 23090 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23098 neissex 23092 |
| [BourbakiTop1] p. | Proposition 1 | neips 23078 neiss 23074 ucncn 24249 ustund 24187 ustuqtop 24211 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23232 neiptopreu 23098 utop2nei 24215 utop3cls 24216 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24256 uspreg 24238 utopreg 24217 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23656 imasncls 23657 imasnopn 23655 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23965 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24173 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24175 |
| [BourbakiTop1] p. | Property V_iii | elnei 23076 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24267 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24172 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24176 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23352 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23811 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22859 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 33997 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46490 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46492 stoweid 46491 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46429 stoweidlem10 46438 stoweidlem14 46442 stoweidlem15 46443 stoweidlem35 46463 stoweidlem36 46464 stoweidlem37 46465 stoweidlem38 46466 stoweidlem40 46468 stoweidlem41 46469 stoweidlem43 46471 stoweidlem44 46472 stoweidlem46 46474 stoweidlem5 46433 stoweidlem50 46478 stoweidlem52 46480 stoweidlem53 46481 stoweidlem55 46483 stoweidlem56 46484 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46451 stoweidlem24 46452 stoweidlem27 46455 stoweidlem28 46456 stoweidlem30 46458 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46462 stoweidlem59 46487 stoweidlem60 46488 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46473 stoweidlem49 46477 stoweidlem7 46435 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46459 stoweidlem39 46467 stoweidlem42 46470 stoweidlem48 46476 stoweidlem51 46479 stoweidlem54 46482 stoweidlem57 46485 stoweidlem58 46486 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46453 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46445 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46439 stoweidlem13 46441 stoweidlem26 46454 stoweidlem61 46489 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46446 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48670 df-mgm 18608 df-mgm2 48689 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18687 df-sgrp2 48691 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19015 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5168 |
| [Church] p. 129 | Section II.24 | df-ifp 1064 dfifp2 1065 |
| [Clemente] p. 10 | Definition IT | natded 30473 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30473 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30473 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30473 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30473 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30473 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30473 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30473 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30473 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30473 |
| [Clemente] p. 14 | Proof 5.11 | natded 30473 |
| [Clemente] p. 14 | Definition E` `n | natded 30473 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30475 ex-natded5.2 30474 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30478 ex-natded5.3 30477 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30480 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30482 ex-natded5.7 30481 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30484 ex-natded5.8 30483 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30486 ex-natded5.13 30485 |
| [Clemente] p. 32 | Definition I` `n | natded 30473 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30473 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30473 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30473 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30487 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30488 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30490 ex-natded9.26 30489 |
| [Cohen] p. 301 | Remark | relogoprlem 26555 |
| [Cohen] p. 301 | Property 2 | relogmul 26556 relogmuld 26589 |
| [Cohen] p. 301 | Property 3 | relogdiv 26557 relogdivd 26590 |
| [Cohen] p. 301 | Property 4 | relogexp 26560 |
| [Cohen] p. 301 | Property 1a | log1 26549 |
| [Cohen] p. 301 | Property 1b | loge 26550 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26751 |
| [Cohen4] p. 349 | Property | relogbf 26755 |
| [Cohen4] p. 352 | Definition | elogb 26734 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26741 |
| [Cohen4] p. 361 | Property 3 | logbrec 26746 relogbdiv 26743 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26739 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26744 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26732 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26733 |
| [Cohen4] p. 367 | Property | logbchbase 26735 |
| [Cohen4] p. 377 | Property 2 | logblt 26748 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34429 sxbrsigalem4 34431 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18523 acsinfd 18522 acsinfdimd 18524 acsmap2d 18521 acsmapd 18520 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34434 |
| [Connell] p. 57 | Definition | df-scmat 22456 df-scmatalt 48869 |
| [Conway] p. 4 | Definition | lesrec 27791 lesrecd 27792 |
| [Conway] p. 5 | Definition | addsval 27954 addsval2 27955 df-adds 27952 df-muls 28099 df-negs 28013 |
| [Conway] p. 7 | Theorem | 0lt1s 27804 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28454 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 27853 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 27852 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27731 |
| [Conway] p. 17 | Theorem 3 | addsass 27997 addsassd 27998 addscom 27958 addscomd 27959 addsrid 27956 addsridd 27957 |
| [Conway] p. 17 | Definition | df-0s 27799 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28036 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28033 negsidd 28034 |
| [Conway] p. 18 | Theorem 5 | leadds1 27981 leadds1d 27987 |
| [Conway] p. 18 | Definition | df-1s 27800 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28028 negscld 28029 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27972 |
| [Conway] p. 19 | Note | mulsunif2 28162 |
| [Conway] p. 19 | Theorem 7 | addsdi 28147 addsdid 28148 addsdird 28149 mulnegs1d 28152 mulnegs2d 28153 mulsass 28158 mulsassd 28159 mulscom 28131 mulscomd 28132 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28126 mulscld 28127 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28130 ltmuls 28128 ltmulsd 28129 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28136 mulsgt0d 28137 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28210 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27796 |
| [Conway] p. 24 | Definition | df-reno 28482 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28491 remulscl 28494 renegscl 28490 |
| [Conway] p. 27 | Definition | df-ons 28244 elons2 28250 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28254 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28256 onswe 28264 |
| [Conway] p. 29 | Remark | madebday 27892 newbday 27894 oldbday 27893 |
| [Conway] p. 29 | Definition | df-made 27819 df-new 27821 df-old 27820 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13820 |
| [Crawley] p. 1 | Definition of poset | df-poset 18279 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39832 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40636 dalaw 40332 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42407 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40436 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40552 df-ldil 40550 isldil 40556 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40551 df-trnN 40553 isltrn 40565 ltrnu 40567 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40237 cdlema2N 40238 exatleN 39850 |
| [Crawley] p. 112 | Lemma B | 1cvrat 39922 cdlemb 40240 cdlemb2 40487 cdlemb3 41052 idltrn 40596 l1cvat 39501 lhpat 40489 lhpat2 40491 lshpat 39502 ltrnel 40585 ltrnmw 40597 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40637 cdlemc2 40638 ltrnnidn 40620 trlat 40615 trljat1 40612 trljat2 40613 trljat3 40614 trlne 40631 trlnidat 40619 trlnle 40632 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40437 |
| [Crawley] p. 113 | Lemma C | cdlemc 40643 cdlemc3 40639 cdlemc4 40640 |
| [Crawley] p. 113 | Lemma D | cdlemd 40653 cdlemd1 40644 cdlemd2 40645 cdlemd3 40646 cdlemd4 40647 cdlemd5 40648 cdlemd6 40649 cdlemd7 40650 cdlemd8 40651 cdlemd9 40652 cdleme31sde 40831 cdleme31se 40828 cdleme31se2 40829 cdleme31snd 40832 cdleme32a 40887 cdleme32b 40888 cdleme32c 40889 cdleme32d 40890 cdleme32e 40891 cdleme32f 40892 cdleme32fva 40883 cdleme32fva1 40884 cdleme32fvcl 40886 cdleme32le 40893 cdleme48fv 40945 cdleme4gfv 40953 cdleme50eq 40987 cdleme50f 40988 cdleme50f1 40989 cdleme50f1o 40992 cdleme50laut 40993 cdleme50ldil 40994 cdleme50lebi 40986 cdleme50rn 40991 cdleme50rnlem 40990 cdlemeg49le 40957 cdlemeg49lebilem 40985 |
| [Crawley] p. 113 | Lemma E | cdleme 41006 cdleme00a 40655 cdleme01N 40667 cdleme02N 40668 cdleme0a 40657 cdleme0aa 40656 cdleme0b 40658 cdleme0c 40659 cdleme0cp 40660 cdleme0cq 40661 cdleme0dN 40662 cdleme0e 40663 cdleme0ex1N 40669 cdleme0ex2N 40670 cdleme0fN 40664 cdleme0gN 40665 cdleme0moN 40671 cdleme1 40673 cdleme10 40700 cdleme10tN 40704 cdleme11 40716 cdleme11a 40706 cdleme11c 40707 cdleme11dN 40708 cdleme11e 40709 cdleme11fN 40710 cdleme11g 40711 cdleme11h 40712 cdleme11j 40713 cdleme11k 40714 cdleme11l 40715 cdleme12 40717 cdleme13 40718 cdleme14 40719 cdleme15 40724 cdleme15a 40720 cdleme15b 40721 cdleme15c 40722 cdleme15d 40723 cdleme16 40731 cdleme16aN 40705 cdleme16b 40725 cdleme16c 40726 cdleme16d 40727 cdleme16e 40728 cdleme16f 40729 cdleme16g 40730 cdleme19a 40749 cdleme19b 40750 cdleme19c 40751 cdleme19d 40752 cdleme19e 40753 cdleme19f 40754 cdleme1b 40672 cdleme2 40674 cdleme20aN 40755 cdleme20bN 40756 cdleme20c 40757 cdleme20d 40758 cdleme20e 40759 cdleme20f 40760 cdleme20g 40761 cdleme20h 40762 cdleme20i 40763 cdleme20j 40764 cdleme20k 40765 cdleme20l 40768 cdleme20l1 40766 cdleme20l2 40767 cdleme20m 40769 cdleme20y 40748 cdleme20zN 40747 cdleme21 40783 cdleme21d 40776 cdleme21e 40777 cdleme22a 40786 cdleme22aa 40785 cdleme22b 40787 cdleme22cN 40788 cdleme22d 40789 cdleme22e 40790 cdleme22eALTN 40791 cdleme22f 40792 cdleme22f2 40793 cdleme22g 40794 cdleme23a 40795 cdleme23b 40796 cdleme23c 40797 cdleme26e 40805 cdleme26eALTN 40807 cdleme26ee 40806 cdleme26f 40809 cdleme26f2 40811 cdleme26f2ALTN 40810 cdleme26fALTN 40808 cdleme27N 40815 cdleme27a 40813 cdleme27cl 40812 cdleme28c 40818 cdleme3 40683 cdleme30a 40824 cdleme31fv 40836 cdleme31fv1 40837 cdleme31fv1s 40838 cdleme31fv2 40839 cdleme31id 40840 cdleme31sc 40830 cdleme31sdnN 40833 cdleme31sn 40826 cdleme31sn1 40827 cdleme31sn1c 40834 cdleme31sn2 40835 cdleme31so 40825 cdleme35a 40894 cdleme35b 40896 cdleme35c 40897 cdleme35d 40898 cdleme35e 40899 cdleme35f 40900 cdleme35fnpq 40895 cdleme35g 40901 cdleme35h 40902 cdleme35h2 40903 cdleme35sn2aw 40904 cdleme35sn3a 40905 cdleme36a 40906 cdleme36m 40907 cdleme37m 40908 cdleme38m 40909 cdleme38n 40910 cdleme39a 40911 cdleme39n 40912 cdleme3b 40675 cdleme3c 40676 cdleme3d 40677 cdleme3e 40678 cdleme3fN 40679 cdleme3fa 40682 cdleme3g 40680 cdleme3h 40681 cdleme4 40684 cdleme40m 40913 cdleme40n 40914 cdleme40v 40915 cdleme40w 40916 cdleme41fva11 40923 cdleme41sn3aw 40920 cdleme41sn4aw 40921 cdleme41snaw 40922 cdleme42a 40917 cdleme42b 40924 cdleme42c 40918 cdleme42d 40919 cdleme42e 40925 cdleme42f 40926 cdleme42g 40927 cdleme42h 40928 cdleme42i 40929 cdleme42k 40930 cdleme42ke 40931 cdleme42keg 40932 cdleme42mN 40933 cdleme42mgN 40934 cdleme43aN 40935 cdleme43bN 40936 cdleme43cN 40937 cdleme43dN 40938 cdleme5 40686 cdleme50ex 41005 cdleme50ltrn 41003 cdleme51finvN 41002 cdleme51finvfvN 41001 cdleme51finvtrN 41004 cdleme6 40687 cdleme7 40695 cdleme7a 40689 cdleme7aa 40688 cdleme7b 40690 cdleme7c 40691 cdleme7d 40692 cdleme7e 40693 cdleme7ga 40694 cdleme8 40696 cdleme8tN 40701 cdleme9 40699 cdleme9a 40697 cdleme9b 40698 cdleme9tN 40703 cdleme9taN 40702 cdlemeda 40744 cdlemedb 40743 cdlemednpq 40745 cdlemednuN 40746 cdlemefr27cl 40849 cdlemefr32fva1 40856 cdlemefr32fvaN 40855 cdlemefrs32fva 40846 cdlemefrs32fva1 40847 cdlemefs27cl 40859 cdlemefs32fva1 40869 cdlemefs32fvaN 40868 cdlemesner 40742 cdlemeulpq 40666 |
| [Crawley] p. 114 | Lemma E | 4atex 40522 4atexlem7 40521 cdleme0nex 40736 cdleme17a 40732 cdleme17c 40734 cdleme17d 40944 cdleme17d1 40735 cdleme17d2 40941 cdleme18a 40737 cdleme18b 40738 cdleme18c 40739 cdleme18d 40741 cdleme4a 40685 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40771 cdleme21at 40774 cdleme21b 40772 cdleme21c 40773 cdleme21ct 40775 cdleme21f 40778 cdleme21g 40779 cdleme21h 40780 cdleme21i 40781 cdleme22gb 40740 |
| [Crawley] p. 116 | Lemma F | cdlemf 41009 cdlemf1 41007 cdlemf2 41008 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41013 cdlemg16 41103 cdlemg28 41150 cdlemg28a 41139 cdlemg28b 41149 cdlemg3a 41043 cdlemg42 41175 cdlemg43 41176 cdlemg44 41179 cdlemg44a 41177 cdlemg46 41181 cdlemg47 41182 cdlemg9 41080 ltrnco 41165 ltrncom 41184 tgrpabl 41197 trlco 41173 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41189 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41123 cdlemg17b 41108 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41202 df-edring 41203 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41206 |
| [Crawley] p. 118 | Remark | tendopltp 41226 |
| [Crawley] p. 118 | Lemma H | cdlemh 41263 cdlemh1 41261 cdlemh2 41262 |
| [Crawley] p. 118 | Lemma I | cdlemi 41266 cdlemi1 41264 cdlemi2 41265 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41267 cdlemj2 41268 cdlemj3 41269 tendocan 41270 |
| [Crawley] p. 118 | Lemma K | cdlemk 41420 cdlemk1 41277 cdlemk10 41289 cdlemk11 41295 cdlemk11t 41392 cdlemk11ta 41375 cdlemk11tb 41377 cdlemk11tc 41391 cdlemk11u-2N 41335 cdlemk11u 41317 cdlemk12 41296 cdlemk12u-2N 41336 cdlemk12u 41318 cdlemk13-2N 41322 cdlemk13 41298 cdlemk14-2N 41324 cdlemk14 41300 cdlemk15-2N 41325 cdlemk15 41301 cdlemk16-2N 41326 cdlemk16 41303 cdlemk16a 41302 cdlemk17-2N 41327 cdlemk17 41304 cdlemk18-2N 41332 cdlemk18-3N 41346 cdlemk18 41314 cdlemk19-2N 41333 cdlemk19 41315 cdlemk19u 41416 cdlemk1u 41305 cdlemk2 41278 cdlemk20-2N 41338 cdlemk20 41320 cdlemk21-2N 41337 cdlemk21N 41319 cdlemk22-3 41347 cdlemk22 41339 cdlemk23-3 41348 cdlemk24-3 41349 cdlemk25-3 41350 cdlemk26-3 41352 cdlemk26b-3 41351 cdlemk27-3 41353 cdlemk28-3 41354 cdlemk29-3 41357 cdlemk3 41279 cdlemk30 41340 cdlemk31 41342 cdlemk32 41343 cdlemk33N 41355 cdlemk34 41356 cdlemk35 41358 cdlemk36 41359 cdlemk37 41360 cdlemk38 41361 cdlemk39 41362 cdlemk39u 41414 cdlemk4 41280 cdlemk41 41366 cdlemk42 41387 cdlemk42yN 41390 cdlemk43N 41409 cdlemk45 41393 cdlemk46 41394 cdlemk47 41395 cdlemk48 41396 cdlemk49 41397 cdlemk5 41282 cdlemk50 41398 cdlemk51 41399 cdlemk52 41400 cdlemk53 41403 cdlemk54 41404 cdlemk55 41407 cdlemk55u 41412 cdlemk56 41417 cdlemk5a 41281 cdlemk5auN 41306 cdlemk5u 41307 cdlemk6 41283 cdlemk6u 41308 cdlemk7 41294 cdlemk7u-2N 41334 cdlemk7u 41316 cdlemk8 41284 cdlemk9 41285 cdlemk9bN 41286 cdlemki 41287 cdlemkid 41382 cdlemkj-2N 41328 cdlemkj 41309 cdlemksat 41292 cdlemksel 41291 cdlemksv 41290 cdlemksv2 41293 cdlemkuat 41312 cdlemkuel-2N 41330 cdlemkuel-3 41344 cdlemkuel 41311 cdlemkuv-2N 41329 cdlemkuv2-2 41331 cdlemkuv2-3N 41345 cdlemkuv2 41313 cdlemkuvN 41310 cdlemkvcl 41288 cdlemky 41372 cdlemkyyN 41408 tendoex 41421 |
| [Crawley] p. 120 | Remark | dva1dim 41431 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41422 cdleml2N 41423 cdleml3N 41424 cdleml4N 41425 cdleml5N 41426 cdleml6 41427 cdleml7 41428 cdleml8 41429 cdleml9 41430 dia1dim 41507 |
| [Crawley] p. 120 | Lemma M | dia11N 41494 diaf11N 41495 dialss 41492 diaord 41493 dibf11N 41607 djajN 41583 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41478 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41564 dia2dimlem1 41510 dia2dimlem2 41511 dia2dimlem3 41512 dia2dimlem4 41513 dia2dimlem5 41514 diaf1oN 41576 diarnN 41575 dvheveccl 41558 dvhopN 41562 |
| [Crawley] p. 121 | Lemma N | cdlemn 41658 cdlemn10 41652 cdlemn11 41657 cdlemn11a 41653 cdlemn11b 41654 cdlemn11c 41655 cdlemn11pre 41656 cdlemn2 41641 cdlemn2a 41642 cdlemn3 41643 cdlemn4 41644 cdlemn4a 41645 cdlemn5 41647 cdlemn5pre 41646 cdlemn6 41648 cdlemn7 41649 cdlemn8 41650 cdlemn9 41651 diclspsn 41640 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41619 |
| [Crawley] p. 122 | Lemma N | dih11 41711 dihf11 41713 dihjust 41663 dihjustlem 41662 dihord 41710 dihord1 41664 dihord10 41669 dihord11b 41668 dihord11c 41670 dihord2 41673 dihord2a 41665 dihord2b 41666 dihord2cN 41667 dihord2pre 41671 dihord2pre2 41672 dihordlem6 41659 dihordlem7 41660 dihordlem7b 41661 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41676 dihfval 41677 dihval 41678 |
| [Diestel] p. 3 | Definition | df-gric 48351 df-grim 48348 isuspgrim 48366 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29481 df-nbgr 29402 |
| [Diestel] p. 3 | Definition by | df-grisom 48347 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48331 df-subgr 29337 uhgrspan1 29372 uhgrspansubgr 29360 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29623 vtxdgoddnumeven 29622 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29128 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34008 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34020 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34012 zarcls1 34013 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34023 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34026 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34029 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3893 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9568 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8775 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9576 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9904 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10477 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5241 |
| [Enderton] p. 19 | Definition | df-tp 4573 |
| [Enderton] p. 26 | Exercise 5 | unissb 4884 |
| [Enderton] p. 26 | Exercise 10 | pwel 5324 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5524 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5022 iinin2 5021 iinun2 5016 iunin1 5015 iunin1f 32627 iunin2 5014 uniin1 32621 uniin2 32622 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5020 iundif2 5017 |
| [Enderton] p. 32 | Exercise 20 | unineq 4229 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5041 |
| [Enderton] p. 33 | Exercise 25 | iununi 5042 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5049 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7725 iunpwss 5050 |
| [Enderton] p. 36 | Definition | opthwiener 5469 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5403 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4889 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5424 rnex 7861 rnexg 7853 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5870 rnuni 6113 |
| [Enderton] p. 42 | Definition of a function | dffun7 6526 dffun8 6527 |
| [Enderton] p. 43 | Definition of function value | funfv2 6929 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6568 |
| [Enderton] p. 44 | Definition (d) | dfima2 6028 dfima3 6029 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6938 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10395 ac7g 10396 df-ac 10038 dfac2 10054 dfac2a 10052 dfac2b 10053 dfac3 10043 dfac7 10055 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7201 |
| [Enderton] p. 52 | Definition | df-map 8775 |
| [Enderton] p. 53 | Exercise 21 | coass 6231 |
| [Enderton] p. 53 | Exercise 27 | dmco 6220 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6575 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6068 |
| [Enderton] p. 54 | Remark | ixpf 8868 ixpssmap 8880 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8846 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10405 ac9s 10415 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39015 erref 8664 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39018 erthi 8700 |
| [Enderton] p. 57 | Definition | df-ec 8645 |
| [Enderton] p. 58 | Definition | df-qs 8649 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8645 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5866 |
| [Enderton] p. 68 | Definition of successor | df-suc 6330 |
| [Enderton] p. 71 | Definition | df-tr 5194 dftr4 5199 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6405 unisucg 6404 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6405 unisucg 6404 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5209 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5211 trintALT 45307 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8540 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8542 onasuc 8463 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7370 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8541 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8543 onmsuc 8464 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8558 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8545 nnacom 8553 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8559 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8560 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8562 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8546 nnmsucr 8561 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8574 |
| [Enderton] p. 129 | Definition | df-en 8894 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7321 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9937 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16180 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9141 |
| [Enderton] p. 135 | Corollary 6C | php3 9143 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9140 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9172 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9174 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9103 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9107 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9079 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10102 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10103 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10098 dju1en 10094 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9253 unifi 9254 unifi2 9255 |
| [Enderton] p. 144 | Corollary 6K | undif2 4418 unfi 9105 unfi2 9220 |
| [Enderton] p. 145 | Figure 38 | ffoss 7899 |
| [Enderton] p. 145 | Definition | df-dom 8895 |
| [Enderton] p. 146 | Example 1 | domen 8908 domeng 8909 |
| [Enderton] p. 146 | Example 3 | nndomo 9152 nnsdom 9575 nnsdomg 9209 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10106 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9080 xpdom1 9014 xpdom1g 9012 xpdom2g 9011 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9086 |
| [Enderton] p. 151 | Theorem 6M | zorn 10429 zorng 10426 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10414 dfac5 10051 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10498 |
| [Enderton] p. 164 | Example | infdif 10130 |
| [Enderton] p. 168 | Definition | df-po 5539 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6439 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6371 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6438 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6379 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7790 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7735 |
| [Enderton] p. 194 | Remark | onprc 7732 |
| [Enderton] p. 194 | Exercise 16 | suc11 6433 |
| [Enderton] p. 197 | Definition | df-card 9863 |
| [Enderton] p. 197 | Theorem 7P | carden 10473 |
| [Enderton] p. 200 | Exercise 25 | tfis 7806 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9700 |
| [Enderton] p. 202 | Definition | df-r1 9688 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9710 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9791 rankval4b 35243 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9527 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9781 rankprb 9775 rankpw 9767 rankpwi 9747 rankuniss 9790 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9539 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9540 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10032 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 9998 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10012 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8281 |
| [Enderton] p. 222 | Definition of kard | karden 9819 kardex 9818 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8533 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8535 |
| [Enderton] p. 240 | Exercise 25 | oarec 8497 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10172 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17608 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17550 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18519 mrieqv2d 17605 mrieqvd 17604 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17609 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17614 mreexexlem2d 17611 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18525 mreexfidimd 17616 |
| [Frege1879] p. 11 | Statement | df3or2 44195 |
| [Frege1879] p. 12 | Statement | df3an2 44196 dfxor4 44193 dfxor5 44194 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44217 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44218 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44222 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44226 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44227 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44233 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44235 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44236 axfrege8 44234 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37761 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44239 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44247 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44241 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44240 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44249 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44250 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44253 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44243 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44248 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44245 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44251 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44255 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44254 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44246 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44252 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44242 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44244 rp-frege25 44232 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44237 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44257 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44238 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44258 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44261 axfrege31 44260 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44259 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44262 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44263 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44264 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44265 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44266 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44267 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44268 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44269 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44270 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44272 axfrege41 44271 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44273 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44274 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44275 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44276 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44277 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44278 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44279 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44280 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44281 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44284 ax-frege52c 44315 frege52aid 44285 frege52b 44316 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44289 ax-frege54c 44319 frege54b 44320 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44282 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3731 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44287 frege53aid 44286 frege53b 44317 frege53c 44341 |
| [Frege1879] p. 50 | Proposition 54 | biid 261 eqid 2737 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44295 frege55aid 44292 frege55b 44324 frege55c 44345 frege55cor1a 44296 frege55lem2a 44294 frege55lem2b 44323 frege55lem2c 44344 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44298 frege56aid 44297 frege56b 44325 frege56c 44346 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44302 ax-frege58b 44328 frege58bid 44329 frege58c 44348 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44300 frege57aid 44299 frege57b 44326 frege57c 44347 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3742 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44304 frege59b 44331 frege59c 44349 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44305 frege60b 44332 frege60c 44350 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44306 frege61b 44333 frege61c 44351 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44307 frege62b 44334 frege62c 44352 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44308 frege63b 44335 frege63c 44353 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44309 frege64b 44336 frege64c 44354 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44310 frege65b 44337 frege65c 44355 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44311 frege66b 44338 frege66c 44356 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44312 frege67b 44339 frege67c 44357 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44313 frege68b 44340 frege68c 44358 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44359 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44360 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44361 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44362 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44363 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44366 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44364 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44365 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44367 frege77d 44173 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44368 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44369 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44370 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44371 frege81d 44174 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44372 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44373 frege83d 44175 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44374 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44375 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44376 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44377 frege87d 44177 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44378 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44379 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44380 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44381 frege91d 44178 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44382 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44383 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44384 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44385 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44389 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44386 frege96d 44176 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44387 frege97d 44179 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44388 frege98d 44180 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44390 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44391 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44392 frege102d 44181 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44393 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44394 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44395 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44396 frege106d 44182 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44397 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44398 frege108d 44183 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44399 frege109d 44184 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44400 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44401 frege111d 44186 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44402 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44403 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44404 frege114d 44185 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44405 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44406 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44407 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44408 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44409 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44410 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44411 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44412 frege122d 44187 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44413 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44414 frege124d 44188 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44415 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44416 frege126d 44189 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44417 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44418 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44419 frege129d 44190 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44420 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44421 frege131d 44191 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44422 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44423 frege133d 44192 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46741 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47064 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46764 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46879 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46899 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46890 meadjunre 46904 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46891 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46892 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46888 meaiunle 46897 meaiunlelem 46896 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 46909 meaiuninc2 46910 meaiuninc3 46913 meaiuninc3v 46912 meaiunincf 46911 meaiuninclem 46908 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 46915 meaiininc2 46916 meaiininclem 46914 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 46934 caragendifcl 46942 caratheodory 46956 omelesplit 46946 |
| [Fremlin1] p. 19 | Definition 113A | isome 46922 isomennd 46959 isomenndlem 46958 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 46944 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 46963 voncmpl 47049 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 46926 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 46951 carageniuncllem1 46949 carageniuncllem2 46950 caragenuncl 46941 caragenuncllem 46940 caragenunicl 46952 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 46960 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 46954 caratheodorylem2 46955 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 46963 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47022 hoidmv1lelem1 47019 hoidmv1lelem2 47020 hoidmv1lelem3 47021 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47066 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47022 hoidmvle 47028 hoidmvlelem1 47023 hoidmvlelem2 47024 hoidmvlelem3 47025 hoidmvlelem4 47026 hoidmvlelem5 47027 hsphoidmvle2 47013 hsphoif 47004 hsphoival 47007 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 46976 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 46984 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47011 hoidmvn0val 47012 hoidmvval 47005 hoidmvval0 47015 hoidmvval0b 47018 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47016 hsphoidmvle 47014 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 46965 df-voln 46967 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47032 ovn0 46994 ovn0lem 46993 ovnf 46991 ovnome 47001 ovnssle 46989 ovnsslelem 46988 ovnsupge0 46985 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47031 ovnhoilem1 47029 ovnhoilem2 47030 vonhoi 47095 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47048 hoidifhspf 47046 hoidifhspval 47036 hoidifhspval2 47043 hoidifhspval3 47047 hspmbl 47057 hspmbllem1 47054 hspmbllem2 47055 hspmbllem3 47056 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47049 vonmea 47002 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47000 ovnsubadd2 47074 ovnsubadd2lem 47073 ovnsubaddlem1 46998 ovnsubaddlem2 46999 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47059 hoimbl2 47093 hoimbllem 47058 hspdifhsp 47044 opnvonmbl 47062 opnvonmbllem2 47061 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47064 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47107 iccvonmbllem 47106 ioovonmbl 47105 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47113 vonicclem2 47112 vonioo 47110 vonioolem2 47109 vonn0icc 47116 vonn0icc2 47120 vonn0ioo 47115 vonn0ioo2 47118 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47117 snvonmbl 47114 vonct 47121 vonsn 47119 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46787 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46786 subsaliuncllem 46785 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47153 salpreimalegt 47137 salpreimaltle 47154 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47156 issmff 47162 issmflem 47155 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47173 issmflelem 47172 smfpreimale 47182 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47184 issmfgtlem 47183 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47124 issmf 47156 issmff 47162 issmfge 47198 issmfgelem 47197 issmfgt 47184 issmfgtlem 47183 issmfle 47173 issmflelem 47172 issmflem 47155 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47135 salpreimagtlt 47158 salpreimalelt 47157 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47198 issmfgelem 47197 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47181 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47179 cnfsmf 47168 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47195 decsmflem 47194 incsmf 47170 incsmflem 47169 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47129 pimconstlt1 47130 smfconst 47177 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47193 smfaddlem1 47191 smfaddlem2 47192 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47224 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47223 smfmullem1 47219 smfmullem2 47220 smfmullem3 47221 smfmullem4 47222 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47225 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47228 smfpimbor1lem2 47227 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47230 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47218 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47217 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47226 smfresal 47216 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47205 smflim2 47234 smflimlem1 47199 smflimlem2 47200 smflimlem3 47201 smflimlem4 47202 smflimlem5 47203 smflimlem6 47204 smflimmpt 47238 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47242 smfsuplem1 47239 smfsuplem2 47240 smfsuplem3 47241 smfsupmpt 47243 smfsupxr 47244 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47246 smfinflem 47245 smfinfmpt 47247 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47205 smflim2 47234 smflimmpt 47238 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47236 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47266 smfdivdmmbl2 47269 smfinfdmmbl 47277 smfinfdmmbllem 47276 smfsupdmmbl 47273 smfsupdmmbllem 47272 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47256 smflimsuplem2 47249 smflimsuplem6 47253 smflimsuplem7 47254 smflimsuplem8 47255 smflimsupmpt 47257 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47259 smfliminflem 47258 smfliminfmpt 47260 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47124 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47270 fsupdm2 47271 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47261 adddmmbl2 47262 finfdm 47274 finfdm2 47275 fsupdm 47270 fsupdm2 47271 muldmmbl 47263 muldmmbl2 47264 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47274 finfdm2 47275 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25503 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25546 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25556 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38019 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38022 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9559 inf1 9543 inf2 9544 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10834 enqer 10844 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10839 df-nq 10835 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10831 df-plq 10837 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7604 df-mpq 10832 df-mq 10838 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10840 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10898 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10899 ltbtwnnq 10901 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10894 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10895 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10902 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10904 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10916 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10918 |
| [Gleason] p. 122 | Definition | df-1p 10905 |
| [Gleason] p. 122 | Remark (1) | prub 10917 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10956 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10908 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10955 psslinpr 10954 supexpr 10977 suplem1pr 10975 suplem2pr 10976 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10941 addclprlem1 10939 addclprlem2 10940 df-plp 10906 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10945 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10944 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10957 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10966 ltexprlem1 10959 ltexprlem2 10960 ltexprlem3 10961 ltexprlem4 10962 ltexprlem5 10963 ltexprlem6 10964 ltexprlem7 10965 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10968 ltaprlem 10967 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10969 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10970 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10907 mulclpr 10943 mulclprlem 10942 reclem2pr 10971 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10952 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10947 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10946 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10951 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10974 reclem3pr 10972 reclem4pr 10973 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10978 enrer 10986 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10983 df-1r 10984 df-nr 10979 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10981 df-plr 10980 negexsr 11025 recexsr 11030 recexsrlem 11026 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10982 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12154 creur 12153 cru 12151 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11111 axcnre 11087 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15077 crimd 15194 crimi 15155 crre 15076 crred 15193 crrei 15154 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15079 remimd 15160 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15246 absval2d 15410 absval2i 15360 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15103 cjaddd 15182 cjaddi 15150 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15104 cjmuld 15183 cjmuli 15151 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15102 cjcjd 15161 cjcji 15133 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15101 cjreb 15085 cjrebd 15164 cjrebi 15136 cjred 15188 rere 15084 rereb 15082 rerebd 15163 rerebi 15135 rered 15186 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15110 addcjd 15174 addcji 15145 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15200 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15241 abscjd 15415 abscji 15364 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15251 abs00d 15411 abs00i 15361 absne0d 15412 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15284 releabsd 15416 releabsi 15365 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15256 absmuld 15419 absmuli 15367 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15244 sqabsaddi 15368 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15293 abstrid 15421 abstrii 15371 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14024 exp0 14027 expp1 14030 expp1d 14109 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26643 cxpaddd 26681 expadd 14066 expaddd 14110 expaddz 14068 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26652 cxpmuld 26701 expmul 14069 expmuld 14111 expmulz 14070 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26649 mulcxpd 26692 mulexp 14063 mulexpd 14123 mulexpz 14064 |
| [Gleason] p. 140 | Exercise 1 | znnen 16179 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13463 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15594 rlimadd 15605 rlimdiv 15608 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15596 rlimsub 15606 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15595 rlimmul 15607 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15599 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15545 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15566 climcj 15567 climim 15569 climre 15568 rlimabs 15571 rlimcj 15572 rlimim 15574 rlimre 15573 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11184 df-xr 11183 ltxr 13066 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15433 limsupval 15436 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15632 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15641 caucvgb 15642 caucvgbf 45917 caucvgr 15638 climcau 15633 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15779 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15848 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15298 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13787 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21346 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24308 xmet0 24307 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24324 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24315 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24317 mstri 24434 xmettri 24316 xmstri 24433 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24347 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23613 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25277 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24505 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24831 addcn2 15556 mulcn 24833 mulcn2 15558 subcn 24832 subcn2 15557 |
| [Gleason] p. 295 | Remark | bcval3 14268 bcval4 14269 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14283 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14266 df-bc 14265 |
| [Gleason] p. 296 | Remark | bcn0 14272 bcnn 14274 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15795 |
| [Gleason] p. 308 | Equation 2 | ef0 16056 |
| [Gleason] p. 308 | Equation 3 | efcj 16057 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16063 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16068 |
| [Gleason] p. 310 | Equation 14 | sinadd 16131 |
| [Gleason] p. 310 | Equation 15 | cosadd 16132 |
| [Gleason] p. 311 | Equation 17 | sincossq 16143 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16148 sinbnd 16147 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14178 sqeqori 14176 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16037 |
| [Godowski] p. 730 | Equation SF | goeqi 32344 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31739 |
| [Golan] p. 1 | Remark | srgisid 20190 |
| [Golan] p. 1 | Definition | df-srg 20168 |
| [Golan] p. 149 | Definition | df-slmd 33262 |
| [Gonshor] p. 7 | Definition | df-cuts 27752 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27791 lesrecd 27792 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27912 cofcut1d 27913 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27914 cofcut2d 27915 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27916 cofcutr1d 27917 cofcutr2d 27918 |
| [Gonshor] p. 13 | Definition | df-adds 27952 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27968 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27994 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28122 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28142 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28450 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28452 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28451 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28487 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28010 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36341 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17548 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17550 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48658 df-cllaw 48656 df-comlaw 48657 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48670 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48691 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39189 dfmembpart2 39194 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32136 riesz2 32137 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32012 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32244 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32256 elpjidm 32255 pjnmopi 32219 |
| [Halmos] p. 44 | Remark | pjinormi 31758 pjinormii 31747 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32260 pjrn 31778 pjrni 31773 pjvec 31767 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31798 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32225 hmopidmpji 32223 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32262 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32251 pjocvec 31768 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32240 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32243 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32246 pjssdif2i 32245 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31926 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1797 |
| [Hatcher] p. 25 | Definition | df-phtpc 24959 df-phtpy 24938 |
| [Hatcher] p. 26 | Definition | df-pco 24972 df-pi1 24975 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24962 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25017 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22455 df-dmatalt 48868 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48287 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48272 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48284 bgoldbtbnd 48279 bgoldbtbnd 48279 tgblthelfgott 48285 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34786 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34787 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34801 hgt750lemb 34800 hgt750leme 34802 hgt750lemf 34797 hgt750lemg 34798 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48281 tgoldbachgt 34807 tgoldbachgtALTV 48282 tgoldbachgtd 34806 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34788 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30564 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18920 grpoideu 30580 mndideu 18713 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18950 grpoinveu 30590 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18981 grpo2inv 30602 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18994 grpoinvop 30604 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19016 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1770 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1771 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1773 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32491 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32504 cdj3i 32512 cdj3lem1 32505 cdjreui 32503 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32502 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42407 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42337 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42359 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42360 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42357 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42363 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42282 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42377 |
| [Holland95] p. 204 | Definition of involution | df-srng 20817 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 39949 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 41974 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 41927 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40379 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41823 poml4N 40399 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 41914 pexmidALTN 40424 pexmidN 40415 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 41979 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39570 ldualset 39571 |
| [Holland95] p. 222 | Item 1 | df-lines 39947 df-pointsN 39948 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40349 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40393 omllaw4 39692 pol1N 40356 polcon3N 40363 |
| [Holland95] p. 223 | Definition | df-psubclN 40381 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40352 |
| [Holmes] p. 40 | Definition | df-xrn 38701 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31155 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32253 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32034 eigre 31906 eigrei 31905 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32035 eigorth 31909 eigorthi 31908 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31907 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30379 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30375 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30376 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30377 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30395 frgrregorufr0 30394 frgrregorufrg 30396 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30402 frrusgrord 30411 frrusgrord0 30410 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30158 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30385 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30388 frgrwopreg2 30389 frgrwopregasn 30386 frgrwopregbsn 30387 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30391 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30405 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30408 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30156 numclwlk1 30441 numclwlk1lem1 30439 numclwlk1lem2 30440 numclwwlk1 30431 numclwwlk8 30462 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30382 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29839 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30417 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30443 numclwwlkovh0 30442 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30451 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30048 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30455 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30458 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30461 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30473 natded 30473 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30473 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30473 natded 30473 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30473 |
| [Jech] p. 4 | Definition of class | cv 1541 cvjust 2731 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10502 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10500 alephmul 10501 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10499 infmap2 10139 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9738 |
| [Jech] p. 72 | Equation 9.3 | scott0 9810 scottex 9809 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9791 rankval4b 35243 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9815 |
| [Jech] p. 78 | Note | opthprc 5695 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43343 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43431 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43432 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43355 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43359 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43360 rmyp1 43361 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43362 rmym1 43363 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43353 rmx1 43354 rmxluc 43364 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43357 rmy1 43358 rmyluc 43365 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43367 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43368 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43388 jm2.17b 43389 jm2.17c 43390 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43421 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43425 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43416 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43391 jm2.24nn 43387 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43430 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43436 rmygeid 43392 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43448 |
| [Juillerat] p. 11 | Section *5 | etransc 46711 etransclem47 46709 etransclem48 46710 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46706 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46708 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46694 |
| [Juillerat] p. 13 | Proof | etransclem35 46697 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46700 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46686 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46703 |
| [Juillerat] p. 14 | Proof | etransclem23 46685 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1969 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2014 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2019 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2009 cbvaliw 2008 wl-cbvmotv 37838 wl-motae 37840 wl-moteq 37839 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1988 spimw 1972 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2035 spw 2036 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31587 chabs1i 31589 chabs2 31588 chabs2i 31590 chjass 31604 chjassi 31557 latabs1 18441 latabs2 18442 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32409 ela 32410 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32354 cvrval2 39720 |
| [Kalmbach] p. 16 | Definition | df-ol 39624 df-oml 39625 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31655 cmbri 31661 cmtvalN 39657 df-cm 31654 df-cmtN 39623 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39693 pjoml5 31684 pjoml5i 31659 |
| [Kalmbach] p. 22 | Definition | pjoml2 31682 pjoml2i 31656 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31685 cmcmi 31663 cmcmii 31668 cmtcomN 39695 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39691 omlsi 31475 pjoml 31507 pjomli 31506 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39690 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31667 cmcm3 31686 cmcm3i 31665 cmcm3ii 31670 cmcm4i 31666 cmt3N 39697 cmt4N 39698 cmtbr2N 39699 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31679 cmbr3i 31671 cmtbr3N 39700 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31689 fh1i 31692 fh2 31690 fh2i 31693 omlfh1N 39704 |
| [Kalmbach] p. 65 | Remark | chjatom 32428 chslej 31569 chsleji 31529 shslej 31451 shsleji 31441 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31566 chocini 31525 chsupcl 31411 chsupval2 31481 h0elch 31326 helch 31314 hsupval2 31480 ocin 31367 ococss 31364 shococss 31365 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31383 |
| [Kalmbach] p. 66 | Remark | df-pjh 31466 pjssmi 32236 pjssmii 31752 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31716 osumi 31713 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32271 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32471 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32381 |
| [Kalmbach] p. 140 | Remark | hatomic 32431 hatomici 32430 hatomistici 32433 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39765 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32452 lsatexch 39489 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32426 cvlcvr1 39785 cvr1 39856 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32445 cvexchi 32440 cvrexch 39866 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32435 hlrelat 39848 hlrelat5N 39847 lrelat 39460 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21139 lsmsatcv 39456 spansncv 31724 spansncvi 31723 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39475 spansncv2 32364 |
| [Kalmbach] p. 266 | Definition | df-st 32282 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31920 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10569 fpwwe2 10566 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10570 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10577 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10572 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10574 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10587 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10591 gchxpidm 10592 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10603 gchhar 10602 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10137 unxpwdom 9504 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10593 |
| [Kreyszig] p. 3 | Property M1 | metcl 24297 xmetcl 24296 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24304 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24537 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11872 muleqadd 11794 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24403 |
| [Kreyszig] p. 19 | Remark | mopntopon 24404 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24463 mopnm 24409 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24461 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24466 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24507 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23223 lmmbr 25225 lmmbr2 25226 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23345 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25280 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25243 iscmet2 25261 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25283 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23426 metelcls 25272 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25273 metcld2 25274 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25066 lmodvneg1 20900 nvinv 30710 vcm 30647 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25062 lmod0vs 20890 slmd0vs 33285 vc0 30645 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20891 slmdvs0 33286 vcz 30646 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30762 ngpmet 24568 nrmmetd 24539 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30757 imsdval2 30758 ncvspds 25128 ngpds 24569 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24554 nvnd 30759 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24583 nmge0 24582 nvge0 30744 nvz 30740 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24589 nvabs 30743 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30872 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30816 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30878 blocni 30876 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30877 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25171 ipeq0 21618 ipz 30790 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25183 pythi 30921 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30925 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25205 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15821 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25403 minveco 30955 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30821 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25296 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 30944 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32194 leopg 32193 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32212 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 30989 |
| [Kulpa] p. 547 | Theorem | poimir 37974 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 37973 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 37972 |
| [Kulpa] p. 548 | Theorem | broucube 37975 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 37967 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 37968 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2388 axnul 5241 |
| [Kunen] p. 11 | Axiom 3 | axnul 5241 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5225 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8785 mapvalg 8783 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10444 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7892 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9688 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9730 r1elssi 9729 |
| [Kunen] p. 107 | Exercise 4 | rankop 9782 rankopb 9776 rankuni 9787 rankxplim 9803 rankxpsuc 9806 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45381 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45389 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45388 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45390 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45395 rexabso 45396 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45402 n0abso 45403 ssabso 45401 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45404 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45414 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45409 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45412 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45413 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45408 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45420 wfaxpr 45425 wfaxreg 45427 wfaxrep 45421 wfaxsep 45422 wfaxun 45426 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45411 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45424 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45420 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45419 omelaxinf2 45416 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45429 wfaxinf2 45428 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45442 permaxext 45432 permaxinf2 45440 permaxnul 45435 permaxpow 45436 permaxpr 45437 permaxrep 45433 permaxsep 45434 permaxun 45438 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45430 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45441 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4947 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33809 |
| [Lang] p. | Definition | df-rn 5642 |
| [Lang] p. 3 | Statement | lidrideqd 18637 mndbn0 18718 |
| [Lang] p. 3 | Definition | df-mnd 18703 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18655 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18809 |
| [Lang] p. 5 | Equation | gsumreidx 19892 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48652 |
| [Lang] p. 6 | Example | nn0mnd 48649 |
| [Lang] p. 6 | Equation | gsumxp2 19955 |
| [Lang] p. 6 | Statement | cycsubm 19177 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19056 |
| [Lang] p. 6 | Observation | mndlsmidm 19645 |
| [Lang] p. 7 | Definition | dfgrp2e 18939 |
| [Lang] p. 30 | Definition | df-tocyc 33168 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33213 |
| [Lang] p. 32 | Property (b) | cyc3conja 33218 cycpmconjv 33203 |
| [Lang] p. 53 | Definition | df-cat 17634 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18064 cat1lem 18063 |
| [Lang] p. 54 | Definition | df-iso 17716 |
| [Lang] p. 57 | Definition | df-inito 17951 df-termo 17952 |
| [Lang] p. 58 | Example | irinitoringc 21459 |
| [Lang] p. 58 | Statement | initoeu1 17978 termoeu1 17985 |
| [Lang] p. 62 | Definition | df-func 17825 |
| [Lang] p. 65 | Definition | df-nat 17913 |
| [Lang] p. 91 | Note | df-ringc 20623 |
| [Lang] p. 92 | Statement | mxidlprm 33530 |
| [Lang] p. 92 | Definition | isprmidlc 33507 |
| [Lang] p. 128 | Remark | dsmmlmod 21725 |
| [Lang] p. 129 | Proof | lincscm 48900 lincscmcl 48902 lincsum 48899 lincsumcl 48901 |
| [Lang] p. 129 | Statement | lincolss 48904 |
| [Lang] p. 129 | Observation | dsmmfi 21718 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33771 qusdimsum 33772 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33752 |
| [Lang] p. 147 | Definition | snlindsntor 48941 |
| [Lang] p. 504 | Statement | mat1 22412 matring 22408 |
| [Lang] p. 504 | Definition | df-mamu 22356 |
| [Lang] p. 505 | Statement | mamuass 22367 mamutpos 22423 matassa 22409 mattposvs 22420 tposmap 22422 |
| [Lang] p. 513 | Definition | mdet1 22566 mdetf 22560 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22656 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22552 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22576 |
| [Lang] p. 515 | Definition | df-minmar1 22600 smadiadetr 22640 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22575 mdetralt 22573 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22588 |
| [Lang] p. 518 | Definition | df-madu 22599 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22610 madurid 22609 matinv 22642 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22855 |
| [Lang], p. 190 | Chapter 6 | vieta 33724 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33838 finextalg 33842 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33807 fedgmul 33775 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33869 |
| [Lang], p. 561 | Remark | chpmatply1 22797 |
| [Lang], p. 561 | Definition | df-chpmat 22792 |
| [Lang2] p. 3 | Notations | df-ind 12160 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44761 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44756 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44762 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5241 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2716 wl-df.clab 37823 |
| [Levy] p. 59 | Definition | df-ttrcl 9629 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9675 |
| [Levy] p. 338 | Axiom | df-clel 2812 df-cleq 2729 wl-df.clel 37827 wl-df.cleq 37824 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2812 df-cleq 2729 wl-df.clel 37827 wl-df.cleq 37824 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2716 wl-df.clab 37823 |
| [Levy] p. 358 | Axiom | df-clab 2716 wl-df.clab 37823 |
| [Levy58] p. 2 | Definition I | isfin1-3 10308 |
| [Levy58] p. 2 | Definition II | df-fin2 10208 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10207 |
| [Levy58] p. 2 | Definition III | df-fin3 10210 |
| [Levy58] p. 3 | Definition V | df-fin5 10211 |
| [Levy58] p. 3 | Definition IV | df-fin4 10209 |
| [Levy58] p. 4 | Definition VI | df-fin6 10212 |
| [Levy58] p. 4 | Definition VII | df-fin7 10213 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10337 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27650 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27661 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27693 nosupbnd1 27678 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27695 nosupbnd2 27680 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27699 noetasuplem4 27700 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27696 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1770 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1771 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1773 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32479 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32483 mdsymi 32482 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32477 mdsymlem6 32479 mdsymlem7 32480 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32481 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32384 ssdmd2 32385 ssmd1 32382 ssmd2 32383 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32380 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32352 df-md 32351 mdbr 32365 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32402 mdslj1i 32390 mdslj2i 32391 mdslle1i 32388 mdslle2i 32389 mdslmd1i 32400 mdslmd2i 32401 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32392 mdsl2bi 32394 mdsl2i 32393 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32406 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32403 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32404 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32381 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32386 mdsl3 32387 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32405 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32500 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39767 hlrelat1 39846 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39485 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32407 cvmdi 32395 cvnbtwn4 32360 cvrnbtwn4 39725 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32408 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39786 cvp 32446 cvrp 39862 lcvp 39486 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32470 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32469 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39779 hlexch4N 39838 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32472 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 39889 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40195 atpsubN 40199 df-pointsN 39948 pointpsubN 40197 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 39950 pmap11 40208 pmaple 40207 pmapsub 40214 pmapval 40203 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40211 pmap1N 40213 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40216 pmapglb2N 40217 pmapglb2xN 40218 pmapglbx 40215 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40298 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 39923 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40242 paddclN 40288 paddidm 40287 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 39924 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40284 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 39923 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 39924 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19650 lsmmod2 19651 lssats 39458 shatomici 32429 shatomistici 32432 shmodi 31461 shmodsi 31460 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32371 mdsymlem7 32480 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31660 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31564 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32486 |
| [Margaris] p. 40 | Rule C | exlimiv 1932 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 396 df-ex 1782 df-or 849 dfbi2 474 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30470 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45341 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45342 |
| [Margaris] p. 79 | Rule C | exinst01 45052 exinst11 45053 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1978 19.2g 2196 r19.2z 4440 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2210 rr19.3v 3610 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2165 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1828 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1783 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2189 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2213 19.9h 2293 exlimd 2226 exlimdh 2297 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2168 excomim 2169 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2333 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30471 conventions-labels 30471 conventions-labels 30471 conventions-labels 30471 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1829 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44805 albi 1820 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2233 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2234 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44807 exbi 1849 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2237 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44804 2alimdv 1920 alimd 2220 alimdh 1819 alimdv 1918 ax-4 1811 ralimdaa 3239 ralimdv 3152 ralimdva 3150 ralimdvva 3185 sbcimdv 3798 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2215 19.21h 2294 19.21t 2214 19.21vv 44803 alrimd 2223 alrimdd 2222 alrimdh 1865 alrimdv 1931 alrimi 2221 alrimih 1826 alrimiv 1929 alrimivv 1930 bj-alrimdh 36889 hbralrimi 3128 r19.21be 3231 r19.21bi 3230 ralrimd 3243 ralrimdv 3136 ralrimdva 3138 ralrimdvv 3182 ralrimdvva 3193 ralrimi 3236 ralrimia 3237 ralrimiv 3129 ralrimiva 3130 ralrimivv 3179 ralrimivva 3181 ralrimivvva 3184 ralrimivw 3134 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44806 2eximdv 1921 bj-exim 36904 exim 1836 eximd 2224 eximdh 1866 eximdv 1919 rexim 3079 reximd2a 3248 reximdai 3240 reximdd 45578 reximddv 3154 reximddv2 3197 reximddv3 3155 reximdv 3153 reximdv2 3148 reximdva 3151 reximdvai 3149 reximdvva 3186 reximi2 3071 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2219 19.23bi 2199 19.23h 2295 19.23t 2218 exlimdv 1935 exlimdvv 1936 exlimexi 44951 exlimiv 1932 exlimivv 1934 rexlimd3 45574 rexlimdv 3137 rexlimdv3a 3143 rexlimdva 3139 rexlimdva2 3141 rexlimdvaa 3140 rexlimdvv 3194 rexlimdvva 3195 rexlimdvvva 3196 rexlimdvw 3144 rexlimiv 3132 rexlimiva 3131 rexlimivv 3180 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1993 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1882 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1872 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2235 r19.27z 4451 r19.27zv 4452 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2236 19.28vv 44813 r19.28z 4443 r19.28zf 45589 r19.28zv 4447 rr19.28v 3611 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1875 r19.29d2r 3125 r19.29imd 3103 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1883 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2242 19.31vv 44811 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2241 r19.32 47540 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44809 19.33 1886 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1994 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1879 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2238 19.36vv 44810 r19.36zv 4453 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2240 19.37vv 44812 r19.37zv 4448 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1841 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1992 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1889 19.40 1888 r19.40 3104 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2243 19.41rg 44977 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2244 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1884 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2245 r19.44zv 4450 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2246 r19.45zv 4449 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2611 |
| [Mayet] p. 370 | Remark | jpi 32341 largei 32338 stri 32328 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32283 ishst 32285 |
| [Mayet3] p. 10 | Theorem | hstrbi 32337 hstri 32336 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31799 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31800 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32349 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31403 chsupcl 31411 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32431 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32425 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32452 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40429 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18453 latj32 18451 latjass 18449 |
| [Megill] p. 444 | Axiom C5 | ax-5 1912 ax5ALT 39353 |
| [Megill] p. 444 | Section 7 | conventions 30470 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39347 ax-c11n 39334 axc11n 2431 |
| [Megill] p. 446 | Lemma L17 | equtrr 2024 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39342 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39374 hbnae 2437 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2486 sbid 2263 sbidd-misc 50188 sbidd 50187 |
| [Megill] p. 448 | Remark 9.6 | axc14 2468 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39330 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39329 sp 2191 |
| [Megill] p. 448 | Scheme C6' | ax-11 2163 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39331 |
| [Megill] p. 448 | Scheme C8' | ax-7 2010 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39336 |
| [Megill] p. 448 | Scheme C10' | ax-6 1969 ax-c10 39332 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39333 |
| [Megill] p. 448 | Scheme C12' | ax-8 2116 |
| [Megill] p. 448 | Scheme C13' | ax-9 2124 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39337 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39335 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39338 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39350 dral1 2444 dral2-o 39376 dral2 2443 drex1 2446 drex2 2447 drsb1 2500 drsb2 2274 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2179 sbequ 2089 sbid2v 2514 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39343 hba1 2300 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47334 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3818 rspsbca 3819 stdpc4 2074 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39330 ra4 3825 stdpc5 2216 |
| [Mendelson] p. 81 | Rule C | exlimiv 1932 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2030 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2258 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3727 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5469 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4339 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4340 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4218 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4275 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4219 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4082 |
| [Mendelson] p. 231 | Definition of union | dfun3 4217 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5404 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4848 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5522 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4560 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5523 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4875 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5782 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6234 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7729 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6330 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8531 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9078 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8999 xpsneng 9000 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9006 xpcomeng 9007 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9009 |
| [Mendelson] p. 255 | Definition | brsdom 8921 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9002 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8777 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8984 mapsnend 8983 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9084 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9083 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8830 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8987 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9003 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10101 djucomen 10100 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10105 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10099 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8466 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8493 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10481 |
| [Mendelson] p. 281 | Definition | df-r1 9688 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9737 |
| [Mendelson] p. 287 | Axiom system MK | ru 3727 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30329 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30364 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30366 vdgn1frgrv3 30367 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30368 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30361 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30354 2pthfrgrrn 30352 2pthfrgrrn2 30353 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31323 |
| [Monk1] p. 22 | Remark | conventions 30470 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30470 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4180 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5739 ssrelf 32688 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5740 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5149 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6228 coi2 6229 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5876 rn0 5882 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6106 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5649 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5885 rnxp 6135 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5730 xp0 5731 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6043 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6040 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7865 imaexg 7864 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6037 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7028 funfvop 7003 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6895 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6906 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6545 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7209 dff13f 7210 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7174 funrnex 7907 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7202 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6192 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4907 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7959 df-1st 7942 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7960 df-2nd 7943 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9778 ranksnb 9751 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9779 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9780 rankunb 9774 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9762 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9688 r1val2 9761 |
| [Monk1] p. 117 | Lemma | zorn2 10428 zorn2g 10425 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9910 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10483 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9905 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1811 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2010 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2185 ax-c15 39335 ax12v2 2187 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39330 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2163 |
| [Monk2] p. 109 | Lemma 15 | equvini 2460 equvinv 2031 eqvinop 5441 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1912 ax5ALT 39353 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2147 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2163 |
| [Monk2] p. 114 | Lemma 21 | sp 2191 |
| [Monk2] p. 114 | Lemma 22 | axc4 2327 hba1-o 39343 hba1 2300 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2159 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2182 nfra2 3339 nfra2w 3274 |
| [Moore] p. 53 | Part I | df-mre 17548 |
| [Munkres] p. 77 | Example 2 | distop 22960 indistop 22967 indistopon 22966 |
| [Munkres] p. 77 | Example 3 | fctop 22969 fctop2 22970 |
| [Munkres] p. 77 | Example 4 | cctop 22971 |
| [Munkres] p. 78 | Definition of basis | df-bases 22911 isbasis3g 22914 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17406 tgval2 22921 |
| [Munkres] p. 79 | Remark | tgcl 22934 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22928 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22952 tgss3 22951 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22953 basgen2 22954 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37665 topdifinfeq 37666 topdifinffin 37664 topdifinfindis 37662 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23125 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23003 topcld 23000 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23004 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23006 |
| [Munkres] p. 94 | Definition of closure | clsval 23002 |
| [Munkres] p. 94 | Definition of interior | ntrval 23001 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23040 elcls 23038 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23048 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23113 neindisj 23082 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23115 |
| [Munkres] p. 97 | Definition of limit point | islp2 23110 lpval 23104 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23280 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23192 iscn 23200 iscn2 23203 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23245 cncnp2 23246 cncnpi 23243 df-cnp 23193 iscnp 23202 iscnp2 23204 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24508 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25278 |
| [Nathanson] p. 123 | Remark | reprgt 34765 reprinfz1 34766 reprlt 34763 |
| [Nathanson] p. 123 | Definition | df-repr 34753 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34785 |
| [Nathanson] p. 123 | Proposition | breprexp 34777 breprexpnat 34778 itgexpif 34750 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32175 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48280 |
| [Pfenning] p. 17 | Definition XM | natded 30473 |
| [Pfenning] p. 17 | Definition NNC | natded 30473 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30473 |
| [Pfenning] p. 18 | Rule" | natded 30473 |
| [Pfenning] p. 18 | Definition /\I | natded 30473 |
| [Pfenning] p. 18 | Definition ` `E | natded 30473 natded 30473 natded 30473 natded 30473 natded 30473 |
| [Pfenning] p. 18 | Definition ` `I | natded 30473 natded 30473 natded 30473 natded 30473 natded 30473 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30473 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30473 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30473 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30473 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30473 |
| [Pfenning] p. 127 | Definition =E | natded 30473 |
| [Pfenning] p. 127 | Definition =I | natded 30473 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25169 df-dip 30772 dip0l 30789 ip0l 21616 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25210 ipval 30774 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30785 ipcj 21614 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25172 dipdir 30913 ipdir 21619 ipdiri 30901 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30781 nmsq 25161 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30896 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30898 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30899 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25178 dipass 30916 ipass 21625 ipassi 30912 |
| [Prugovecki] p. 186 | Definition of bra | braval 32015 df-bra 31921 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31922 kbval 32025 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32453 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40334 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32467 atcvat4i 32468 cvrat3 39888 cvrat4 39889 lsatcvat3 39498 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32353 cvrval 39715 df-cv 32350 df-lcv 39465 lspsncv0 21144 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40346 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40347 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2716 rabid 3411 rabidd 45585 wl-df.clab 37823 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2286 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2729 wl-df.cleq 37824 |
| [Quine] p. 19 | Definition 2.9 | conventions 30470 df-v 3432 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2876 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2873 abid2f 2930 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2283 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2091 sbalex 2250 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2812 wl-df.clel 37827 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2737 eqid1 30537 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2744 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3730 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3731 dfsbcq2 3732 |
| [Quine] p. 43 | Theorem 6.8 | vex 3434 |
| [Quine] p. 43 | Theorem 6.9 | isset 3444 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3534 spcgv 3539 spcimgf 3496 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3742 spsbcd 3743 |
| [Quine] p. 44 | Theorem 6.12 | elex 3451 |
| [Quine] p. 44 | Theorem 6.13 | elab 3623 elabg 3620 elabgf 3618 |
| [Quine] p. 44 | Theorem 6.14 | noel 4279 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4662 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4571 df-sn 4569 |
| [Quine] p. 49 | Theorem 7.4 | snss 4729 snssg 4728 |
| [Quine] p. 49 | Theorem 7.5 | prss 4764 prssg 4763 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4707 prid1g 4705 prid2 4708 prid2g 4706 snid 4607 snidg 4605 |
| [Quine] p. 51 | Theorem 7.12 | snex 5382 |
| [Quine] p. 51 | Theorem 7.13 | prex 5381 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4870 unisnALT 45352 unisng 4869 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4874 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4882 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4879 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6469 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47528 dfiota2 6456 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47537 iotaval 6473 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6479 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6475 |
| [Quine] p. 58 | Definition 9.1 | df-op 4575 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5480 opabidw 5479 opelopab 5497 opelopaba 5491 opelopabaf 5499 opelopabf 5500 opelopabg 5493 opelopabga 5488 opelopabgf 5495 oprabid 7399 oprabidw 7398 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5637 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5639 |
| [Quine] p. 64 | Definition 9.15 | df-id 5526 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6564 |
| [Quine] p. 65 | Theorem 10.4 | funi 6531 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6552 funsng 6550 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6501 |
| [Quine] p. 65 | Definition 10.2 | args 6058 dffv4 6838 |
| [Quine] p. 68 | Definition 10.11 | conventions 30470 df-fv 6507 fv2 6836 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14234 nn0opth2i 14233 nn0opthi 14232 omopthi 8597 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8349 |
| [Quine] p. 232 | Equation i | carddom 10476 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6587 funimaexg 6586 |
| [Quine] p. 331 | Axiom system NF | ru 3727 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31155 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30772 polid 31230 polid2i 31228 polidi 31229 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30884 |
| [ReedSimon] p. 195 | Remark | lnophm 32090 lnophmi 32089 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32203 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32205 leopmuli 32204 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32208 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31923 leoppos 32197 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32207 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32196 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48081 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48089 |
| [Roman] p. 4 | Definition | df-dmat 22455 df-dmatalt 48868 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20134 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20216 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 48955 |
| [Roman] p. 112 | Note | isldepslvec2 48955 ldepsnlinc 48978 zlmodzxznm 48967 |
| [Roman] p. 112 | Example | zlmodzxzequa 48966 zlmodzxzequap 48969 zlmodzxzldep 48974 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22855 |
| [Rosenlicht] p. 80 | Theorem | heicant 37976 |
| [Rosser] p. 281 | Definition | df-op 4575 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34789 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34790 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48836 pmtr3ncom 19450 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19446 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19389 cayleyth 19390 |
| [Rudin] p. 164 | Equation 27 | efcan 16061 |
| [Rudin] p. 164 | Equation 30 | efzval 16069 |
| [Rudin] p. 167 | Equation 48 | absefi 16163 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 197 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1773 |
| [Sanford] p. 39 | Rule 4 | mptxor 1771 |
| [Sanford] p. 40 | Rule 1 | mptnan 1770 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6079 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6082 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6078 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6076 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17548 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17549 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17549 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17551 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10059 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43490 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10368 axdc3 10376 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20218 isrngo 38218 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31613 |
| [Schechter] p. 276 | Definition of span | df-span 31380 spanval 31404 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22958 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6349 onelord 43679 ordelon 6348 ordelord 6346 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43680 sucidg 6407 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6379 onsuc 7764 ord0 6378 ordsuci 7762 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43681 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5197 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43456 elon2 6335 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6330 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5534 epelg 5532 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9514 epirron 43682 ordirr 6342 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43684 oneptr 43683 ontr1 6371 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6367 oneptri 43685 ordtri3or 6356 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8436 ord0eln0 6380 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6393 onsucss 43694 trsucss 6414 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7769 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6420 ordnbtwn 6419 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43696 ordnexbtwnsuc 43695 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10323 onsucf1lem 43697 onsucf1o 43700 onsucf1olem 43698 onsucrn 43699 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43701 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7796 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43690 ordne0gt0 43689 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43692 limnsuc 43693 onsucelab 43691 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9564 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7811 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9567 ordom 7827 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9568 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8576 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7734 ssorduni 7733 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8466 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9571 limom 7833 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8405 df1o2 8412 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8451 oa0suclim 43703 oalim 8467 oasuc 8459 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8452 om0suclim 43704 omlim 8468 omsuc 8461 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8457 oe0m1 8456 oe0suclim 43705 oelim 8469 oesuc 8462 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43657 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43707 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43708 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43709 limexissupab 43711 limiun 43710 limuni 6386 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8473 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8477 om1om1r 43712 om1r 8478 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8470 oaomoecl 43706 oecl 8472 omcl 8471 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43659 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8479 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8480 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43713 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43714 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8547 nnamecl 43715 nnecl 8549 nnmcl 8548 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43716 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8487 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8488 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8495 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43718 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43719 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43721 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8494 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43725 omword1 8508 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43724 oaordnrex 43723 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43720 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43726 omword2 8509 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43727 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43728 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43729 omordi 8501 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8503 omord2com 43730 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43731 df-2o 8406 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43734 oewordi 8527 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43735 oeworde 8529 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43736 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43737 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43733 omnord1ex 43732 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43738 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43740 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43744 oenord1ex 43743 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43745 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8496 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43739 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8514 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8515 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43747 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8533 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43748 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43749 cantnfub2 43750 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43753 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 28983 axtgcgrrflx 28530 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 28984 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 28985 axtgcgrid 28531 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28516 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 28996 axtgsegcon 28532 df-trkgcb 28518 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29007 axtg5seg 28533 df-trkgcb 28518 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29008 axtgbtwnid 28534 df-trkgb 28517 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29010 axtgpasch 28535 df-trkgb 28517 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29029 df-trkg2d 34809 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28538 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28539 df-trkg2d 34809 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29032 axtgeucl 28540 df-trkge 28519 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29045 axtgcont 28537 axtgcont1 28536 df-trkgb 28517 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36169 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36171 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36174 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36178 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36179 tgcgrcomimp 28545 tgcgrcoml 28547 tgcgrcomr 28546 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36184 tgcgrtriv 28552 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36188 tg5segofs 34817 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34814 df-ofs 36165 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36190 tgcgrextend 28553 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36192 tgsegconeq 28554 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36204 btwntriv2 36194 tgbtwntriv2 28555 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36195 tgbtwncom 28556 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36198 tgbtwntriv1 28559 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36199 tgbtwnswapid 28560 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36205 btwnintr 36201 tgbtwnexch2 28564 tgbtwnintr 28561 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36207 btwnexch3 36202 tgbtwnexch 28566 tgbtwnexch3 28562 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36206 tgbtwnouttr 28565 tgbtwnouttr2 28563 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29028 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36209 tgbtwndiff 28574 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28567 trisegint 36210 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36226 tgifscgr 28576 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28626 colrot1 28627 colrot2 28628 lncom 28690 lnrot1 28691 lnrot2 28692 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36222 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36227 tgcgrsub 28577 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36237 tgcgrxfr 28586 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28585 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36223 df-cgrg 28579 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28579 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36238 tgbtwnxfr 28598 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36244 colinearperm2 36246 colinearperm3 36245 colinearperm4 36247 colinearperm5 36248 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28601 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36221 tgellng 28621 tglng 28614 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36249 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36257 lnxfr 28634 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36258 lnext 28635 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36262 tgfscgr 28636 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36263 lncgr 28637 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36224 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36265 lnid 28638 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36266 tgidinside 28639 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36283 tgbtwnconn1 28643 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36284 tgbtwnconn2 28644 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36285 tgbtwnconn3 28645 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36291 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36289 legov 28653 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28654 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28667 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36292 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36294 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36296 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36297 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36298 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36295 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36300 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28655 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28657 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28658 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28659 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28660 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36307 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36308 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36303 df-outsideof 36302 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36304 ishlg 28670 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28675 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28677 outsideofrflx 36309 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28671 hlcomd 28672 outsideofcom 36310 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28678 outsideoftr 36311 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28686 outsideofeu 36313 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36320 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36321 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36314 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36329 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36330 tglineelsb2 28700 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36332 linerflx1 36331 linerflx2 36333 tglinecom 28703 tglinerflx1 28701 tglinerflx2 28702 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36335 tglinethru 28704 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36319 tglng 28614 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28662 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36338 tglinethrueu 28707 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36339 tglineineq 28711 tglineinteq 28713 tglineintmo 28710 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28717 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28718 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28719 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28734 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28730 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28722 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28721 ismir 28727 mirbtwn 28726 mircgr 28725 mirfv 28724 mirval 28723 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28732 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28733 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28734 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28737 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28738 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28743 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28740 mirbtwni 28739 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28741 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28753 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28757 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28754 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28755 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28756 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28759 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28760 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28766 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28762 israg 28765 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28767 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28768 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28770 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28771 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28772 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28773 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28774 ragncol 28777 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28775 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28781 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28785 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28782 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28764 isperp 28780 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28783 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28790 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28798 colperpexlem2 28799 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28801 colperpexlem3 28800 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28806 midex 28805 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28803 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28812 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28807 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28816 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28819 opphllem6 28820 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28822 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28535 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28823 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28831 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28826 hpgbr 28828 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28833 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28832 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28834 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28835 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28836 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28837 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28838 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28852 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28842 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28856 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28857 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28858 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28859 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28860 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28863 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28865 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28843 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28866 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28869 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28870 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28871 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28872 trgcopyeu 28874 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28898 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28877 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28886 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28884 cgrahl2 28885 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28887 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28888 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28890 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28891 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28894 cgrahl 28895 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28899 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28900 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28901 acopyeu 28902 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28909 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28913 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28906 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28921 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28914 isleag 28915 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28923 tgsas1 28922 tgsas2 28924 tgsas3 28925 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28927 tgasa1 28926 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28928 tgsss2 28929 tgsss3 28930 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27234 dchrsum 27232 dchrsum2 27231 sumdchr 27235 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27236 sum2dchr 27237 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20043 ablfacrp2 20044 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27179 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27180 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27187 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27445 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27448 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27502 vmalogdivsum2 27501 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27492 dirith2 27491 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27490 rpvmasum 27489 rpvmasum2 27475 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27450 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27488 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27455 dchrisumlem1 27452 dchrisumlem2 27453 dchrisumlem3 27454 dchrisumlema 27451 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27458 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27487 dchrmusumlem 27485 dchrvmasumlem 27486 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27457 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27459 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27483 dchrisum0re 27476 dchrisumn0 27484 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27469 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27473 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27474 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27529 pntrsumbnd2 27530 pntrsumo1 27528 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27493 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27495 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27497 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27500 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27505 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27506 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27511 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27513 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27514 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27522 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27523 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27520 selberg3lem2 27521 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27524 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27518 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27531 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27532 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27533 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27547 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27559 pntlemb 27560 pntlemc 27558 pntlemd 27557 pntlemg 27561 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27559 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27551 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27556 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27559 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27572 pntleml 27574 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33887 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33874 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 33906 constrinvcl 33917 constrmulcl 33915 constrnegcl 33907 constrsqrtcl 33923 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 33893 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 33903 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 33925 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 33935 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4247 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4346 dif0 4319 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4432 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4416 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4238 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4239 |
| [Stoll] p. 20 | Remark | invdif 4220 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4577 |
| [Stoll] p. 43 | Definition | uniiun 5002 |
| [Stoll] p. 44 | Definition | intiin 5003 |
| [Stoll] p. 45 | Definition | df-iin 4937 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4936 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 401 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4247 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44762 |
| [Suppes] p. 22 | Theorem 2 | eq0 4291 eq0f 4288 |
| [Suppes] p. 22 | Theorem 4 | eqss 3938 eqssd 3940 eqssi 3939 |
| [Suppes] p. 23 | Theorem 5 | ss0 4343 ss0b 4342 |
| [Suppes] p. 23 | Theorem 6 | sstr 3931 sstrALT2 45261 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4044 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4045 |
| [Suppes] p. 23 | Theorem 9 | psstr 4048 |
| [Suppes] p. 23 | Theorem 10 | pssss 4039 |
| [Suppes] p. 25 | Theorem 12 | elin 3906 elun 4094 |
| [Suppes] p. 26 | Theorem 15 | inidm 4168 |
| [Suppes] p. 26 | Theorem 16 | in0 4336 |
| [Suppes] p. 27 | Theorem 23 | unidm 4098 |
| [Suppes] p. 27 | Theorem 24 | un0 4335 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4119 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4127 |
| [Suppes] p. 27 | Theorem 27 | unss 4131 |
| [Suppes] p. 27 | Theorem 28 | indir 4227 |
| [Suppes] p. 27 | Theorem 29 | undir 4228 |
| [Suppes] p. 28 | Theorem 32 | difid 4317 |
| [Suppes] p. 29 | Theorem 33 | difin 4213 |
| [Suppes] p. 29 | Theorem 34 | indif 4221 |
| [Suppes] p. 29 | Theorem 35 | undif1 4417 |
| [Suppes] p. 29 | Theorem 36 | difun2 4422 |
| [Suppes] p. 29 | Theorem 37 | difin0 4415 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4413 |
| [Suppes] p. 29 | Theorem 39 | difundi 4231 |
| [Suppes] p. 29 | Theorem 40 | difindi 4233 |
| [Suppes] p. 30 | Theorem 41 | nalset 5250 |
| [Suppes] p. 39 | Theorem 61 | uniss 4859 |
| [Suppes] p. 39 | Theorem 65 | uniop 5470 |
| [Suppes] p. 41 | Theorem 70 | intsn 4927 |
| [Suppes] p. 42 | Theorem 71 | intpr 4925 intprg 4924 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5425 |
| [Suppes] p. 42 | Theorem 78 | intun 4923 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4975 dfiun2g 4973 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4976 |
| [Suppes] p. 47 | Theorem 86 | elpw 4546 elpw2 5276 elpw2g 5275 elpwg 4545 elpwgdedVD 45343 |
| [Suppes] p. 47 | Theorem 87 | pwid 4564 |
| [Suppes] p. 47 | Theorem 89 | pw0 4756 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4757 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5646 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5789 xpindir 5790 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5700 xpundir 5701 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9512 |
| [Suppes] p. 58 | Theorem 2 | relss 5738 |
| [Suppes] p. 59 | Theorem 4 | eldm 5856 eldm2 5857 eldm2g 5855 eldmg 5854 |
| [Suppes] p. 59 | Definition 3 | df-dm 5641 |
| [Suppes] p. 60 | Theorem 6 | dmin 5867 |
| [Suppes] p. 60 | Theorem 8 | rnun 6110 |
| [Suppes] p. 60 | Theorem 9 | rnin 6111 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5844 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5838 brcnvg 5835 |
| [Suppes] p. 62 | Equation 5 | elcnv 5832 elcnv2 5833 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6070 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6109 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6107 |
| [Suppes] p. 63 | Definition | dftrrels2 38980 |
| [Suppes] p. 63 | Theorem 20 | co02 6226 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5931 |
| [Suppes] p. 63 | Definition 7 | df-co 5640 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5841 |
| [Suppes] p. 64 | Theorem 27 | coass 6231 |
| [Suppes] p. 65 | Theorem 31 | resundi 5959 |
| [Suppes] p. 65 | Theorem 34 | elima 6031 elima2 6032 elima3 6033 elimag 6030 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6114 |
| [Suppes] p. 66 | Theorem 40 | dminss 6118 |
| [Suppes] p. 66 | Theorem 41 | imainss 6119 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6122 |
| [Suppes] p. 81 | Definition 34 | dfec2 8646 |
| [Suppes] p. 82 | Theorem 72 | elec 8690 elecALTV 38592 elecg 8688 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39016 erth 8698 erth2 8699 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39019 erdisj 8701 |
| [Suppes] p. 83 | Definition 35, | df-parts 39189 dfmembpart2 39194 |
| [Suppes] p. 89 | Theorem 96 | map0b 8831 |
| [Suppes] p. 89 | Theorem 97 | map0 8835 map0g 8832 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8836 mapsnd 8834 |
| [Suppes] p. 89 | Theorem 99 | mapss 8837 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 9990 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 9989 |
| [Suppes] p. 92 | Theorem 1 | enref 8932 enrefg 8931 |
| [Suppes] p. 92 | Theorem 2 | ensym 8950 ensymb 8949 ensymi 8951 |
| [Suppes] p. 92 | Theorem 3 | entr 8953 |
| [Suppes] p. 92 | Theorem 4 | unen 8992 |
| [Suppes] p. 94 | Theorem 15 | endom 8926 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8947 |
| [Suppes] p. 94 | Theorem 17 | domtr 8954 |
| [Suppes] p. 95 | Theorem 18 | sbth 9035 |
| [Suppes] p. 97 | Theorem 23 | canth2 9068 canth2g 9069 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9039 df-sdom 8896 dfsdom2 9038 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9052 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9041 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9040 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9050 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8929 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9053 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9048 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8978 fundmeng 8979 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9013 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9049 |
| [Suppes] p. 104 | Theorem 37 | fofi 9223 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9229 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9229 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10473 |
| [Suppes] p. 130 | Definition 3 | df-tr 5194 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7734 |
| [Suppes] p. 134 | Definition 6 | df-suc 6330 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7851 finds 7847 finds1 7850 finds2 7849 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9573 isfinite2 9208 isfiniteg 9210 unbnn 9206 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10841 df-ltpq 10833 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7814 tfinds 7811 tfinds2 7815 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8486 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8488 |
| [Suppes] p. 211 | Theorem 25 | oaass 8496 |
| [Suppes] p. 225 | Definition 8 | iscard2 9900 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10485 |
| [Suppes] p. 228 | Theorem 59 | harcard 9902 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 9988 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6376 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7747 onminsb 7748 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10495 |
| [Suppes] p. 229 | Theorem 65 | alephcard 9992 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 9999 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 9993 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9864 |
| [Suppes] p. 242 | Theorem 6 | weth 10417 |
| [Suppes] p. 242 | Theorem 8 | entric 10479 |
| [Suppes] p. 242 | Theorem 9 | carden 10473 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35878 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35882 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2709 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2729 wl-df.cleq 37824 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2812 wl-df.clel 37827 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2731 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2757 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7371 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3727 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5364 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4593 elpr2 4595 elpr2g 4594 elprg 4591 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4583 elsn2 4610 elsn2g 4609 elsng 4582 velsn 4584 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5421 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4578 sneqr 4784 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4589 dfsn2 4581 dfsn2ALT 4590 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7695 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5430 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5417 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5401 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7698 unexg 7697 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4636 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4852 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3897 df-un 3895 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4868 uniprg 4867 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5320 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4634 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6396 elsucg 6394 sstr2 3929 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4099 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4150 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4113 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4169 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4225 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4226 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3910 df-ss 3907 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4544 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4128 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3908 sseqin2 4164 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3945 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4178 inss2 4179 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3987 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4862 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5402 sspwimp 45344 sspwimpALT 45351 sspwimpALT2 45354 sspwimpcf 45346 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5409 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5213 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3391 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5243 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3893 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 36835 dfnul2 4277 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4317 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4294 n0f 4290 neq0 4293 neq0f 4289 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9511 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9653 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9668 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3432 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5256 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4341 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5263 ssexg 5265 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5259 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9522 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9514 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4307 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4076 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4241 undif3VD 45308 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4077 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4084 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3053 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3063 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7707 xpexg 7704 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5638 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6570 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6746 fun11 6573 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6512 svrelfun 6571 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5843 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5845 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5643 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5644 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5640 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6159 dfrel2 6154 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5647 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5767 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5774 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5787 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5971 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5951 opelresi 5953 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5978 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5967 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5972 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6541 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6074 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6539 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6748 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2610 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30470 df-fv 6507 fv3 6859 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7876 cnvexg 7875 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7860 dmexg 7852 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7861 rnexg 7853 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44880 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7871 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6854 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47616 tz6.12-1-afv2 47683 tz6.12-1 6864 tz6.12-afv 47615 tz6.12-afv2 47682 tz6.12 6865 tz6.12c-afv2 47684 tz6.12c 6863 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47679 tz6.12-2 6828 tz6.12i-afv2 47685 tz6.12i 6867 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6502 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6503 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6505 wfo 6497 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6504 wf1 6496 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6506 wf1o 6498 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6984 eqfnfv2 6985 eqfnfv2f 6988 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6939 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7172 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7170 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6587 funimaexg 6586 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5087 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5540 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5592 dffr3 6065 eliniseg 6060 iniseg 6063 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5531 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5608 fr3nr 7726 frirr 5607 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5584 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7728 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5595 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5617 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6312 tz6.26i 6313 wefrc 5625 wereu2 5628 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6314 wfii 6315 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6508 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7284 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7285 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7291 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7292 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7293 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7297 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7304 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7306 |
| [TakeutiZaring] p. 35 | Notation | wtr 5193 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44881 tz7.2 5614 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5198 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6337 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6345 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6346 ordelordALT 44964 ordelordALTVD 45293 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6352 ordelssne 6351 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6350 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6354 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7736 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7737 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6328 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6356 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 44976 ordon 7731 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7732 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7804 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6372 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5195 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7746 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7782 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6430 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6429 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7733 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4882 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6330 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6406 sucidg 6407 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7764 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6420 ordnbtwn 6419 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7779 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6329 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7832 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7837 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7792 ordelsuc 7771 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7773 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7802 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7819 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7840 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7841 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7842 |
| [TakeutiZaring] p. 43 | Remark | omon 7829 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9556 omex 9564 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7827 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7846 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7843 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7844 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7822 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4905 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5212 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4906 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5286 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7749 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6375 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4891 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9581 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7744 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8315 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8336 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8337 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8338 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8345 tz7.44-2 8346 tz7.44-3 8347 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8307 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8302 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8286 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8384 tz7.49c 8385 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8382 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8381 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8383 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2657 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9933 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9934 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8467 oasuc 8459 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7812 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8470 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8451 oa0r 8473 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8471 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8483 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8555 nnaordi 8554 oaord 8482 oaordi 8481 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4993 uniss2 4885 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8485 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8490 oawordex 8492 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8547 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8584 |
| [TakeutiZaring] p. 60 | Remark | oancom 9572 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8495 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8552 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8487 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8454 omlim 8468 omsuc 8461 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8452 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8549 nnmcl 8548 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8568 nnmordi 8567 omord 8503 omordi 8501 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8504 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8572 omwordri 8507 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8474 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8477 om1r 8478 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8510 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8512 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8513 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8514 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8515 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8544 oe0 8457 oelim 8469 oesuc 8462 onesuc 8465 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8455 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8522 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8523 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8456 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8480 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8524 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8530 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8528 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8529 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8533 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8535 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9649 tz9.1 9650 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9688 r10 9692 r1lim 9696 r1limg 9695 r1suc 9694 r1sucg 9693 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9704 r1ord2 9705 r1ordg 9702 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9714 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9739 tz9.13 9715 tz9.13g 9716 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9689 rankval 9740 rankvalb 9721 rankvalg 9741 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9763 rankelb 9748 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9777 rankval3 9764 rankval3b 9750 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9753 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9719 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9758 rankr1c 9745 rankr1g 9756 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9759 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9773 rankssb 9772 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9766 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9765 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10397 dfac3 10043 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9952 numth 10394 numth2 10393 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10468 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10469 cardid2 9877 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9884 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10473 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9883 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9868 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9889 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9881 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9088 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8965 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9093 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9017 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9887 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10020 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9140 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9148 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10021 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9145 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10010 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 9988 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9896 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10138 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9233 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8897 isfi 8922 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9149 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10456 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9010 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10448 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10108 unxpdom 9169 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9898 cardsdomelir 9897 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9171 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9936 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8775 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10484 infxpidm2 9939 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10129 infxp 10136 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9022 pw2f1o 9020 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9081 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10409 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10404 ac6s5 10413 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10465 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10466 uniimadomf 10467 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10196 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10191 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10176 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10173 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10179 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10186 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10195 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10505 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10174 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10198 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10019 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10018 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10030 alephfp2 10031 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10622 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10034 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10492 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10506 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10507 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39329 |
| [Tarski] p. 67 | Scheme B5 | sp 2191 |
| [Tarski] p. 68 | Lemma 6 | avril1 30533 equid 2014 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2019 |
| [Tarski] p. 70 | Lemma 14 | spim 2392 spime 2394 spimew 1973 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2185 ax-c15 39335 ax12i 1968 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2091 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1970 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1912 ax5ALT 39353 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2010 ax-8 2116 ax-9 2124 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28532 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28533 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28535 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28535 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28536 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16210 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 37980 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 37982 |
| [Weierstrass] p. 272 | Definition | df-mdet 22550 mdetuni 22587 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 904 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 869 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 870 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 920 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 970 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37761 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44227 imim2 58 wl-luk-imim2 37756 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47461 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 897 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2664 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37759 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 898 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45353 wl-luk-notnotr 37760 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44257 axfrege28 44256 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 868 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 925 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37753 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 890 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 942 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30471 pm2.27 42 wl-luk-pm2.27 37751 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 923 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38692 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 924 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 972 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 973 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 971 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 907 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 908 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 945 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 882 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 885 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 886 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 852 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 853 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 900 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 943 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 944 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 892 pm2.67 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 975 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 901 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 203 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 976 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 977 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 934 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 978 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 933 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 469 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 995 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 996 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 997 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 998 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 471 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 459 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 402 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 803 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 448 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 482 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 484 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 765 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 766 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 808 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 623 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 810 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 492 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 963 pm3.44 962 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 809 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 473 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 966 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 316 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 261 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 807 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 833 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 222 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 806 bitr 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 563 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 905 pm4.25 906 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 460 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1010 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 871 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 468 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 922 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 634 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 638 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 979 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1008 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1054 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1025 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 999 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1001 pm4.45 1000 pm4.45im 828 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 545 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 988 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 990 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 986 pm4.56 991 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 992 pm4.57 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 857 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 397 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 850 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 851 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 557 pm4.71d 561 pm4.71i 559 pm4.71r 558 pm4.71rd 562 pm4.71ri 560 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 952 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 937 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 517 pm4.76 518 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 964 pm4.77 965 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1006 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 392 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1026 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1027 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 387 impexp 450 pm4.87 844 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 824 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 947 pm5.11g 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 948 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 950 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 949 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1015 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1016 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1014 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 383 pm5.18 381 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 386 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 825 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1017 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1050 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1051 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 902 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 572 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 388 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1004 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 956 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 831 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 836 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 826 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 389 pm5.41 390 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 542 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1007 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 951 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1030 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 270 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1031 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 36886 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44785 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44786 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1872 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44787 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44788 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44789 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1895 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44790 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44791 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44792 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44793 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44794 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44796 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44797 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44798 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44795 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2096 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44801 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44802 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2076 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2166 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1831 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1832 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44803 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44804 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44805 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44806 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44808 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44807 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1889 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44810 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44811 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44809 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1830 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44812 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44813 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1848 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44814 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2351 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1862 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44819 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44815 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44816 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44817 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44818 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44823 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44820 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44821 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44822 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44824 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2570 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44834 pm13.13b 44835 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44836 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3014 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3015 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3609 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44842 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44843 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44837 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 44979 pm13.193 44838 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44839 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44840 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44841 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44848 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44847 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44846 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3792 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44849 pm14.122b 44850 pm14.122c 44851 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44852 pm14.123b 44853 pm14.123c 44854 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44856 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44855 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44857 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6480 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44858 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6481 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44859 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44861 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2634 eupickbi 2637 sbaniota 44862 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44860 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2585 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44863 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30470 df-fv 6507 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9925 pm54.43lem 9924 |
| [Young] p. 141 | Definition of operator ordering | leop2 32195 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32201 idleop 32202 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43256 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43263 pellexlem1 43257 |