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 17723 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17723 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18132 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17744 0funcg 49830 df-termc 50218 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50295 prsthinc 50209 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50323 df-mndtc 50323 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50319 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17767 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50311 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50336 oppgoppchom 50335 oppgoppcid 50337 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17837 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17825 invisoinvl 17846 |
| [Adamek] p. 28 | Example 3.13 | idinv 17845 idiso 17844 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17830 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17804 df-iso 17805 dfiso2 17828 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17811 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17862 cicerALT 49791 |
| [Adamek] p. 29 | Definition 3.15 | cic 17855 df-cic 17852 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17914 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17826 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17827 isoco 17833 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17914 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17937 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50049 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17930 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50319 discthing 50206 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50163 prsthinc 50209 thincciso 50198 thincciso2 50200 thincciso3 50201 thinccisod 50199 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50323 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17944 cofucla 49841 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49907 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18167 catcisoi 50145 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18222 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17963 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17962 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18222 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17987 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17993 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17992 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18207 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18207 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49877 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49868 funcoppc 17931 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18155 elcatchom 50142 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17981 fthoppf 49909 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17980 fulloppf 49908 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18164 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49830 df-catc 18155 |
| [Adamek] p. 45 | Exercise 3G | incat 50346 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50349 nelsubc3 49816 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49896 imasubc2 49897 imasubc3 49901 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17894 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17895 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49816 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17906 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17868 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49905 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49904 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49906 ressffth 17996 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50347 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18002 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18023 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18027 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18003 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18029 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49830 df-inito 18040 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49830 df-termc 50218 initc 49836 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21608 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18041 oppctermo 49981 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18068 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18072 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49982 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18042 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21609 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18075 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17803 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50214 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50213 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50178 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17838 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17840 |
| [Adamek] p. 185 | Section 10.67 | updjud 9919 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50390 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50390 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50390 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50391 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50391 |
| [Adamek] p. 478 | Item Rng | df-ringc 20730 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49295 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49317 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14608 df-pfx 14709 df-substr 14679 df-word 14551 lencl 14570 wrd0 14576 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24844 df-nmoo 31063 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32471 hmopidmchi 32469 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32519 pjcmul2i 32520 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32236 unoplin 32238 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32237 unopadj2 32256 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32331 lnopunii 32330 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32404 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28096 |
| [Alling] p. 184 | Axiom B | bdayfo 27817 |
| [Alling] p. 184 | Axiom O | ltsso 27816 |
| [Alling] p. 184 | Axiom SD | nodense 27832 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27924 |
| [Alling] p. 185 | Theorem | conway 27948 |
| [Alling] p. 185 | Axiom FE | noeta 27883 |
| [Alling] p. 186 | Theorem 4 | lesrec 27968 lesrecd 27969 |
| [Alling], p. 2 | Definition | rp-brsslt 44119 |
| [Alling], p. 3 | Note | nla0001 44122 nla0002 44120 nla0003 44121 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11393 addcan2d 11413 addcan2i 11403 addcand 11412 addcani 11402 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11446 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11505 negsubd 11574 negsubi 11535 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11507 negnegd 11559 negnegi 11527 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11646 subdid 11669 subdii 11662 subdir 11647 subdird 11670 subdiri 11663 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11388 mul01d 11408 mul01i 11399 mul02 11387 mul02d 11407 mul02i 11398 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11850 mulcan2d 11847 mulcand 11846 mulcani 11852 |
| [Apostol] p. 18 | Theorem I.8 | receu 11858 xreceu 33207 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11887 divrecd 11993 divreci 11959 divreczi 11952 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11911 recreci 11946 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11853 mul0ord 11861 mul0ori 11860 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11652 mul2negd 11668 mul2negi 11661 mulneg1 11649 mulneg1d 11666 mulneg1i 11659 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11929 divadddivd 12034 divadddivi 11976 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11914 divmuldivd 12031 divmuldivi 11974 rdivmuldivd 20494 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11915 divdivdivd 12037 divdivdivi 11977 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13039 rpaddcld 13074 rpmulcl 13040 rpmulcld 13075 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13049 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13052 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11335 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11806 ltadd1dd 11824 ltadd1i 11767 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12064 ltmul1a 12063 ltmul1i 12132 ltmul1ii 12142 ltmul2 12065 ltmul2d 13101 ltmul2dd 13115 ltmul2i 12135 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11733 msqgt0d 11780 msqgt0i 11750 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11735 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11719 lt0neg1d 11782 ltneg 11713 ltnegd 11791 ltnegi 11757 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11698 lt2addd 11836 lt2addi 11775 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13016 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12060 recgt0d 12148 recgt0i 12119 recgt0ii 12120 |
| [Apostol] p. 22 | Definition of integers | df-z 12591 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12246 |
| [Apostol] p. 22 | Definition of rationals | df-q 12972 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9413 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12499 |
| [Apostol] p. 26 | Theorem I.29 | arch 12500 archd 45850 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12698 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12501 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12970 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12969 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13224 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16396 zneo 12678 zneoALTV 48401 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26871 msqsqrtd 15494 resqrtth 15306 sqrtth 15416 sqrtthi 15422 sqsqrtd 15493 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12235 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12936 |
| [Apostol] p. 361 | Remark | crreczi 14264 |
| [Apostol] p. 363 | Remark | absgt0i 15451 |
| [Apostol] p. 363 | Example | abssubd 15507 abssubi 15455 |
| [ApostolNT] p. 7 | Remark | fmtno0 48259 fmtno1 48260 fmtno2 48269 fmtno3 48270 fmtno4 48271 fmtno5fac 48301 fmtnofz04prm 48296 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48247 |
| [ApostolNT] p. 8 | Definition | df-ppi 27240 |
| [ApostolNT] p. 14 | Definition | df-dvds 16310 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16326 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16351 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16346 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16339 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16341 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16327 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16328 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16333 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16368 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16370 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16372 |
| [ApostolNT] p. 15 | Definition | df-gcd 16552 dfgcd2 16603 |
| [ApostolNT] p. 16 | Definition | isprm2 16739 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16710 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16974 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16570 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16604 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16606 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16585 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16577 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16769 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16771 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16987 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16981 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16460 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16644 |
| [ApostolNT] p. 24 | Definition | df-mu 27241 |
| [ApostolNT] p. 25 | Definition | df-phi 16824 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27331 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16849 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16834 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16838 |
| [ApostolNT] p. 32 | Definition | df-vma 27238 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27333 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27356 |
| [ApostolNT] p. 38 | Remark | df-sgm 27242 |
| [ApostolNT] p. 38 | Definition | df-sgm 27242 |
| [ApostolNT] p. 75 | Definition | df-chp 27239 df-cht 27237 |
| [ApostolNT] p. 104 | Definition | congr 16721 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16313 |
| [ApostolNT] p. 106 | Definition | moddvds 16320 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16403 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16404 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13921 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13961 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14274 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16345 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16724 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17133 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16726 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16841 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16860 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16842 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27212 |
| [ApostolNT] p. 179 | Definition | df-lgs 27435 lgsprme0 27479 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27480 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27456 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27471 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27528 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27547 2lgsoddprm 27556 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27514 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27523 |
| [ApostolNT] p. 188 | Definition | df-lgs 27435 lgs1 27481 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27472 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27474 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27482 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27483 |
| [Baer] p. 40 | Property (b) | mapdord 42380 |
| [Baer] p. 40 | Property (c) | mapd11 42381 |
| [Baer] p. 40 | Property (e) | mapdin 42404 mapdlsm 42406 |
| [Baer] p. 40 | Property (f) | mapd0 42407 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42367 mapd1o 42390 |
| [Baer] p. 41 | Property (g) | mapdat 42409 |
| [Baer] p. 44 | Part (1) | mapdpg 42448 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42543 mapdheq 42470 mapdheq2 42471 mapdheq2biN 42472 |
| [Baer] p. 45 | Part (3) | baerlem3 42455 |
| [Baer] p. 46 | Part (4) | mapdheq4 42474 mapdheq4lem 42473 |
| [Baer] p. 46 | Part (5) | baerlem5a 42456 baerlem5abmN 42460 baerlem5amN 42458 baerlem5b 42457 baerlem5bmN 42459 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42563 hdmap1l6a 42551 hdmap1l6e 42556 hdmap1l6f 42557 hdmap1l6g 42558 hdmap1l6lem1 42549 hdmap1l6lem2 42550 mapdh6N 42489 mapdh6aN 42477 mapdh6eN 42482 mapdh6fN 42483 mapdh6gN 42484 mapdh6lem1N 42475 mapdh6lem2N 42476 |
| [Baer] p. 48 | Part 9 | hdmapval 42570 |
| [Baer] p. 48 | Part 10 | hdmap10 42582 |
| [Baer] p. 48 | Part 11 | hdmapadd 42585 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42559 mapdh6hN 42485 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42495 mapdh75d 42496 mapdh75e 42494 mapdh75fN 42497 mapdh7cN 42491 mapdh7dN 42492 mapdh7eN 42490 mapdh7fN 42493 |
| [Baer] p. 48 | Part (8) | mapdh8 42530 mapdh8a 42517 mapdh8aa 42518 mapdh8ab 42519 mapdh8ac 42520 mapdh8ad 42521 mapdh8b 42522 mapdh8c 42523 mapdh8d 42525 mapdh8d0N 42524 mapdh8e 42526 mapdh8g 42527 mapdh8i 42528 mapdh8j 42529 |
| [Baer] p. 48 | Part (9) | mapdh9a 42531 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42511 |
| [Baer] p. 49 | Part 12 | hdmap11 42590 hdmapeq0 42586 hdmapf1oN 42607 hdmapneg 42588 hdmaprnN 42606 hdmaprnlem1N 42591 hdmaprnlem3N 42592 hdmaprnlem3uN 42593 hdmaprnlem4N 42595 hdmaprnlem6N 42596 hdmaprnlem7N 42597 hdmaprnlem8N 42598 hdmaprnlem9N 42599 hdmapsub 42589 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42610 hdmap14lem10 42619 hdmap14lem1a 42608 hdmap14lem2N 42611 hdmap14lem2a 42609 hdmap14lem3 42612 hdmap14lem8 42617 hdmap14lem9 42618 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42620 hdmap14lem12 42621 hdmap14lem13 42622 hdmap14lem14 42623 hdmap14lem15 42624 hgmapval 42629 |
| [Baer] p. 50 | Part 15 | hgmapadd 42636 hgmapmul 42637 hgmaprnlem2N 42639 hgmapvs 42633 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42643 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42659 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42660 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42661 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42662 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42664 hgmapvv 42668 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42663 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42665 |
| [Baer] p. 111 | Line 15 | hdmapg 42672 hdmapglem7 42671 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26872 2irrexpqALT 26941 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2595 |
| [BellMachover] p. 460 | Notation | df-mo 2565 |
| [BellMachover] p. 460 | Definition | mo3 2590 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2733 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2737 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5245 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5256 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37666 sepex 5262 |
| [BellMachover] p. 466 | Problem | axpow2 5338 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5339 |
| [BellMachover] p. 466 | Axiom Union | axun2 7734 |
| [BellMachover] p. 468 | Definition | df-ord 6363 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6378 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6385 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6380 |
| [BellMachover] p. 471 | Definition of N | df-om 7862 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7799 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6365 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9610 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7877 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9735 |
| [BellMachover] p. 478 | Definition | rankval2 9789 rankval2b 35458 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9753 r1ord3g 9750 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9557 |
| [BellMachover] p. 488 | Axiom AC | ac5 10460 dfac4 10105 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10093 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40061 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32671 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32713 chirredi 32712 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32701 |
| [Beran] p. 3 | Definition of join | sshjval3 31672 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31934 cmcm2i 31911 cmcm2ii 31916 cmt2N 39992 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31935 lecmi 31920 lecmii 31921 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31909 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31938 cm2ji 31943 cm2mi 31944 |
| [Beran] p. 95 | Definition | df-sh 31525 issh2 31527 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31404 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31417 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31408 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32146 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32148 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32147 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32149 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31400 his1i 31418 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31401 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31402 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31403 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31286 dfhnorm2 31440 normval 31442 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31502 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31291 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31559 |
| [Beran] p. 96 | Definition of converge | df-hlim 31290 hlimi 31506 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31451 norm-i 31447 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31455 norm-ii 31456 normlem0 31427 normlem1 31428 normlem2 31429 normlem3 31430 normlem4 31431 normlem5 31432 normlem6 31433 normlem7 31434 normlem7tALT 31437 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31457 norm-iii 31458 |
| [Beran] p. 98 | Remark 3.4 | bcs 31499 bcsiALT 31497 bcsiHIL 31498 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31439 normpar 31473 normpari 31472 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31464 normpyth 31463 normpythi 31460 |
| [Beran] p. 99 | Remark | lnfn0 32365 lnfn0i 32360 lnop0 32284 lnop0i 32288 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32344 nmcfnex 32371 nmcfnexi 32369 nmcopex 32347 nmcopexi 32345 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32372 nmcfnlbi 32370 nmcoplb 32348 nmcoplbi 32346 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32374 lnfnconi 32373 lnopcon 32353 lnopconi 32352 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31474 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31471 norm3adifii 31466 norm3dif 31468 norm3difi 31465 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31619 pjhth 31711 pjhtheu 31712 pjpjhth 31743 pjpjhthi 31744 pjth 25577 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31724 ococi 31723 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32379 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32380 riesz4 32382 riesz4i 32381 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32397 cnlnadjeu 32396 cnlnadjeui 32395 cnlnadji 32394 cnlnadjlem1 32385 nmopadjlei 32406 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32409 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32408 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32410 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32254 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32420 nmopcoadji 32419 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32411 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32421 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32418 pjadj2coi 32522 pjadjcoi 32479 |
| [Beran] p. 107 | Definition | df-ch 31539 isch2 31541 |
| [Beran] p. 107 | Remark 3.12 | choccl 31624 isch3 31559 occl 31622 ocsh 31601 shoccl 31623 shocsh 31602 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31726 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31650 |
| [Beran] p. 109 | Property (i) | pjadj2 32505 pjadj3 32506 pjadji 32003 pjadjii 31992 |
| [Beran] p. 109 | Property (ii) | pjidmco 32499 pjidmcoi 32495 pjidmi 31991 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32491 |
| [Beran] p. 111 | Remark | ho0val 32068 pjch1 31988 |
| [Beran] p. 111 | Definition | df-hfmul 32052 df-hfsum 32051 df-hodif 32050 df-homul 32049 df-hosum 32048 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31989 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32012 pjchi 31750 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31757 pjoc2i 31756 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31998 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32483 pjssmii 31999 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32482 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32481 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32486 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32484 pjssge0ii 32000 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32485 pjdifnormii 32001 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1804 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1802 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1805 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1800 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34648 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34656 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34654 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34658 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34678 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34709 df-sitm 34687 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34709 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34686 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29364 isuhgrop 29386 isusgrop 29478 isuspgrop 29477 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48593 df-subgr 29584 uhgrspan1 29619 uhgrspansubgr 29607 |
| [Bollobas] p. 3 | Definition | df-gric 48613 gricuspgr 48650 isuspgrim 48628 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29770 df-clnbgr 48551 df-cusgr 29728 df-nbgr 29649 fusgrmaxsize 29780 |
| [Bollobas] p. 4 | Definition | df-upwlks 48866 df-wlks 29915 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29866 finsumvtxdgeven 29868 fusgr1th 29867 fusgrvtxdgonume 29870 vtxdgoddnumeven 29869 |
| [Bollobas] p. 5 | Notation | df-pths 30029 |
| [Bollobas] p. 5 | Definition | df-crcts 30101 df-cycls 30102 df-trls 30006 df-wlkson 29916 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29375 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48932 df-cllaw 48918 df-mgm 18697 df-mgm2 48951 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48933 df-asslaw 48920 df-sgrp 18776 df-sgrp2 48953 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48952 df-comlaw 48919 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18792 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33312 mndlactf1o 33316 mndractf1 33314 mndractf1o 33317 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20316 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20230 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33989 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33993 assarrginv 33992 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34034 fldextrspunfld 34032 fldextrspunlem1 34031 fldextrspunlem2 34033 fldextrspunlsp 34030 fldextrspunlsplem 34029 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33793 dfufd2 33806 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7285 fcofo 7286 |
| [BourbakiTop1] p. | Remark | xnegmnf 13235 xnegpnf 13234 |
| [BourbakiTop1] p. | Remark | rexneg 13236 |
| [BourbakiTop1] p. | Remark 3 | ust0 24356 ustfilxp 24349 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24226 |
| [BourbakiTop1] p. | Criterion | ishmeo 23895 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24419 iducn 24418 snfil 24000 |
| [BourbakiTop1] p. | Example 2 | neifil 24016 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24203 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24439 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34313 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23999 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24411 df-ust 24337 filintn0 23997 filn0 23998 istgp 24213 ucnprima 24417 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24422 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24433 df-usp 24393 df-utop 24367 trust 24365 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34212 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23252 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23405 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24342 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24345 |
| [BourbakiTop1] p. | Property V_ii | innei 23261 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23269 neissex 23263 |
| [BourbakiTop1] p. | Proposition 1 | neips 23249 neiss 23245 ucncn 24420 ustund 24358 ustuqtop 24382 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23403 neiptopreu 23269 utop2nei 24386 utop3cls 24387 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24427 uspreg 24409 utopreg 24388 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23827 imasncls 23828 imasnopn 23826 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24136 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24344 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24346 |
| [BourbakiTop1] p. | Property V_iii | elnei 23247 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24438 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24343 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24347 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23523 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23982 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23030 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34209 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46746 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46748 stoweid 46747 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46685 stoweidlem10 46694 stoweidlem14 46698 stoweidlem15 46699 stoweidlem35 46719 stoweidlem36 46720 stoweidlem37 46721 stoweidlem38 46722 stoweidlem40 46724 stoweidlem41 46725 stoweidlem43 46727 stoweidlem44 46728 stoweidlem46 46730 stoweidlem5 46689 stoweidlem50 46734 stoweidlem52 46736 stoweidlem53 46737 stoweidlem55 46739 stoweidlem56 46740 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46707 stoweidlem24 46708 stoweidlem27 46711 stoweidlem28 46712 stoweidlem30 46714 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46718 stoweidlem59 46743 stoweidlem60 46744 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46729 stoweidlem49 46733 stoweidlem7 46691 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46715 stoweidlem39 46723 stoweidlem42 46726 stoweidlem48 46732 stoweidlem51 46735 stoweidlem54 46738 stoweidlem57 46741 stoweidlem58 46742 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46709 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46701 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46695 stoweidlem13 46697 stoweidlem26 46710 stoweidlem61 46745 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46702 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48932 df-mgm 18697 df-mgm2 48951 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18776 df-sgrp2 48953 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19104 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5192 |
| [Church] p. 129 | Section II.24 | df-ifp 1077 dfifp2 1078 |
| [Clemente] p. 10 | Definition IT | natded 30720 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30720 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30720 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30720 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30720 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30720 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30720 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30720 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30720 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30720 |
| [Clemente] p. 14 | Proof 5.11 | natded 30720 |
| [Clemente] p. 14 | Definition E` `n | natded 30720 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30722 ex-natded5.2 30721 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30725 ex-natded5.3 30724 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30727 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30729 ex-natded5.7 30728 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30731 ex-natded5.8 30730 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30733 ex-natded5.13 30732 |
| [Clemente] p. 32 | Definition I` `n | natded 30720 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30720 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30720 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30720 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30734 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30735 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30737 ex-natded9.26 30736 |
| [Cohen] p. 301 | Remark | relogoprlem 26732 |
| [Cohen] p. 301 | Property 2 | relogmul 26733 relogmuld 26766 |
| [Cohen] p. 301 | Property 3 | relogdiv 26734 relogdivd 26767 |
| [Cohen] p. 301 | Property 4 | relogexp 26737 |
| [Cohen] p. 301 | Property 1a | log1 26726 |
| [Cohen] p. 301 | Property 1b | loge 26727 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26928 |
| [Cohen4] p. 349 | Property | relogbf 26932 |
| [Cohen4] p. 352 | Definition | elogb 26911 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26918 |
| [Cohen4] p. 361 | Property 3 | logbrec 26923 relogbdiv 26920 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26916 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26921 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26909 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26910 |
| [Cohen4] p. 367 | Property | logbchbase 26912 |
| [Cohen4] p. 377 | Property 2 | logblt 26925 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34641 sxbrsigalem4 34643 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18612 acsinfd 18611 acsinfdimd 18613 acsmap2d 18610 acsmapd 18609 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34646 |
| [Connell] p. 57 | Definition | df-scmat 22627 df-scmatalt 49146 |
| [Conway] p. 4 | Definition | lesrec 27968 lesrecd 27969 |
| [Conway] p. 5 | Definition | addsval 28131 addsval2 28132 df-adds 28129 df-muls 28276 df-negs 28190 |
| [Conway] p. 7 | Theorem | 0lt1s 27981 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28631 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28030 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28029 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27907 |
| [Conway] p. 17 | Theorem 3 | addsass 28174 addsassd 28175 addscom 28135 addscomd 28136 addsrid 28133 addsridd 28134 |
| [Conway] p. 17 | Definition | df-0s 27976 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28213 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28210 negsidd 28211 |
| [Conway] p. 18 | Theorem 5 | leadds1 28158 leadds1d 28164 |
| [Conway] p. 18 | Definition | df-1s 27977 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28205 negscld 28206 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28149 |
| [Conway] p. 19 | Note | mulsunif2 28339 |
| [Conway] p. 19 | Theorem 7 | addsdi 28324 addsdid 28325 addsdird 28326 mulnegs1d 28329 mulnegs2d 28330 mulsass 28335 mulsassd 28336 mulscom 28308 mulscomd 28309 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28303 mulscld 28304 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28307 ltmuls 28305 ltmulsd 28306 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28313 mulsgt0d 28314 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28387 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27973 |
| [Conway] p. 24 | Definition | df-reno 28659 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28668 remulscl 28671 renegscl 28667 |
| [Conway] p. 27 | Definition | df-ons 28421 elons2 28427 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28431 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28433 onswe 28441 |
| [Conway] p. 29 | Remark | madebday 28069 newbday 28071 oldbday 28070 |
| [Conway] p. 29 | Definition | df-made 27996 df-new 27998 df-old 27997 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13894 |
| [Crawley] p. 1 | Definition of poset | df-poset 18368 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40128 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40932 dalaw 40628 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42703 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40732 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40848 df-ldil 40846 isldil 40852 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40847 df-trnN 40849 isltrn 40861 ltrnu 40863 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40533 cdlema2N 40534 exatleN 40146 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40218 cdlemb 40536 cdlemb2 40783 cdlemb3 41348 idltrn 40892 l1cvat 39797 lhpat 40785 lhpat2 40787 lshpat 39798 ltrnel 40881 ltrnmw 40893 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40933 cdlemc2 40934 ltrnnidn 40916 trlat 40911 trljat1 40908 trljat2 40909 trljat3 40910 trlne 40927 trlnidat 40915 trlnle 40928 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40733 |
| [Crawley] p. 113 | Lemma C | cdlemc 40939 cdlemc3 40935 cdlemc4 40936 |
| [Crawley] p. 113 | Lemma D | cdlemd 40949 cdlemd1 40940 cdlemd2 40941 cdlemd3 40942 cdlemd4 40943 cdlemd5 40944 cdlemd6 40945 cdlemd7 40946 cdlemd8 40947 cdlemd9 40948 cdleme31sde 41127 cdleme31se 41124 cdleme31se2 41125 cdleme31snd 41128 cdleme32a 41183 cdleme32b 41184 cdleme32c 41185 cdleme32d 41186 cdleme32e 41187 cdleme32f 41188 cdleme32fva 41179 cdleme32fva1 41180 cdleme32fvcl 41182 cdleme32le 41189 cdleme48fv 41241 cdleme4gfv 41249 cdleme50eq 41283 cdleme50f 41284 cdleme50f1 41285 cdleme50f1o 41288 cdleme50laut 41289 cdleme50ldil 41290 cdleme50lebi 41282 cdleme50rn 41287 cdleme50rnlem 41286 cdlemeg49le 41253 cdlemeg49lebilem 41281 |
| [Crawley] p. 113 | Lemma E | cdleme 41302 cdleme00a 40951 cdleme01N 40963 cdleme02N 40964 cdleme0a 40953 cdleme0aa 40952 cdleme0b 40954 cdleme0c 40955 cdleme0cp 40956 cdleme0cq 40957 cdleme0dN 40958 cdleme0e 40959 cdleme0ex1N 40965 cdleme0ex2N 40966 cdleme0fN 40960 cdleme0gN 40961 cdleme0moN 40967 cdleme1 40969 cdleme10 40996 cdleme10tN 41000 cdleme11 41012 cdleme11a 41002 cdleme11c 41003 cdleme11dN 41004 cdleme11e 41005 cdleme11fN 41006 cdleme11g 41007 cdleme11h 41008 cdleme11j 41009 cdleme11k 41010 cdleme11l 41011 cdleme12 41013 cdleme13 41014 cdleme14 41015 cdleme15 41020 cdleme15a 41016 cdleme15b 41017 cdleme15c 41018 cdleme15d 41019 cdleme16 41027 cdleme16aN 41001 cdleme16b 41021 cdleme16c 41022 cdleme16d 41023 cdleme16e 41024 cdleme16f 41025 cdleme16g 41026 cdleme19a 41045 cdleme19b 41046 cdleme19c 41047 cdleme19d 41048 cdleme19e 41049 cdleme19f 41050 cdleme1b 40968 cdleme2 40970 cdleme20aN 41051 cdleme20bN 41052 cdleme20c 41053 cdleme20d 41054 cdleme20e 41055 cdleme20f 41056 cdleme20g 41057 cdleme20h 41058 cdleme20i 41059 cdleme20j 41060 cdleme20k 41061 cdleme20l 41064 cdleme20l1 41062 cdleme20l2 41063 cdleme20m 41065 cdleme20y 41044 cdleme20zN 41043 cdleme21 41079 cdleme21d 41072 cdleme21e 41073 cdleme22a 41082 cdleme22aa 41081 cdleme22b 41083 cdleme22cN 41084 cdleme22d 41085 cdleme22e 41086 cdleme22eALTN 41087 cdleme22f 41088 cdleme22f2 41089 cdleme22g 41090 cdleme23a 41091 cdleme23b 41092 cdleme23c 41093 cdleme26e 41101 cdleme26eALTN 41103 cdleme26ee 41102 cdleme26f 41105 cdleme26f2 41107 cdleme26f2ALTN 41106 cdleme26fALTN 41104 cdleme27N 41111 cdleme27a 41109 cdleme27cl 41108 cdleme28c 41114 cdleme3 40979 cdleme30a 41120 cdleme31fv 41132 cdleme31fv1 41133 cdleme31fv1s 41134 cdleme31fv2 41135 cdleme31id 41136 cdleme31sc 41126 cdleme31sdnN 41129 cdleme31sn 41122 cdleme31sn1 41123 cdleme31sn1c 41130 cdleme31sn2 41131 cdleme31so 41121 cdleme35a 41190 cdleme35b 41192 cdleme35c 41193 cdleme35d 41194 cdleme35e 41195 cdleme35f 41196 cdleme35fnpq 41191 cdleme35g 41197 cdleme35h 41198 cdleme35h2 41199 cdleme35sn2aw 41200 cdleme35sn3a 41201 cdleme36a 41202 cdleme36m 41203 cdleme37m 41204 cdleme38m 41205 cdleme38n 41206 cdleme39a 41207 cdleme39n 41208 cdleme3b 40971 cdleme3c 40972 cdleme3d 40973 cdleme3e 40974 cdleme3fN 40975 cdleme3fa 40978 cdleme3g 40976 cdleme3h 40977 cdleme4 40980 cdleme40m 41209 cdleme40n 41210 cdleme40v 41211 cdleme40w 41212 cdleme41fva11 41219 cdleme41sn3aw 41216 cdleme41sn4aw 41217 cdleme41snaw 41218 cdleme42a 41213 cdleme42b 41220 cdleme42c 41214 cdleme42d 41215 cdleme42e 41221 cdleme42f 41222 cdleme42g 41223 cdleme42h 41224 cdleme42i 41225 cdleme42k 41226 cdleme42ke 41227 cdleme42keg 41228 cdleme42mN 41229 cdleme42mgN 41230 cdleme43aN 41231 cdleme43bN 41232 cdleme43cN 41233 cdleme43dN 41234 cdleme5 40982 cdleme50ex 41301 cdleme50ltrn 41299 cdleme51finvN 41298 cdleme51finvfvN 41297 cdleme51finvtrN 41300 cdleme6 40983 cdleme7 40991 cdleme7a 40985 cdleme7aa 40984 cdleme7b 40986 cdleme7c 40987 cdleme7d 40988 cdleme7e 40989 cdleme7ga 40990 cdleme8 40992 cdleme8tN 40997 cdleme9 40995 cdleme9a 40993 cdleme9b 40994 cdleme9tN 40999 cdleme9taN 40998 cdlemeda 41040 cdlemedb 41039 cdlemednpq 41041 cdlemednuN 41042 cdlemefr27cl 41145 cdlemefr32fva1 41152 cdlemefr32fvaN 41151 cdlemefrs32fva 41142 cdlemefrs32fva1 41143 cdlemefs27cl 41155 cdlemefs32fva1 41165 cdlemefs32fvaN 41164 cdlemesner 41038 cdlemeulpq 40962 |
| [Crawley] p. 114 | Lemma E | 4atex 40818 4atexlem7 40817 cdleme0nex 41032 cdleme17a 41028 cdleme17c 41030 cdleme17d 41240 cdleme17d1 41031 cdleme17d2 41237 cdleme18a 41033 cdleme18b 41034 cdleme18c 41035 cdleme18d 41037 cdleme4a 40981 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41067 cdleme21at 41070 cdleme21b 41068 cdleme21c 41069 cdleme21ct 41071 cdleme21f 41074 cdleme21g 41075 cdleme21h 41076 cdleme21i 41077 cdleme22gb 41036 |
| [Crawley] p. 116 | Lemma F | cdlemf 41305 cdlemf1 41303 cdlemf2 41304 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41309 cdlemg16 41399 cdlemg28 41446 cdlemg28a 41435 cdlemg28b 41445 cdlemg3a 41339 cdlemg42 41471 cdlemg43 41472 cdlemg44 41475 cdlemg44a 41473 cdlemg46 41477 cdlemg47 41478 cdlemg9 41376 ltrnco 41461 ltrncom 41480 tgrpabl 41493 trlco 41469 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41485 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41419 cdlemg17b 41404 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41498 df-edring 41499 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41502 |
| [Crawley] p. 118 | Remark | tendopltp 41522 |
| [Crawley] p. 118 | Lemma H | cdlemh 41559 cdlemh1 41557 cdlemh2 41558 |
| [Crawley] p. 118 | Lemma I | cdlemi 41562 cdlemi1 41560 cdlemi2 41561 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41563 cdlemj2 41564 cdlemj3 41565 tendocan 41566 |
| [Crawley] p. 118 | Lemma K | cdlemk 41716 cdlemk1 41573 cdlemk10 41585 cdlemk11 41591 cdlemk11t 41688 cdlemk11ta 41671 cdlemk11tb 41673 cdlemk11tc 41687 cdlemk11u-2N 41631 cdlemk11u 41613 cdlemk12 41592 cdlemk12u-2N 41632 cdlemk12u 41614 cdlemk13-2N 41618 cdlemk13 41594 cdlemk14-2N 41620 cdlemk14 41596 cdlemk15-2N 41621 cdlemk15 41597 cdlemk16-2N 41622 cdlemk16 41599 cdlemk16a 41598 cdlemk17-2N 41623 cdlemk17 41600 cdlemk18-2N 41628 cdlemk18-3N 41642 cdlemk18 41610 cdlemk19-2N 41629 cdlemk19 41611 cdlemk19u 41712 cdlemk1u 41601 cdlemk2 41574 cdlemk20-2N 41634 cdlemk20 41616 cdlemk21-2N 41633 cdlemk21N 41615 cdlemk22-3 41643 cdlemk22 41635 cdlemk23-3 41644 cdlemk24-3 41645 cdlemk25-3 41646 cdlemk26-3 41648 cdlemk26b-3 41647 cdlemk27-3 41649 cdlemk28-3 41650 cdlemk29-3 41653 cdlemk3 41575 cdlemk30 41636 cdlemk31 41638 cdlemk32 41639 cdlemk33N 41651 cdlemk34 41652 cdlemk35 41654 cdlemk36 41655 cdlemk37 41656 cdlemk38 41657 cdlemk39 41658 cdlemk39u 41710 cdlemk4 41576 cdlemk41 41662 cdlemk42 41683 cdlemk42yN 41686 cdlemk43N 41705 cdlemk45 41689 cdlemk46 41690 cdlemk47 41691 cdlemk48 41692 cdlemk49 41693 cdlemk5 41578 cdlemk50 41694 cdlemk51 41695 cdlemk52 41696 cdlemk53 41699 cdlemk54 41700 cdlemk55 41703 cdlemk55u 41708 cdlemk56 41713 cdlemk5a 41577 cdlemk5auN 41602 cdlemk5u 41603 cdlemk6 41579 cdlemk6u 41604 cdlemk7 41590 cdlemk7u-2N 41630 cdlemk7u 41612 cdlemk8 41580 cdlemk9 41581 cdlemk9bN 41582 cdlemki 41583 cdlemkid 41678 cdlemkj-2N 41624 cdlemkj 41605 cdlemksat 41588 cdlemksel 41587 cdlemksv 41586 cdlemksv2 41589 cdlemkuat 41608 cdlemkuel-2N 41626 cdlemkuel-3 41640 cdlemkuel 41607 cdlemkuv-2N 41625 cdlemkuv2-2 41627 cdlemkuv2-3N 41641 cdlemkuv2 41609 cdlemkuvN 41606 cdlemkvcl 41584 cdlemky 41668 cdlemkyyN 41704 tendoex 41717 |
| [Crawley] p. 120 | Remark | dva1dim 41727 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41718 cdleml2N 41719 cdleml3N 41720 cdleml4N 41721 cdleml5N 41722 cdleml6 41723 cdleml7 41724 cdleml8 41725 cdleml9 41726 dia1dim 41803 |
| [Crawley] p. 120 | Lemma M | dia11N 41790 diaf11N 41791 dialss 41788 diaord 41789 dibf11N 41903 djajN 41879 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41774 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41860 dia2dimlem1 41806 dia2dimlem2 41807 dia2dimlem3 41808 dia2dimlem4 41809 dia2dimlem5 41810 diaf1oN 41872 diarnN 41871 dvheveccl 41854 dvhopN 41858 |
| [Crawley] p. 121 | Lemma N | cdlemn 41954 cdlemn10 41948 cdlemn11 41953 cdlemn11a 41949 cdlemn11b 41950 cdlemn11c 41951 cdlemn11pre 41952 cdlemn2 41937 cdlemn2a 41938 cdlemn3 41939 cdlemn4 41940 cdlemn4a 41941 cdlemn5 41943 cdlemn5pre 41942 cdlemn6 41944 cdlemn7 41945 cdlemn8 41946 cdlemn9 41947 diclspsn 41936 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41915 |
| [Crawley] p. 122 | Lemma N | dih11 42007 dihf11 42009 dihjust 41959 dihjustlem 41958 dihord 42006 dihord1 41960 dihord10 41965 dihord11b 41964 dihord11c 41966 dihord2 41969 dihord2a 41961 dihord2b 41962 dihord2cN 41963 dihord2pre 41967 dihord2pre2 41968 dihordlem6 41955 dihordlem7 41956 dihordlem7b 41957 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41972 dihfval 41973 dihval 41974 |
| [Diestel] p. 3 | Definition | df-gric 48613 df-grim 48610 isuspgrim 48628 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29728 df-nbgr 29649 |
| [Diestel] p. 3 | Definition by | df-grisom 48609 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48593 df-subgr 29584 uhgrspan1 29619 uhgrspansubgr 29607 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29870 vtxdgoddnumeven 29869 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29375 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34220 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34232 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34224 zarcls1 34225 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34235 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34238 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34241 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3907 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9615 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8825 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9623 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9965 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10538 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5267 |
| [Enderton] p. 19 | Definition | df-tp 4593 |
| [Enderton] p. 26 | Exercise 5 | unissb 4905 |
| [Enderton] p. 26 | Exercise 10 | pwel 5352 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5554 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5044 iinin2 5043 iinun2 5036 iunin1 5035 iunin1f 32868 iunin2 5034 uniin1 5038 uniin2 5039 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5042 iundif2 5037 |
| [Enderton] p. 32 | Exercise 20 | unineq 4240 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5063 |
| [Enderton] p. 33 | Exercise 25 | iununi 5064 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5071 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7769 iunpwss 5072 |
| [Enderton] p. 36 | Definition | opthwiener 5497 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5431 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4910 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5452 rnex 7906 rnexg 7898 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5904 rnuni 6146 |
| [Enderton] p. 42 | Definition of a function | dffun7 6563 dffun8 6564 |
| [Enderton] p. 43 | Definition of function value | funfv2 6969 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6605 |
| [Enderton] p. 44 | Definition (d) | dfima2 6064 dfima3 6065 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6978 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10456 ac7g 10457 df-ac 10099 dfac2 10114 dfac2a 10112 dfac2b 10113 dfac3 10104 dfac7 10115 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7244 |
| [Enderton] p. 52 | Definition | df-map 8825 |
| [Enderton] p. 53 | Exercise 21 | coass 6267 |
| [Enderton] p. 53 | Exercise 27 | dmco 6256 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6612 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6104 |
| [Enderton] p. 54 | Remark | ixpf 8917 ixpssmap 8929 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8895 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10466 ac9s 10476 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39311 erref 8714 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39314 erthi 8750 |
| [Enderton] p. 57 | Definition | df-ec 8695 |
| [Enderton] p. 58 | Definition | df-qs 8699 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8695 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5900 |
| [Enderton] p. 68 | Definition of successor | df-suc 6366 |
| [Enderton] p. 71 | Definition | df-tr 5218 dftr4 5223 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5233 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5235 trintALT 45559 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8589 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8591 onasuc 8512 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7413 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8590 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8592 onmsuc 8513 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8607 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8594 nnacom 8602 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8608 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8609 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8611 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8595 nnmsucr 8610 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8623 |
| [Enderton] p. 129 | Definition | df-en 8943 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7364 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9998 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16268 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9190 |
| [Enderton] p. 135 | Corollary 6C | php3 9192 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9189 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9221 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9223 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9152 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9156 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9128 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10162 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10163 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10158 dju1en 10154 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9299 unifi 9300 unifi2 9301 |
| [Enderton] p. 144 | Corollary 6K | undif2 4437 unfi 9154 unfi2 9269 |
| [Enderton] p. 145 | Figure 38 | ffoss 7942 |
| [Enderton] p. 145 | Definition | df-dom 8944 |
| [Enderton] p. 146 | Example 1 | domen 8957 domeng 8958 |
| [Enderton] p. 146 | Example 3 | nndomo 9201 nnsdom 9622 nnsdomg 9258 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10166 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9129 xpdom1 9063 xpdom1g 9061 xpdom2g 9060 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9135 |
| [Enderton] p. 151 | Theorem 6M | zorn 10490 zorng 10487 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10475 dfac5 10111 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10559 |
| [Enderton] p. 164 | Example | infdif 10190 |
| [Enderton] p. 168 | Definition | df-po 5569 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6476 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6408 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6475 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6416 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7834 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7779 |
| [Enderton] p. 194 | Remark | onprc 7776 |
| [Enderton] p. 194 | Exercise 16 | suc11 6470 |
| [Enderton] p. 197 | Definition | df-card 9924 |
| [Enderton] p. 197 | Theorem 7P | carden 10534 |
| [Enderton] p. 200 | Exercise 25 | tfis 7850 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9747 |
| [Enderton] p. 202 | Definition | df-r1 9735 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9757 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9838 rankval4b 35459 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9574 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9828 rankprb 9822 rankpw 9814 rankpwi 9794 rankuniss 9837 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9586 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9587 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10093 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10059 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10073 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8327 |
| [Enderton] p. 222 | Definition | df-kard 35529 |
| [Enderton] p. 222 | Definition of kard | karden 9880 kardex 9879 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8582 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8584 |
| [Enderton] p. 240 | Exercise 25 | oarec 8546 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10232 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17697 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17639 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18608 mrieqv2d 17694 mrieqvd 17693 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17698 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17703 mreexexlem2d 17700 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18614 mreexfidimd 17705 |
| [Frege1879] p. 11 | Statement | df3or2 44464 |
| [Frege1879] p. 12 | Statement | df3an2 44465 dfxor4 44462 dfxor5 44463 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44486 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44487 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44491 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44495 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44496 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44502 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44504 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44505 axfrege8 44503 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38057 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44508 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44516 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44510 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44509 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44518 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44519 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44522 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44512 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44517 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44514 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44520 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44524 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44523 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44515 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44521 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44511 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44513 rp-frege25 44501 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44506 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44526 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44507 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44527 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44530 axfrege31 44529 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44528 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44531 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44532 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44533 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44534 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44535 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44536 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44537 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44538 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44539 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44541 axfrege41 44540 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44542 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44543 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44544 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44545 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44546 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44547 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44548 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44549 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44550 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44553 ax-frege52c 44584 frege52aid 44554 frege52b 44585 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44558 ax-frege54c 44588 frege54b 44589 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44551 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3745 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44556 frege53aid 44555 frege53b 44586 frege53c 44610 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2761 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44564 frege55aid 44561 frege55b 44593 frege55c 44614 frege55cor1a 44565 frege55lem2a 44563 frege55lem2b 44592 frege55lem2c 44613 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44567 frege56aid 44566 frege56b 44594 frege56c 44615 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44571 ax-frege58b 44597 frege58bid 44598 frege58c 44617 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44569 frege57aid 44568 frege57b 44595 frege57c 44616 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3756 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44573 frege59b 44600 frege59c 44618 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44574 frege60b 44601 frege60c 44619 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44575 frege61b 44602 frege61c 44620 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44576 frege62b 44603 frege62c 44621 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44577 frege63b 44604 frege63c 44622 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44578 frege64b 44605 frege64c 44623 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44579 frege65b 44606 frege65c 44624 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44580 frege66b 44607 frege66c 44625 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44581 frege67b 44608 frege67c 44626 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44582 frege68b 44609 frege68c 44627 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44628 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44629 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44630 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44631 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44632 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44635 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44633 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44634 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44636 frege77d 44442 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44637 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44638 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44639 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44640 frege81d 44443 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44641 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44642 frege83d 44444 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44643 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44644 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44645 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44646 frege87d 44446 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44647 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44648 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44649 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44650 frege91d 44447 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44651 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44652 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44653 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44654 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44658 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44655 frege96d 44445 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44656 frege97d 44448 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44657 frege98d 44449 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44659 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44660 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44661 frege102d 44450 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44662 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44663 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44664 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44665 frege106d 44451 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44666 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44667 frege108d 44452 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44668 frege109d 44453 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44669 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44670 frege111d 44455 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44671 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44672 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44673 frege114d 44454 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44674 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44675 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44676 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44677 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44678 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44679 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44680 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44681 frege122d 44456 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44682 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44683 frege124d 44457 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44684 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44685 frege126d 44458 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44686 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44687 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44688 frege129d 44459 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44689 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44690 frege131d 44460 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44691 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44692 frege133d 44461 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46997 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47320 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47020 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47135 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47155 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47146 meadjunre 47160 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47147 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47148 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47144 meaiunle 47153 meaiunlelem 47152 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47165 meaiuninc2 47166 meaiuninc3 47169 meaiuninc3v 47168 meaiunincf 47167 meaiuninclem 47164 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47171 meaiininc2 47172 meaiininclem 47170 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47190 caragendifcl 47198 caratheodory 47212 omelesplit 47202 |
| [Fremlin1] p. 19 | Definition 113A | isome 47178 isomennd 47215 isomenndlem 47214 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47200 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47219 voncmpl 47305 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47182 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47207 carageniuncllem1 47205 carageniuncllem2 47206 caragenuncl 47197 caragenuncllem 47196 caragenunicl 47208 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47216 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47210 caratheodorylem2 47211 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47219 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47278 hoidmv1lelem1 47275 hoidmv1lelem2 47276 hoidmv1lelem3 47277 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47322 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47278 hoidmvle 47284 hoidmvlelem1 47279 hoidmvlelem2 47280 hoidmvlelem3 47281 hoidmvlelem4 47282 hoidmvlelem5 47283 hsphoidmvle2 47269 hsphoif 47260 hsphoival 47263 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47232 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47240 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47267 hoidmvn0val 47268 hoidmvval 47261 hoidmvval0 47271 hoidmvval0b 47274 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47272 hsphoidmvle 47270 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47221 df-voln 47223 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47288 ovn0 47250 ovn0lem 47249 ovnf 47247 ovnome 47257 ovnssle 47245 ovnsslelem 47244 ovnsupge0 47241 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47287 ovnhoilem1 47285 ovnhoilem2 47286 vonhoi 47351 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47304 hoidifhspf 47302 hoidifhspval 47292 hoidifhspval2 47299 hoidifhspval3 47303 hspmbl 47313 hspmbllem1 47310 hspmbllem2 47311 hspmbllem3 47312 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47305 vonmea 47258 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47256 ovnsubadd2 47330 ovnsubadd2lem 47329 ovnsubaddlem1 47254 ovnsubaddlem2 47255 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47315 hoimbl2 47349 hoimbllem 47314 hspdifhsp 47300 opnvonmbl 47318 opnvonmbllem2 47317 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47320 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47363 iccvonmbllem 47362 ioovonmbl 47361 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47369 vonicclem2 47368 vonioo 47366 vonioolem2 47365 vonn0icc 47372 vonn0icc2 47376 vonn0ioo 47371 vonn0ioo2 47374 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47373 snvonmbl 47370 vonct 47377 vonsn 47375 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47043 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47042 subsaliuncllem 47041 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47409 salpreimalegt 47393 salpreimaltle 47410 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47412 issmff 47418 issmflem 47411 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47429 issmflelem 47428 smfpreimale 47438 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47440 issmfgtlem 47439 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47380 issmf 47412 issmff 47418 issmfge 47454 issmfgelem 47453 issmfgt 47440 issmfgtlem 47439 issmfle 47429 issmflelem 47428 issmflem 47411 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47391 salpreimagtlt 47414 salpreimalelt 47413 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47454 issmfgelem 47453 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47437 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47435 cnfsmf 47424 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47451 decsmflem 47450 incsmf 47426 incsmflem 47425 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47385 pimconstlt1 47386 smfconst 47433 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47449 smfaddlem1 47447 smfaddlem2 47448 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47480 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47479 smfmullem1 47475 smfmullem2 47476 smfmullem3 47477 smfmullem4 47478 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47481 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47484 smfpimbor1lem2 47483 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47486 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47474 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47473 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47482 smfresal 47472 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47461 smflim2 47490 smflimlem1 47455 smflimlem2 47456 smflimlem3 47457 smflimlem4 47458 smflimlem5 47459 smflimlem6 47460 smflimmpt 47494 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47498 smfsuplem1 47495 smfsuplem2 47496 smfsuplem3 47497 smfsupmpt 47499 smfsupxr 47500 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47502 smfinflem 47501 smfinfmpt 47503 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47461 smflim2 47490 smflimmpt 47494 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47492 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47522 smfdivdmmbl2 47525 smfinfdmmbl 47533 smfinfdmmbllem 47532 smfsupdmmbl 47529 smfsupdmmbllem 47528 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47512 smflimsuplem2 47505 smflimsuplem6 47509 smflimsuplem7 47510 smflimsuplem8 47511 smflimsupmpt 47513 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47515 smfliminflem 47514 smfliminfmpt 47516 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47380 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47526 fsupdm2 47527 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47517 adddmmbl2 47518 finfdm 47530 finfdm2 47531 fsupdm 47526 fsupdm2 47527 muldmmbl 47519 muldmmbl2 47520 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47530 finfdm2 47531 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25674 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25717 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25727 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38315 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38318 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9606 inf1 9590 inf2 9591 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10895 enqer 10905 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10900 df-nq 10896 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10892 df-plq 10898 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7647 df-mpq 10893 df-mq 10899 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10901 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10959 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10960 ltbtwnnq 10962 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10955 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10956 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10963 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10965 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10977 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10979 |
| [Gleason] p. 122 | Definition | df-1p 10966 |
| [Gleason] p. 122 | Remark (1) | prub 10978 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11017 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10969 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11016 psslinpr 11015 supexpr 11038 suplem1pr 11036 suplem2pr 11037 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11002 addclprlem1 11000 addclprlem2 11001 df-plp 10967 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11006 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11005 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11018 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11027 ltexprlem1 11020 ltexprlem2 11021 ltexprlem3 11022 ltexprlem4 11023 ltexprlem5 11024 ltexprlem6 11025 ltexprlem7 11026 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11029 ltaprlem 11028 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11030 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11031 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10968 mulclpr 11004 mulclprlem 11003 reclem2pr 11032 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11013 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11008 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11007 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11012 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11035 reclem3pr 11033 reclem4pr 11034 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11039 enrer 11047 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11044 df-1r 11045 df-nr 11040 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11042 df-plr 11041 negexsr 11086 recexsr 11091 recexsrlem 11087 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11043 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12212 creur 12211 cru 12209 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11172 axcnre 11148 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15166 crimd 15283 crimi 15244 crre 15165 crred 15282 crrei 15243 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15168 remimd 15249 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15335 absval2d 15499 absval2i 15449 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15192 cjaddd 15271 cjaddi 15239 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15193 cjmuld 15272 cjmuli 15240 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15191 cjcjd 15250 cjcji 15222 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15190 cjreb 15174 cjrebd 15253 cjrebi 15225 cjred 15277 rere 15173 rereb 15171 rerebd 15252 rerebi 15224 rered 15275 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15199 addcjd 15263 addcji 15234 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15289 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15330 abscjd 15504 abscji 15453 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15340 abs00d 15500 abs00i 15450 absne0d 15501 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15373 releabsd 15505 releabsi 15454 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15345 absmuld 15508 absmuli 15456 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15333 sqabsaddi 15457 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15382 abstrid 15510 abstrii 15460 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14098 exp0 14101 expp1 14104 expp1d 14183 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26820 cxpaddd 26858 expadd 14140 expaddd 14184 expaddz 14142 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26829 cxpmuld 26878 expmul 14143 expmuld 14185 expmulz 14144 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26826 mulcxpd 26869 mulexp 14137 mulexpd 14197 mulexpz 14138 |
| [Gleason] p. 140 | Exercise 1 | znnen 16267 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13536 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15683 rlimadd 15694 rlimdiv 15697 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15685 rlimsub 15695 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15684 rlimmul 15696 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15688 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15634 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15655 climcj 15656 climim 15658 climre 15657 rlimabs 15660 rlimcj 15661 rlimim 15663 rlimre 15662 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11247 df-xr 11246 ltxr 13139 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15522 limsupval 15525 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15721 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15730 caucvgb 15731 caucvgbf 46173 caucvgr 15727 climcau 15722 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15868 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15937 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15387 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13861 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21495 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24479 xmet0 24478 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24495 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24486 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24488 mstri 24605 xmettri 24487 xmstri 24604 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24518 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23784 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25448 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24676 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25002 addcn2 15645 mulcn 25004 mulcn2 15647 subcn 25003 subcn2 15646 |
| [Gleason] p. 295 | Remark | bcval3 14342 bcval4 14343 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14357 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14340 df-bc 14339 |
| [Gleason] p. 296 | Remark | bcn0 14346 bcnn 14348 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15884 |
| [Gleason] p. 308 | Equation 2 | ef0 16144 |
| [Gleason] p. 308 | Equation 3 | efcj 16145 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16151 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16156 |
| [Gleason] p. 310 | Equation 14 | sinadd 16219 |
| [Gleason] p. 310 | Equation 15 | cosadd 16220 |
| [Gleason] p. 311 | Equation 17 | sincossq 16231 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16236 sinbnd 16235 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14252 sqeqori 14250 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16125 |
| [Godowski] p. 730 | Equation SF | goeqi 32591 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31986 |
| [Golan] p. 1 | Remark | srgisid 20290 |
| [Golan] p. 1 | Definition | df-srg 20268 |
| [Golan] p. 149 | Definition | df-slmd 33487 |
| [Gonshor] p. 7 | Definition | df-cuts 27929 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27968 lesrecd 27969 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28089 cofcut1d 28090 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28091 cofcut2d 28092 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28093 cofcutr1d 28094 cofcutr2d 28095 |
| [Gonshor] p. 13 | Definition | df-adds 28129 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28145 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28171 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28299 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28319 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28627 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28629 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28628 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28664 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28187 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36617 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17637 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17639 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48920 df-cllaw 48918 df-comlaw 48919 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48932 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48953 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39485 dfmembpart2 39490 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32383 riesz2 32384 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32259 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32491 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32503 elpjidm 32502 pjnmopi 32466 |
| [Halmos] p. 44 | Remark | pjinormi 32005 pjinormii 31994 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32507 pjrn 32025 pjrni 32020 pjvec 32014 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32045 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32472 hmopidmpji 32470 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32509 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32498 pjocvec 32015 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32487 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32490 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32493 pjssdif2i 32492 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32173 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1823 |
| [Hatcher] p. 25 | Definition | df-phtpc 25130 df-phtpy 25109 |
| [Hatcher] p. 26 | Definition | df-pco 25143 df-pi1 25146 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25133 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25188 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22626 df-dmatalt 49145 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48549 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48534 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48546 bgoldbtbnd 48541 bgoldbtbnd 48541 tgblthelfgott 48547 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34995 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34996 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35010 hgt750lemb 35009 hgt750leme 35011 hgt750lemf 35006 hgt750lemg 35007 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48543 tgoldbachgt 35016 tgoldbachgtALTV 48544 tgoldbachgtd 35015 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34997 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30811 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19010 grpoideu 30827 mndideu 18802 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19040 grpoinveu 30837 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19071 grpo2inv 30849 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19083 grpoinvop 30851 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19105 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1796 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1797 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1799 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32738 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32751 cdj3i 32759 cdj3lem1 32752 cdjreui 32750 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32749 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42703 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42633 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42655 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42656 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42653 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42659 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42578 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42673 |
| [Holland95] p. 204 | Definition of involution | df-srng 20922 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40245 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42270 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42223 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40675 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42119 poml4N 40695 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42210 pexmidALTN 40720 pexmidN 40711 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42275 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39866 ldualset 39867 |
| [Holland95] p. 222 | Item 1 | df-lines 40243 df-pointsN 40244 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40645 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40689 omllaw4 39988 pol1N 40652 polcon3N 40659 |
| [Holland95] p. 223 | Definition | df-psubclN 40677 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40648 |
| [Holmes] p. 40 | Definition | df-xrn 38997 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31402 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32500 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32281 eigre 32153 eigrei 32152 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32282 eigorth 32156 eigorthi 32155 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32154 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30626 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30622 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30623 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30624 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30642 frgrregorufr0 30641 frgrregorufrg 30643 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30649 frrusgrord 30658 frrusgrord0 30657 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30405 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30632 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30635 frgrwopreg2 30636 frgrwopregasn 30633 frgrwopregbsn 30634 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30638 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30652 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30655 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30403 numclwlk1 30688 numclwlk1lem1 30686 numclwlk1lem2 30687 numclwwlk1 30678 numclwwlk8 30709 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30629 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30086 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30664 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30690 numclwwlkovh0 30689 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30698 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30295 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30702 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30705 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30708 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30720 natded 30720 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30720 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30720 natded 30720 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30720 |
| [Jech] p. 4 | Definition of class | cv 1567 cvjust 2755 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10563 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10561 alephmul 10562 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10560 infmap2 10199 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9785 |
| [Jech] p. 72 | Equation 9.3 | scott0 9859 scottex 9858 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9838 rankval4b 35459 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9876 |
| [Jech] p. 78 | Note | opthprc 5725 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43612 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43700 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43701 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43624 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43628 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43629 rmyp1 43630 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43631 rmym1 43632 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43622 rmx1 43623 rmxluc 43633 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43626 rmy1 43627 rmyluc 43634 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43636 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43637 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43657 jm2.17b 43658 jm2.17c 43659 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43690 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43694 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43685 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43660 jm2.24nn 43656 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43699 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43705 rmygeid 43661 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43717 |
| [Juillerat] p. 11 | Section *5 | etransc 46967 etransclem47 46965 etransclem48 46966 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46962 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46964 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46950 |
| [Juillerat] p. 13 | Proof | etransclem35 46953 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46956 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46942 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46959 |
| [Juillerat] p. 14 | Proof | etransclem23 46941 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1995 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2040 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2045 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2035 cbvaliw 2034 wl-cbvmotv 38134 wl-motae 38136 wl-moteq 38135 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2014 spimw 1998 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2061 spw 2062 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31834 chabs1i 31836 chabs2 31835 chabs2i 31837 chjass 31851 chjassi 31804 latabs1 18530 latabs2 18531 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32656 ela 32657 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32601 cvrval2 40016 |
| [Kalmbach] p. 16 | Definition | df-ol 39920 df-oml 39921 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31902 cmbri 31908 cmtvalN 39953 df-cm 31901 df-cmtN 39919 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39989 pjoml5 31931 pjoml5i 31906 |
| [Kalmbach] p. 22 | Definition | pjoml2 31929 pjoml2i 31903 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31932 cmcmi 31910 cmcmii 31915 cmtcomN 39991 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39987 omlsi 31722 pjoml 31754 pjomli 31753 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39986 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31914 cmcm3 31933 cmcm3i 31912 cmcm3ii 31917 cmcm4i 31913 cmt3N 39993 cmt4N 39994 cmtbr2N 39995 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31926 cmbr3i 31918 cmtbr3N 39996 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31936 fh1i 31939 fh2 31937 fh2i 31940 omlfh1N 40000 |
| [Kalmbach] p. 65 | Remark | chjatom 32675 chslej 31816 chsleji 31776 shslej 31698 shsleji 31688 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31813 chocini 31772 chsupcl 31658 chsupval2 31728 h0elch 31573 helch 31561 hsupval2 31727 ocin 31614 ococss 31611 shococss 31612 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31630 |
| [Kalmbach] p. 66 | Remark | df-pjh 31713 pjssmi 32483 pjssmii 31999 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31963 osumi 31960 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32518 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32718 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32628 |
| [Kalmbach] p. 140 | Remark | hatomic 32678 hatomici 32677 hatomistici 32680 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40061 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32699 lsatexch 39785 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32673 cvlcvr1 40081 cvr1 40152 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32692 cvexchi 32687 cvrexch 40162 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32682 hlrelat 40144 hlrelat5N 40143 lrelat 39756 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21244 lsmsatcv 39752 spansncv 31971 spansncvi 31970 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39771 spansncv2 32611 |
| [Kalmbach] p. 266 | Definition | df-st 32529 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32167 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10630 fpwwe2 10627 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10631 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10638 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10633 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10635 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10648 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10652 gchxpidm 10653 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10664 gchhar 10663 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10197 unxpwdom 9550 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10654 |
| [Kreyszig] p. 3 | Property M1 | metcl 24468 xmetcl 24467 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24475 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24708 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11931 muleqadd 11857 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24574 |
| [Kreyszig] p. 19 | Remark | mopntopon 24575 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24634 mopnm 24580 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24632 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24637 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24678 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23394 lmmbr 25396 lmmbr2 25397 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23516 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25451 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25414 iscmet2 25432 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25454 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23597 metelcls 25443 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25444 metcld2 25445 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25237 lmodvneg1 21005 nvinv 30957 vcm 30894 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25233 lmod0vs 20995 slmd0vs 33510 vc0 30892 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20996 slmdvs0 33511 vcz 30893 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31009 ngpmet 24739 nrmmetd 24710 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31004 imsdval2 31005 ncvspds 25299 ngpds 24740 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24725 nvnd 31006 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24754 nmge0 24753 nvge0 30991 nvz 30987 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24760 nvabs 30990 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31119 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31063 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31125 blocni 31123 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31124 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25342 ipeq0 21767 ipz 31037 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25354 pythi 31168 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31172 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25376 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15910 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25574 minveco 31202 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31068 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25467 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31191 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32441 leopg 32440 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32459 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31236 |
| [Kulpa] p. 547 | Theorem | poimir 38270 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38269 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38268 |
| [Kulpa] p. 548 | Theorem | broucube 38271 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38263 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38264 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2413 axnul 5267 |
| [Kunen] p. 11 | Axiom 3 | axnul 5267 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5249 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8834 mapvalg 8832 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10505 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7936 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9735 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9777 r1elssi 9776 |
| [Kunen] p. 107 | Exercise 4 | rankop 9829 rankopb 9823 rankuni 9834 rankxplim 9850 rankxpsuc 9853 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45633 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45641 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45640 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45642 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45647 rexabso 45648 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45654 n0abso 45655 ssabso 45653 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45656 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45666 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45661 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45664 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45665 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45660 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45672 wfaxpr 45677 wfaxreg 45679 wfaxrep 45673 wfaxsep 45674 wfaxun 45678 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45663 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45676 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45672 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45671 omelaxinf2 45668 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45681 wfaxinf2 45680 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45694 permaxext 45684 permaxinf2 45692 permaxnul 45687 permaxpow 45688 permaxpr 45689 permaxrep 45685 permaxsep 45686 permaxun 45690 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45682 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45693 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4968 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34021 |
| [Lang] p. | Definition | df-rn 5672 |
| [Lang] p. 3 | Statement | lidrideqd 18726 mndbn0 18807 |
| [Lang] p. 3 | Definition | df-mnd 18792 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18744 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18899 |
| [Lang] p. 5 | Equation | gsumreidx 19986 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48914 |
| [Lang] p. 6 | Example | nn0mnd 48911 |
| [Lang] p. 6 | Equation | gsumxp2 20049 |
| [Lang] p. 6 | Statement | cycsubm 19272 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19145 |
| [Lang] p. 6 | Observation | mndlsmidm 19739 |
| [Lang] p. 7 | Definition | dfgrp2e 19029 |
| [Lang] p. 30 | Definition | df-tocyc 33393 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33438 |
| [Lang] p. 32 | Property (b) | cyc3conja 33443 cycpmconjv 33428 |
| [Lang] p. 53 | Definition | df-cat 17723 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18153 cat1lem 18152 |
| [Lang] p. 54 | Definition | df-iso 17805 |
| [Lang] p. 57 | Definition | df-inito 18040 df-termo 18041 |
| [Lang] p. 58 | Example | irinitoringc 21608 |
| [Lang] p. 58 | Statement | initoeu1 18067 termoeu1 18074 |
| [Lang] p. 62 | Definition | df-func 17914 |
| [Lang] p. 65 | Definition | df-nat 18002 |
| [Lang] p. 91 | Note | df-ringc 20730 |
| [Lang] p. 92 | Statement | mxidlprm 33719 |
| [Lang] p. 92 | Definition | isprmidlc 21451 |
| [Lang] p. 128 | Remark | dsmmlmod 21874 |
| [Lang] p. 129 | Proof | lincscm 49177 lincscmcl 49179 lincsum 49176 lincsumcl 49178 |
| [Lang] p. 129 | Statement | lincolss 49181 |
| [Lang] p. 129 | Observation | dsmmfi 21867 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33983 qusdimsum 33984 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33964 |
| [Lang] p. 147 | Definition | snlindsntor 49218 |
| [Lang] p. 504 | Statement | mat1 22583 matring 22579 |
| [Lang] p. 504 | Definition | df-mamu 22527 |
| [Lang] p. 505 | Statement | mamuass 22538 mamutpos 22594 matassa 22580 mattposvs 22591 tposmap 22593 |
| [Lang] p. 513 | Definition | mdet1 22737 mdetf 22731 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22827 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22723 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22747 |
| [Lang] p. 515 | Definition | df-minmar1 22771 smadiadetr 22811 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22746 mdetralt 22744 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22759 |
| [Lang] p. 518 | Definition | df-madu 22770 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22781 madurid 22780 matinv 22813 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23026 |
| [Lang], p. 190 | Chapter 6 | vieta 33936 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34050 finextalg 34054 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34019 fedgmul 33987 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34081 |
| [Lang], p. 561 | Remark | chpmatply1 22968 |
| [Lang], p. 561 | Definition | df-chpmat 22963 |
| [Lang2] p. 3 | Notations | df-ind 12218 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45014 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45009 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45015 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5267 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2740 wl-df.clab 38119 |
| [Levy] p. 59 | Definition | df-ttrcl 9676 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9722 |
| [Levy] p. 338 | Axiom | df-clel 2836 df-cleq 2753 wl-df.cleq 38120 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38123 |
| [Levy] p. 357 | Definition extends to class variables a relation already valid for set variables, and is therefore conservative. This only sketches the conservativity arguement; for details see Appendix | wl-df.clel 38123 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2836 df-cleq 2753 wl-df.cleq 38120 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2740 wl-df.clab 38119 |
| [Levy] p. 358 | Axiom | df-clab 2740 wl-df.clab 38119 |
| [Levy58] p. 2 | Definition I | isfin1-3 10369 |
| [Levy58] p. 2 | Definition II | df-fin2 10269 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10268 |
| [Levy58] p. 2 | Definition III | df-fin3 10271 |
| [Levy58] p. 3 | Definition V | df-fin5 10272 |
| [Levy58] p. 3 | Definition IV | df-fin4 10270 |
| [Levy58] p. 4 | Definition VI | df-fin6 10273 |
| [Levy58] p. 4 | Definition VII | df-fin7 10274 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10398 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27826 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27837 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27869 nosupbnd1 27854 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27871 nosupbnd2 27856 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27875 noetasuplem4 27876 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27872 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1796 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1797 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1799 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32726 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32730 mdsymi 32729 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32724 mdsymlem6 32726 mdsymlem7 32727 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32728 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32631 ssdmd2 32632 ssmd1 32629 ssmd2 32630 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32627 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32599 df-md 32598 mdbr 32612 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32649 mdslj1i 32637 mdslj2i 32638 mdslle1i 32635 mdslle2i 32636 mdslmd1i 32647 mdslmd2i 32648 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32639 mdsl2bi 32641 mdsl2i 32640 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32653 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32650 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32651 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32628 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32633 mdsl3 32634 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32652 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32747 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40063 hlrelat1 40142 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39781 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32654 cvmdi 32642 cvnbtwn4 32607 cvrnbtwn4 40021 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32655 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40082 cvp 32693 cvrp 40158 lcvp 39782 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32717 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32716 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40075 hlexch4N 40134 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32719 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40185 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40491 atpsubN 40495 df-pointsN 40244 pointpsubN 40493 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40246 pmap11 40504 pmaple 40503 pmapsub 40510 pmapval 40499 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40507 pmap1N 40509 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40512 pmapglb2N 40513 pmapglb2xN 40514 pmapglbx 40511 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40594 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40219 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40538 paddclN 40584 paddidm 40583 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40220 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40580 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40219 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40220 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19744 lsmmod2 19745 lssats 39754 shatomici 32676 shatomistici 32679 shmodi 31708 shmodsi 31707 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32618 mdsymlem7 32727 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31907 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31811 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32733 |
| [Margaris] p. 40 | Rule C | exlimiv 1958 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 401 df-ex 1808 df-or 861 dfbi2 479 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 30717 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45593 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45594 |
| [Margaris] p. 79 | Rule C | exinst01 45304 exinst11 45305 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2004 19.2g 2222 r19.2z 4459 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2236 rr19.3v 3625 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2192 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1854 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1809 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2215 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2239 19.9h 2319 exlimd 2252 exlimdh 2323 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2195 excomim 2196 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2358 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30718 conventions-labels 30718 conventions-labels 30718 conventions-labels 30718 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1855 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45058 albi 1846 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2259 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2260 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45060 exbi 1875 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2263 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45057 2alimdv 1946 alimd 2246 alimdh 1845 alimdv 1944 ax-4 1837 ralimdaa 3264 ralimdv 3177 ralimdva 3175 ralimdvva 3210 sbcimdv 3811 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2241 19.21h 2320 19.21t 2240 19.21vv 45056 alrimd 2249 alrimdd 2248 alrimdh 1891 alrimdv 1957 alrimi 2247 alrimih 1852 alrimiv 1955 alrimivv 1956 bj-alrimdh 37183 hbralrimi 3153 r19.21be 3256 r19.21bi 3255 ralrimd 3268 ralrimdv 3161 ralrimdva 3163 ralrimdvv 3207 ralrimdvva 3218 ralrimi 3261 ralrimia 3262 ralrimiv 3154 ralrimiva 3155 ralrimivv 3204 ralrimivva 3206 ralrimivvva 3209 ralrimivw 3159 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45059 2eximdv 1947 bj-exim 37198 exim 1862 eximd 2250 eximdh 1892 eximdv 1945 rexim 3104 reximd2a 3273 reximdai 3265 reximdd 45836 reximddv 3179 reximddv2 3222 reximddv3 3180 reximdv 3178 reximdv2 3173 reximdva 3176 reximdvai 3174 reximdvva 3211 reximi2 3096 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2245 19.23bi 2225 19.23h 2321 19.23t 2244 exlimdv 1961 exlimdvv 1962 exlimexi 45203 exlimiv 1958 exlimivv 1960 rexlimd3 45832 rexlimdv 3162 rexlimdv3a 3168 rexlimdva 3164 rexlimdva2 3166 rexlimdvaa 3165 rexlimdvv 3219 rexlimdvva 3220 rexlimdvvva 3221 rexlimdvw 3169 rexlimiv 3157 rexlimiva 3156 rexlimivv 3205 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2019 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1908 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1898 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2261 r19.27z 4470 r19.27zv 4471 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2262 19.28vv 45066 r19.28z 4462 r19.28zf 45847 r19.28zv 4466 rr19.28v 3626 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1901 r19.29d2r 3150 r19.29imd 3128 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1909 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2268 19.31vv 45064 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2267 r19.32 47802 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45062 19.33 1912 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2020 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1905 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2264 19.36vv 45063 r19.36zv 4472 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2266 19.37vv 45065 r19.37zv 4467 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1867 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2018 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1915 19.40 1914 r19.40 3129 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2269 19.41rg 45229 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2270 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1910 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2271 r19.44zv 4469 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2272 r19.45zv 4468 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2636 |
| [Mayet] p. 370 | Remark | jpi 32588 largei 32585 stri 32575 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32530 ishst 32532 |
| [Mayet3] p. 10 | Theorem | hstrbi 32584 hstri 32583 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32046 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32047 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32596 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31650 chsupcl 31658 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32678 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32672 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32699 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40725 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18542 latj32 18540 latjass 18538 |
| [Megill] p. 444 | Axiom C5 | ax-5 1938 ax5ALT 39649 |
| [Megill] p. 444 | Section 7 | conventions 30717 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39643 ax-c11n 39630 axc11n 2456 |
| [Megill] p. 446 | Lemma L17 | equtrr 2050 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39638 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39670 hbnae 2462 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2511 sbid 2289 sbidd-misc 50464 sbidd 50463 |
| [Megill] p. 448 | Remark 9.6 | axc14 2493 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39626 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39625 sp 2217 |
| [Megill] p. 448 | Scheme C6' | ax-11 2190 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39627 |
| [Megill] p. 448 | Scheme C8' | ax-7 2036 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39632 |
| [Megill] p. 448 | Scheme C10' | ax-6 1995 ax-c10 39628 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39629 |
| [Megill] p. 448 | Scheme C12' | ax-8 2143 |
| [Megill] p. 448 | Scheme C13' | ax-9 2151 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39633 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39631 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39634 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39646 dral1 2469 dral2-o 39672 dral2 2468 drex1 2471 drex2 2472 drsb1 2525 drsb2 2300 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2205 sbequ 2115 sbid2v 2539 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39639 hba1 2326 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47596 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3831 rspsbca 3832 stdpc4 2100 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39626 ra4 3838 stdpc5 2242 |
| [Mendelson] p. 81 | Rule C | exlimiv 1958 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2056 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2284 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3742 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5497 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4354 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4355 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4229 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4286 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4230 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4094 |
| [Mendelson] p. 231 | Definition of union | dfun3 4228 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5432 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4868 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5552 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4579 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5553 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4895 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5813 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6270 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7773 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6366 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8580 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9127 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9048 xpsneng 9049 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9055 xpcomeng 9056 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9058 |
| [Mendelson] p. 255 | Definition | brsdom 8970 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9051 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8827 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9033 mapsnend 9032 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9133 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9132 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8879 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9036 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9052 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10161 djucomen 10160 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10165 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10159 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8515 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8542 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10542 |
| [Mendelson] p. 281 | Definition | df-r1 9735 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9784 |
| [Mendelson] p. 287 | Axiom system MK | ru 3742 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30576 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30611 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30613 vdgn1frgrv3 30614 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30615 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30608 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30601 2pthfrgrrn 30599 2pthfrgrrn2 30600 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31570 |
| [Monk1] p. 22 | Remark | conventions 30717 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30717 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4190 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5769 ssrelf 32926 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5770 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5173 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6264 coi2 6265 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5910 rn0 5916 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5871 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5679 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5919 rnxp 6168 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5760 xp0 5761 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6079 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6076 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7910 imaexg 7909 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6073 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7070 funfvop 7045 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6935 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6946 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6582 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7252 dff13f 7253 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7217 funrnex 7950 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7245 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6228 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4928 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8002 df-1st 7985 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8003 df-2nd 7986 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9825 ranksnb 9798 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9826 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9827 rankunb 9821 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9809 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9735 r1val2 9808 |
| [Monk1] p. 117 | Lemma | zorn2 10489 zorn2g 10486 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9971 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10544 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9966 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1837 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2036 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2211 ax-c15 39631 ax12v2 2213 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39626 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2190 |
| [Monk2] p. 109 | Lemma 15 | equvini 2485 equvinv 2057 eqvinop 5469 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1938 ax5ALT 39649 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2174 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2190 |
| [Monk2] p. 114 | Lemma 21 | sp 2217 |
| [Monk2] p. 114 | Lemma 22 | axc4 2352 hba1-o 39639 hba1 2326 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2186 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2208 nfra2 3363 nfra2w 3299 |
| [Moore] p. 53 | Part I | df-mre 17637 |
| [Munkres] p. 77 | Example 2 | distop 23131 indistop 23138 indistopon 23137 |
| [Munkres] p. 77 | Example 3 | fctop 23140 fctop2 23141 |
| [Munkres] p. 77 | Example 4 | cctop 23142 |
| [Munkres] p. 78 | Definition of basis | df-bases 23082 isbasis3g 23085 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17495 tgval2 23092 |
| [Munkres] p. 79 | Remark | tgcl 23105 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23099 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23123 tgss3 23122 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23124 basgen2 23125 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37961 topdifinfeq 37962 topdifinffin 37960 topdifinfindis 37958 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23296 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23174 topcld 23171 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23175 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23177 |
| [Munkres] p. 94 | Definition of closure | clsval 23173 |
| [Munkres] p. 94 | Definition of interior | ntrval 23172 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23211 elcls 23209 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23219 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23284 neindisj 23253 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23286 |
| [Munkres] p. 97 | Definition of limit point | islp2 23281 lpval 23275 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23451 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23363 iscn 23371 iscn2 23374 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23416 cncnp2 23417 cncnpi 23414 df-cnp 23364 iscnp 23373 iscnp2 23375 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24679 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25449 |
| [Nathanson] p. 123 | Remark | reprgt 34974 reprinfz1 34975 reprlt 34972 |
| [Nathanson] p. 123 | Definition | df-repr 34962 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34994 |
| [Nathanson] p. 123 | Proposition | breprexp 34986 breprexpnat 34987 itgexpif 34959 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32422 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48542 |
| [Pfenning] p. 17 | Definition XM | natded 30720 |
| [Pfenning] p. 17 | Definition NNC | natded 30720 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 30720 |
| [Pfenning] p. 18 | Rule" | natded 30720 |
| [Pfenning] p. 18 | Definition /\I | natded 30720 |
| [Pfenning] p. 18 | Definition ` `E | natded 30720 natded 30720 natded 30720 natded 30720 natded 30720 |
| [Pfenning] p. 18 | Definition ` `I | natded 30720 natded 30720 natded 30720 natded 30720 natded 30720 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30720 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30720 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30720 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30720 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30720 |
| [Pfenning] p. 127 | Definition =E | natded 30720 |
| [Pfenning] p. 127 | Definition =I | natded 30720 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25340 df-dip 31019 dip0l 31036 ip0l 21765 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25381 ipval 31021 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31032 ipcj 21763 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25343 dipdir 31160 ipdir 21768 ipdiri 31148 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31028 nmsq 25332 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31143 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31145 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31146 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25349 dipass 31163 ipass 21774 ipassi 31159 |
| [Prugovecki] p. 186 | Definition of bra | braval 32262 df-bra 32168 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32169 kbval 32272 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32700 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40630 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32714 atcvat4i 32715 cvrat3 40184 cvrat4 40185 lsatcvat3 39794 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32600 cvrval 40011 df-cv 32597 df-lcv 39761 lspsncv0 21249 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40642 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40643 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2740 rabid 3435 rabidd 45843 wl-df.clab 38119 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2312 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2753 wl-df.cleq 38120 |
| [Quine] p. 19 | Definition 2.9 | conventions 30717 df-v 3455 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2900 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2897 abid2f 2953 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2309 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2117 sbalex 2276 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2836 wl-df.clel 38123 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2761 eqid1 30784 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2768 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3744 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3745 dfsbcq2 3746 |
| [Quine] p. 43 | Theorem 6.8 | vex 3457 |
| [Quine] p. 43 | Theorem 6.9 | isset 3467 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3549 spcgv 3554 spcimgf 3517 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3756 spsbcd 3757 |
| [Quine] p. 44 | Theorem 6.12 | elex 3474 |
| [Quine] p. 44 | Theorem 6.13 | elab 3637 elabg 3634 elabgf 3632 |
| [Quine] p. 44 | Theorem 6.14 | noel 4290 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4682 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4591 df-sn 4589 |
| [Quine] p. 49 | Theorem 7.4 | snss 4749 snssg 4748 |
| [Quine] p. 49 | Theorem 7.5 | prss 4785 prssg 4784 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4727 prid1g 4725 prid2 4728 prid2g 4726 snid 4627 snidg 4625 |
| [Quine] p. 51 | Theorem 7.12 | snex 5410 |
| [Quine] p. 51 | Theorem 7.13 | prex 5409 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4890 unisnALT 45604 unisng 4889 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4894 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4903 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4900 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6506 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47790 dfiota2 6493 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47799 iotaval 6510 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6516 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6512 |
| [Quine] p. 58 | Definition 9.1 | df-op 4595 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5509 opabidw 5508 opelopab 5527 opelopaba 5520 opelopabaf 5529 opelopabf 5530 opelopabg 5523 opelopabga 5517 opelopabgf 5525 oprabid 7442 oprabidw 7441 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5667 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5669 |
| [Quine] p. 64 | Definition 9.15 | df-id 5556 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6601 |
| [Quine] p. 65 | Theorem 10.4 | funi 6568 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6589 funsng 6587 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6538 |
| [Quine] p. 65 | Definition 10.2 | args 6094 dffv4 6878 |
| [Quine] p. 68 | Definition 10.11 | conventions 30717 df-fv 6544 fv2 6876 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14308 nn0opth2i 14307 nn0opthi 14306 omopthi 8646 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8396 |
| [Quine] p. 232 | Equation i | carddom 10537 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6623 funimaexg 6622 |
| [Quine] p. 331 | Axiom system NF | ru 3742 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31402 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31019 polid 31477 polid2i 31475 polidi 31476 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31131 |
| [ReedSimon] p. 195 | Remark | lnophm 32337 lnophmi 32336 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32450 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32452 leopmuli 32451 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32455 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32170 leoppos 32444 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32454 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32443 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48343 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48351 |
| [Roman] p. 4 | Definition | df-dmat 22626 df-dmatalt 49145 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20230 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20316 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49232 |
| [Roman] p. 112 | Note | isldepslvec2 49232 ldepsnlinc 49255 zlmodzxznm 49244 |
| [Roman] p. 112 | Example | zlmodzxzequa 49243 zlmodzxzequap 49246 zlmodzxzldep 49251 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23026 |
| [Rosenlicht] p. 80 | Theorem | heicant 38272 |
| [Rosser] p. 281 | Definition | df-op 4595 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34998 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34999 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49113 pmtr3ncom 19544 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19540 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19483 cayleyth 19484 |
| [Rudin] p. 164 | Equation 27 | efcan 16149 |
| [Rudin] p. 164 | Equation 30 | efzval 16157 |
| [Rudin] p. 167 | Equation 48 | absefi 16251 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1799 |
| [Sanford] p. 39 | Rule 4 | mptxor 1797 |
| [Sanford] p. 40 | Rule 1 | mptnan 1796 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6115 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6118 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6114 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6112 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17637 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17638 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17638 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17640 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10119 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43759 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10429 axdc3 10437 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20318 isrngo 38514 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31860 |
| [Schechter] p. 276 | Definition of span | df-span 31627 spanval 31651 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23129 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6385 onelord 43948 ordelon 6384 ordelord 6382 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43949 sucidg 6444 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6416 onsuc 7808 ord0 6415 ordsuci 7806 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43950 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5221 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43725 elon2 6371 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6366 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5564 epelg 5562 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9561 epirron 43951 ordirr 6378 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43953 oneptr 43952 ontr1 6408 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6404 oneptri 43954 ordtri3or 6393 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8485 ord0eln0 6417 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6430 onsucss 43963 trsucss 6451 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7813 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6457 ordnbtwn 6456 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43965 ordnexbtwnsuc 43964 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10384 onsucf1lem 43966 onsucf1o 43969 onsucf1olem 43967 onsucrn 43968 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43970 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7840 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43959 ordne0gt0 43958 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43961 limnsuc 43962 onsucelab 43960 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9611 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7855 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9614 ordom 7871 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9615 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8625 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7778 ssorduni 7777 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8515 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9618 limom 7877 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8452 df1o2 8459 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8500 oa0suclim 43972 oalim 8516 oasuc 8508 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8501 om0suclim 43973 omlim 8517 omsuc 8510 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8506 oe0m1 8505 oe0suclim 43974 oelim 8518 oesuc 8511 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43926 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43976 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43977 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43978 limexissupab 43980 limiun 43979 limuni 6423 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8522 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8526 om1om1r 43981 om1r 8527 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8519 oaomoecl 43975 oecl 8521 omcl 8520 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43928 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8528 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8529 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43982 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43983 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8596 nnamecl 43984 nnecl 8598 nnmcl 8597 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43985 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8536 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8537 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8544 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43987 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43988 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43990 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8543 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43994 omword1 8557 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43993 oaordnrex 43992 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43989 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43995 omword2 8558 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43996 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43997 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43998 omordi 8550 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8552 omord2com 43999 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44000 df-2o 8453 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44003 oewordi 8576 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44004 oeworde 8578 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44005 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44006 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44002 omnord1ex 44001 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44007 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44009 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44013 oenord1ex 44012 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44014 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8545 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44008 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8563 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8564 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44016 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8582 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44017 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44018 cantnfub2 44019 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44022 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29230 axtgcgrrflx 28707 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29231 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29232 axtgcgrid 28708 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28693 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29243 axtgsegcon 28709 df-trkgcb 28695 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29254 axtg5seg 28710 df-trkgcb 28695 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29255 axtgbtwnid 28711 df-trkgb 28694 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29257 axtgpasch 28712 df-trkgb 28694 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29276 df-trkg2d 35018 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28715 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28716 df-trkg2d 35018 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29279 axtgeucl 28717 df-trkge 28696 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29292 axtgcont 28714 axtgcont1 28713 df-trkgb 28694 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29177 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36445 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36447 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36450 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36454 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36455 tgcgrcomimp 28722 tgcgrcoml 28724 tgcgrcomr 28723 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36460 tgcgrtriv 28729 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36464 tg5segofs 35029 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35026 df-ofs 36441 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36466 tgcgrextend 28730 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36468 tgsegconeq 28731 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36480 btwntriv2 36470 tgbtwntriv2 28732 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36471 tgbtwncom 28733 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36474 tgbtwntriv1 28736 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36475 tgbtwnswapid 28737 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36481 btwnintr 36477 tgbtwnexch2 28741 tgbtwnintr 28738 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36483 btwnexch3 36478 tgbtwnexch 28743 tgbtwnexch3 28739 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36482 tgbtwnouttr 28742 tgbtwnouttr2 28740 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29275 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36485 tgbtwndiff 28751 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28744 trisegint 36486 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36502 tgifscgr 28753 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28803 colrot1 28804 colrot2 28805 lncom 28871 lnrot1 28872 lnrot2 28873 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36498 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36503 tgcgrsub 28754 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36513 tgcgrxfr 28763 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28762 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36499 df-cgrg 28756 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28756 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36514 tgbtwnxfr 28775 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36520 colinearperm2 36522 colinearperm3 36521 colinearperm4 36523 colinearperm5 36524 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28778 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36497 tgellng 28798 tglng 28791 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36525 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36533 lnxfr 28811 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36534 lnext 28812 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36538 tgfscgr 28813 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36539 lncgr 28814 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36500 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36541 lnid 28815 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36542 tgidinside 28816 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36559 tgbtwnconn1 28820 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36560 tgbtwnconn2 28821 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36561 tgbtwnconn3 28822 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36567 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36565 legov 28830 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28831 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28844 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36568 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36570 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36572 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36573 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36574 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36571 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36576 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28832 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28834 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28835 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28836 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28837 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36583 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36584 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36579 df-outsideof 36578 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36580 ishlg 28850 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28855 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28857 outsideofrflx 36585 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28851 hlcomd 28852 outsideofcom 36586 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28858 outsideoftr 36587 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 28867 hlcgreu 28866 outsideofeu 36589 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36596 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36597 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36590 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36605 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36606 tglineelsb2 28881 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36608 linerflx1 36607 linerflx2 36609 tglinecom 28884 tglinerflx1 28882 tglinerflx2 28883 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36611 tglinethru 28885 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36595 tglng 28791 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28839 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36614 tglinethrueu 28888 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36615 tglineineq 28892 tglineinsn 28893 tglineinteq 28895 tglineintmo 28891 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28899 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28900 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28901 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28919 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28915 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28907 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28906 ismir 28912 mirbtwn 28911 mircgr 28910 mirfv 28909 mirval 28908 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28917 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28918 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28919 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28922 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28923 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28928 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28925 mirbtwni 28924 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28926 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28938 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28942 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28939 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28940 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28941 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28944 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28945 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28953 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28949 israg 28952 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28954 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28955 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28957 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28958 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28959 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28960 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28961 ragncol 28964 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28962 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28968 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28972 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28969 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28951 isperp 28967 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28970 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28977 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28986 colperpexlem2 28987 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28989 colperpexlem3 28988 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28994 midex 28993 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28991 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29000 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28995 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29004 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29007 opphllem6 29008 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29010 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28712 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29012 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29020 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29015 hpgbr 29017 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29022 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29021 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29023 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29024 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29025 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29026 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29027 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29040 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29042 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29046 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29030 elplng 29036 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29048 lnssplng1 29049 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29053 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29067 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29057 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29071 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29072 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29073 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29074 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29075 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29078 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29080 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29058 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29081 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29084 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29085 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29086 lnperpexs 29087 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29088 trgcopyeu 29090 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29114 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29093 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29102 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29100 cgrahl2 29101 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29103 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29104 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29106 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29107 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29110 cgrahl 29111 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29115 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29116 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29117 acopyeu 29118 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29119 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29120 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29121 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29122 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29124 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29131 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29135 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29128 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29143 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29136 isleag 29137 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29145 tgsas1 29144 tgsas2 29146 tgsas3 29147 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29149 tgasa1 29148 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29150 tgsss2 29151 tgsss3 29152 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29160 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29163 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29164 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29169 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29170 dfprlng3 29171 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29173 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29174 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29177 prlngmo2 29179 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29178 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29180 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29181 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29182 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29183 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27411 dchrsum 27409 dchrsum2 27408 sumdchr 27412 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27413 sum2dchr 27414 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20137 ablfacrp2 20138 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27356 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27357 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27364 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27622 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27625 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27679 vmalogdivsum2 27678 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27669 dirith2 27668 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27667 rpvmasum 27666 rpvmasum2 27652 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27627 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27665 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27632 dchrisumlem1 27629 dchrisumlem2 27630 dchrisumlem3 27631 dchrisumlema 27628 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27635 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27664 dchrmusumlem 27662 dchrvmasumlem 27663 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27634 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27636 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27660 dchrisum0re 27653 dchrisumn0 27661 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27646 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27650 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27651 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27706 pntrsumbnd2 27707 pntrsumo1 27705 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27670 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27672 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27674 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27677 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27682 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27683 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27688 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27690 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27691 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27699 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27700 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27697 selberg3lem2 27698 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27701 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27695 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27708 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27709 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27710 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27724 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27736 pntlemb 27737 pntlemc 27735 pntlemd 27734 pntlemg 27738 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27736 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27728 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27733 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27736 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27749 pntleml 27751 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34099 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34086 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34118 constrinvcl 34129 constrmulcl 34127 constrnegcl 34119 constrsqrtcl 34135 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34105 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34115 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34137 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34147 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4258 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4362 dif0 4333 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4451 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4435 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4249 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4250 |
| [Stoll] p. 20 | Remark | invdif 4231 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4597 |
| [Stoll] p. 43 | Definition | uniiun 5022 |
| [Stoll] p. 44 | Definition | intiin 5023 |
| [Stoll] p. 45 | Definition | df-iin 4958 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4957 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 406 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4258 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45015 |
| [Suppes] p. 22 | Theorem 2 | eq0 4303 eq0f 4300 |
| [Suppes] p. 22 | Theorem 4 | eqss 3951 eqssd 3953 eqssi 3952 |
| [Suppes] p. 23 | Theorem 5 | ss0 4358 ss0b 4357 |
| [Suppes] p. 23 | Theorem 6 | sstr 3944 sstrALT2 45513 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4056 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4058 |
| [Suppes] p. 23 | Theorem 9 | psstr 4061 |
| [Suppes] p. 23 | Theorem 10 | pssss 4051 |
| [Suppes] p. 25 | Theorem 12 | elin 3920 elun 4106 |
| [Suppes] p. 26 | Theorem 15 | inidm 4178 |
| [Suppes] p. 26 | Theorem 16 | in0 4351 |
| [Suppes] p. 27 | Theorem 23 | unidm 4110 |
| [Suppes] p. 27 | Theorem 24 | un0 4350 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4130 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4138 |
| [Suppes] p. 27 | Theorem 27 | unss 4142 |
| [Suppes] p. 27 | Theorem 28 | indir 4238 |
| [Suppes] p. 27 | Theorem 29 | undir 4239 |
| [Suppes] p. 28 | Theorem 32 | difid 4331 |
| [Suppes] p. 29 | Theorem 33 | difin 4224 |
| [Suppes] p. 29 | Theorem 34 | indif 4232 |
| [Suppes] p. 29 | Theorem 35 | undif1 4436 |
| [Suppes] p. 29 | Theorem 36 | difun2 4441 |
| [Suppes] p. 29 | Theorem 37 | difin0 4434 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4432 |
| [Suppes] p. 29 | Theorem 39 | difundi 4242 |
| [Suppes] p. 29 | Theorem 40 | difindi 4244 |
| [Suppes] p. 30 | Theorem 41 | nalset 5276 |
| [Suppes] p. 39 | Theorem 61 | uniss 4879 |
| [Suppes] p. 39 | Theorem 65 | uniop 5498 |
| [Suppes] p. 41 | Theorem 70 | intsn 4948 |
| [Suppes] p. 42 | Theorem 71 | intpr 4946 intprg 4945 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5453 |
| [Suppes] p. 42 | Theorem 78 | intun 4944 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4995 dfiun2g 4993 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4996 |
| [Suppes] p. 47 | Theorem 86 | elpw 4565 elpw2 5304 elpw2g 5303 elpwg 4564 elpwgdedVD 45595 |
| [Suppes] p. 47 | Theorem 87 | pwid 4584 |
| [Suppes] p. 47 | Theorem 89 | pw0 4777 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4778 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5676 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5819 xpindir 5820 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5730 xpundir 5731 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9558 |
| [Suppes] p. 58 | Theorem 2 | relss 5768 |
| [Suppes] p. 59 | Theorem 4 | eldm 5890 eldm2 5891 eldm2g 5889 eldmg 5888 |
| [Suppes] p. 59 | Definition 3 | df-dm 5671 |
| [Suppes] p. 60 | Theorem 6 | dmin 5901 |
| [Suppes] p. 60 | Theorem 8 | rnun 6142 |
| [Suppes] p. 60 | Theorem 9 | rnin 6143 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5878 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5868 brcnvg 5865 |
| [Suppes] p. 62 | Equation 5 | elcnv 5862 elcnv2 5863 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6106 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6141 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6139 |
| [Suppes] p. 63 | Definition | dftrrels2 39276 |
| [Suppes] p. 63 | Theorem 20 | co02 6262 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5965 |
| [Suppes] p. 63 | Definition 7 | df-co 5670 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5875 |
| [Suppes] p. 64 | Theorem 27 | coass 6267 |
| [Suppes] p. 65 | Theorem 31 | resundi 5992 |
| [Suppes] p. 65 | Theorem 34 | elima 6067 elima2 6068 elima3 6069 elimag 6066 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6147 |
| [Suppes] p. 66 | Theorem 40 | dminss 6150 |
| [Suppes] p. 66 | Theorem 41 | imainss 6151 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6154 |
| [Suppes] p. 81 | Definition 34 | dfec2 8696 |
| [Suppes] p. 82 | Theorem 72 | elec 8740 elecALTV 38888 elecg 8738 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39312 erth 8748 erth2 8749 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39315 erdisj 8751 |
| [Suppes] p. 83 | Definition 35, | df-parts 39485 dfmembpart2 39490 |
| [Suppes] p. 89 | Theorem 96 | map0b 8880 |
| [Suppes] p. 89 | Theorem 97 | map0 8884 map0g 8881 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8885 mapsnd 8883 |
| [Suppes] p. 89 | Theorem 99 | mapss 8886 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10051 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10050 |
| [Suppes] p. 92 | Theorem 1 | enref 8981 enrefg 8980 |
| [Suppes] p. 92 | Theorem 2 | ensym 8999 ensymb 8998 ensymi 9000 |
| [Suppes] p. 92 | Theorem 3 | entr 9002 |
| [Suppes] p. 92 | Theorem 4 | unen 9041 |
| [Suppes] p. 94 | Theorem 15 | endom 8975 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8996 |
| [Suppes] p. 94 | Theorem 17 | domtr 9003 |
| [Suppes] p. 95 | Theorem 18 | sbth 9084 |
| [Suppes] p. 97 | Theorem 23 | canth2 9117 canth2g 9118 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9088 df-sdom 8945 dfsdom2 9087 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9101 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9090 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9089 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9099 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8978 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9102 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9097 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9027 fundmeng 9028 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9062 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9098 |
| [Suppes] p. 104 | Theorem 37 | fofi 9272 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9277 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9277 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10534 |
| [Suppes] p. 130 | Definition 3 | df-tr 5218 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7778 |
| [Suppes] p. 134 | Definition 6 | df-suc 6366 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7896 finds 7892 finds1 7895 finds2 7894 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9620 isfinite2 9257 isfiniteg 9259 unbnn 9255 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10902 df-ltpq 10894 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7858 tfinds 7855 tfinds2 7859 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8535 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8537 |
| [Suppes] p. 211 | Theorem 25 | oaass 8545 |
| [Suppes] p. 225 | Definition 8 | iscard2 9961 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10546 |
| [Suppes] p. 228 | Theorem 59 | harcard 9963 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10049 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6413 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7791 onminsb 7792 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10556 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10053 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10060 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10054 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9925 |
| [Suppes] p. 242 | Theorem 6 | weth 10478 |
| [Suppes] p. 242 | Theorem 8 | entric 10540 |
| [Suppes] p. 242 | Theorem 9 | carden 10534 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36154 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36158 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2733 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2753 wl-df.cleq 38120 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2836 wl-df.clel 38123 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2755 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2781 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7414 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3742 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5392 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4613 elpr2 4615 elpr2g 4614 elprg 4611 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4603 elsn2 4630 elsn2g 4629 elsng 4602 velsn 4604 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5449 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4598 sneqr 4804 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4609 dfsn2 4601 dfsn2ALT 4610 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7739 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5458 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5445 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5429 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7742 unexg 7741 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4656 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4872 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3911 df-un 3909 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4888 uniprg 4887 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5348 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4654 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6433 elsucg 6431 sstr2 3943 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4111 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4161 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4124 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4179 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4236 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4237 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3924 df-ss 3921 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4563 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4139 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3922 sseqin2 4175 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3958 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4188 inss2 4189 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4000 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4882 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5430 sspwimp 45596 sspwimpALT 45603 sspwimpALT2 45606 sspwimpcf 45598 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5437 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5237 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3415 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5269 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3907 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37129 dfnul2 4288 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4331 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4306 n0f 4302 neq0 4305 neq0f 4301 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9557 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9700 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9715 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3455 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5282 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4356 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5290 ssexg 5289 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5285 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9569 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9561 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4320 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4088 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4252 undif3VD 45560 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4089 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4096 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3078 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3088 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7751 xpexg 7748 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5668 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6607 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6785 fun11 6610 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6549 svrelfun 6608 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5877 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5879 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5673 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5674 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5670 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6192 dfrel2 6187 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5677 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5798 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5805 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5818 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6004 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5984 opelresi 5986 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6011 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 6000 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6005 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6578 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6110 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6576 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6787 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2635 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30717 df-fv 6544 fv3 6899 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7921 cnvexg 7920 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7905 dmexg 7897 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7906 rnexg 7898 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45132 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7916 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6894 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47878 tz6.12-1-afv2 47945 tz6.12-1 6904 tz6.12-afv 47877 tz6.12-afv2 47944 tz6.12 6905 tz6.12c-afv2 47946 tz6.12c 6903 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47941 tz6.12-2 6868 tz6.12i-afv2 47947 tz6.12i 6907 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6539 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6540 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6542 wfo 6534 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6541 wf1 6533 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6543 wf1o 6535 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7025 eqfnfv2 7026 eqfnfv2f 7029 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6979 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7215 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7213 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6623 funimaexg 6622 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5109 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5570 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5622 dffr3 6101 eliniseg 6096 iniseg 6099 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5561 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5638 fr3nr 7770 frirr 5637 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5614 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7772 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5625 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5647 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6348 tz6.26i 6349 wefrc 5655 wereu2 5658 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6350 wfii 6351 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6545 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7327 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7328 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7335 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7336 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7340 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7347 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7349 |
| [TakeutiZaring] p. 35 | Notation | wtr 5217 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45133 tz7.2 5644 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5222 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6373 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6381 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6382 ordelordALT 45216 ordelordALTVD 45545 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6388 ordelssne 6387 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6386 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6391 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7780 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7781 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6364 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6393 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45228 ordon 7775 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7776 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7848 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6409 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5219 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7790 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7826 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6467 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6466 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7777 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4903 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6366 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6443 sucidg 6444 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7808 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6457 ordnbtwn 6456 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7823 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6365 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7876 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7881 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7836 ordelsuc 7815 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7817 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7846 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7863 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7884 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7885 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7886 |
| [TakeutiZaring] p. 43 | Remark | omon 7873 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9603 omex 9611 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7871 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7891 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7888 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7889 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7866 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4926 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5236 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4927 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5314 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7793 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6412 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4912 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9628 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7788 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8361 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8383 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8384 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8385 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8392 tz7.44-2 8393 tz7.44-3 8394 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8353 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8348 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8332 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8431 tz7.49c 8432 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8429 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8428 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8430 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2681 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9994 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9995 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8516 oasuc 8508 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7856 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8519 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8500 oa0r 8522 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8520 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8532 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8604 nnaordi 8603 oaord 8531 oaordi 8530 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5013 uniss2 4906 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8534 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8539 oawordex 8541 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8596 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8633 |
| [TakeutiZaring] p. 60 | Remark | oancom 9619 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8544 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8601 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8536 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8503 omlim 8517 omsuc 8510 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8501 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8598 nnmcl 8597 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8617 nnmordi 8616 omord 8552 omordi 8550 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8553 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8621 omwordri 8556 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8523 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8526 om1r 8527 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8559 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8561 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8562 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8563 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8564 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8593 oe0 8506 oelim 8518 oesuc 8511 onesuc 8514 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8504 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8571 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8572 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8505 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8529 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8573 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8579 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8577 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8578 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8582 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8584 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9696 tz9.1 9697 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9735 r10 9739 r1lim 9743 r1limg 9742 r1suc 9741 r1sucg 9740 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9751 r1ord2 9752 r1ordg 9749 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9761 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9786 tz9.13 9762 tz9.13g 9763 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9736 rankval 9787 rankvalb 9768 rankvalg 9788 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9810 rankelb 9795 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9824 rankval3 9811 rankval3b 9797 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9800 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9766 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9805 rankr1c 9792 rankr1g 9803 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9806 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9820 rankssb 9819 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9813 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9812 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10458 dfac3 10104 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10013 numth 10455 numth2 10454 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10529 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10530 cardid2 9938 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9945 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10534 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9944 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9929 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9950 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9942 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9137 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9014 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9142 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9066 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9948 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10081 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9189 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9197 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10082 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9194 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10071 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10049 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9957 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10198 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9281 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8946 isfi 8971 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9198 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10517 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9059 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10509 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10168 unxpdom 9218 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9959 cardsdomelir 9958 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9220 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9997 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8825 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10545 infxpidm2 10000 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10189 infxp 10196 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9071 pw2f1o 9069 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9130 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10470 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10465 ac6s5 10474 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10526 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10527 uniimadomf 10528 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10257 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10252 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10236 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10233 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10240 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10247 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10256 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10566 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10234 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10259 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10080 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10079 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10091 alephfp2 10092 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10683 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10095 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10553 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10567 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10568 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39625 |
| [Tarski] p. 67 | Scheme B5 | sp 2217 |
| [Tarski] p. 68 | Lemma 6 | avril1 30780 equid 2040 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2045 |
| [Tarski] p. 70 | Lemma 14 | spim 2417 spime 2419 spimew 1999 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2211 ax-c15 39631 ax12i 1994 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2117 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1996 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1938 ax5ALT 39649 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2036 ax-8 2143 ax-9 2151 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28709 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28710 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28712 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28712 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28713 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16298 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38276 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38278 |
| [Weierstrass] p. 272 | Definition | df-mdet 22721 mdetuni 22758 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 916 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 881 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 932 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38057 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44496 imim2 59 wl-luk-imim2 38052 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47723 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 909 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2688 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 915 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38055 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 907 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 910 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45605 wl-luk-notnotr 38056 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44526 axfrege28 44525 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 880 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 937 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38049 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 902 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30718 pm2.27 43 wl-luk-pm2.27 38047 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 935 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38988 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 936 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1102 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 919 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 894 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 895 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 864 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 901 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 903 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 912 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 904 pm2.67 905 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 911 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 913 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 944 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 474 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 476 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 464 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 407 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 814 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 453 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 487 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 489 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 776 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 819 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 633 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 497 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 820 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 478 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 818 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 845 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 817 bitr 816 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 573 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 917 pm4.25 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 465 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1023 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 883 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 473 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 934 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 644 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 930 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 648 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1103 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1021 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1067 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1038 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 840 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 866 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 554 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 409 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 869 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 402 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 862 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 566 pm4.71d 570 pm4.71i 568 pm4.71r 567 pm4.71rd 571 pm4.71ri 569 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 536 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 949 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 526 pm4.76 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 947 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1019 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 397 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1039 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1040 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 391 impexp 455 pm4.87 856 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 835 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1028 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1027 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 390 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 836 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1063 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1064 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 914 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 582 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 392 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 843 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 848 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 837 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 846 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 393 pm5.41 394 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 551 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1020 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1033 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1034 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1043 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1044 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37180 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45038 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45039 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1898 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45040 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45041 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45042 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1921 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45043 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45044 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45045 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45046 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45047 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45049 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45050 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45051 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45048 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2122 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45054 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45055 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2102 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2193 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1857 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1858 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45056 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45057 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45058 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45059 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45061 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45060 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1915 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45063 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45064 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45062 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1856 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45065 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45066 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1874 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45067 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2376 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1888 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45072 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45068 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45069 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45070 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45071 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45076 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45073 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45074 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45075 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45077 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2595 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45087 pm13.13b 45088 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45089 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3037 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3038 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3624 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45095 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45096 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45090 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45231 pm13.193 45091 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45092 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45093 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45094 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45101 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45100 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45099 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3805 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45102 pm14.122b 45103 pm14.122c 45104 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45105 pm14.123b 45106 pm14.123c 45107 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45109 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45108 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45110 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6517 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45111 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6518 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45112 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45114 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2659 eupickbi 2662 sbaniota 45115 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45113 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2610 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45116 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30717 df-fv 6544 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9986 pm54.43lem 9985 |
| [Young] p. 141 | Definition of operator ordering | leop2 32442 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32448 idleop 32449 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43525 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43532 pellexlem1 43526 |