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 17676 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17676 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18085 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17697 0funcg 49654 df-termc 50042 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50119 prsthinc 50033 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50147 df-mndtc 50147 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50143 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17720 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50135 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50160 oppgoppchom 50159 oppgoppcid 50161 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17790 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17778 invisoinvl 17799 |
| [Adamek] p. 28 | Example 3.13 | idinv 17798 idiso 17797 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17783 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17757 df-iso 17758 dfiso2 17781 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17764 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17815 cicerALT 49615 |
| [Adamek] p. 29 | Definition 3.15 | cic 17808 df-cic 17805 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17867 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17779 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17780 isoco 17786 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17867 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17890 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 49873 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17883 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50143 discthing 50030 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 49987 prsthinc 50033 thincciso 50022 thincciso2 50024 thincciso3 50025 thinccisod 50023 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50147 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17897 cofucla 49665 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49731 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18120 catcisoi 49969 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18175 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17916 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17915 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18175 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17940 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17946 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17945 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18160 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18160 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49701 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49692 funcoppc 17884 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18108 elcatchom 49966 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17934 fthoppf 49733 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17933 fulloppf 49732 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18117 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49654 df-catc 18108 |
| [Adamek] p. 45 | Exercise 3G | incat 50170 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50173 nelsubc3 49640 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49720 imasubc2 49721 imasubc3 49725 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17847 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17848 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49640 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17859 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17821 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49729 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49728 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49730 ressffth 17949 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50171 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17955 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17976 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17980 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17956 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17982 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49654 df-inito 17993 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49654 df-termc 50042 initc 49660 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21504 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17994 oppctermo 49805 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18021 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18025 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 49806 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17995 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21505 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18028 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17756 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50038 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50037 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50002 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17791 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17793 |
| [Adamek] p. 185 | Section 10.67 | updjud 9882 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50214 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50214 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50214 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50215 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50215 |
| [Adamek] p. 478 | Item Rng | df-ringc 20668 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49118 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49140 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14574 df-pfx 14675 df-substr 14645 df-word 14517 lencl 14536 wrd0 14542 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24741 df-nmoo 30887 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32295 hmopidmchi 32293 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32343 pjcmul2i 32344 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32060 unoplin 32062 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32061 unopadj2 32080 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32155 lnopunii 32154 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32228 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27990 |
| [Alling] p. 184 | Axiom B | bdayfo 27711 |
| [Alling] p. 184 | Axiom O | ltsso 27710 |
| [Alling] p. 184 | Axiom SD | nodense 27726 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27818 |
| [Alling] p. 185 | Theorem | conway 27842 |
| [Alling] p. 185 | Axiom FE | noeta 27777 |
| [Alling] p. 186 | Theorem 4 | lesrec 27862 lesrecd 27863 |
| [Alling], p. 2 | Definition | rp-brsslt 43947 |
| [Alling], p. 3 | Note | nla0001 43950 nla0002 43948 nla0003 43949 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11357 addcan2d 11377 addcan2i 11367 addcand 11376 addcani 11366 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11410 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11469 negsubd 11538 negsubi 11499 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11471 negnegd 11523 negnegi 11491 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11610 subdid 11633 subdii 11626 subdir 11611 subdird 11634 subdiri 11627 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11352 mul01d 11372 mul01i 11363 mul02 11351 mul02d 11371 mul02i 11362 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11814 mulcan2d 11811 mulcand 11810 mulcani 11816 |
| [Apostol] p. 18 | Theorem I.8 | receu 11822 xreceu 33053 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11851 divrecd 11960 divreci 11926 divreczi 11919 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11878 recreci 11913 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11817 mul0ord 11825 mul0ori 11824 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11616 mul2negd 11632 mul2negi 11625 mulneg1 11613 mulneg1d 11630 mulneg1i 11623 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11896 divadddivd 12001 divadddivi 11943 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11881 divmuldivd 11998 divmuldivi 11941 rdivmuldivd 20434 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11882 divdivdivd 12004 divdivdivi 11944 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13007 rpaddcld 13042 rpmulcl 13008 rpmulcld 13043 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13017 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13020 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11299 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11770 ltadd1dd 11788 ltadd1i 11731 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12031 ltmul1a 12030 ltmul1i 12100 ltmul1ii 12110 ltmul2 12032 ltmul2d 13069 ltmul2dd 13083 ltmul2i 12103 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11697 msqgt0d 11744 msqgt0i 11714 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11699 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11683 lt0neg1d 11746 ltneg 11677 ltnegd 11755 ltnegi 11721 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11662 lt2addd 11800 lt2addi 11739 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12984 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12027 recgt0d 12116 recgt0i 12087 recgt0ii 12088 |
| [Apostol] p. 22 | Definition of integers | df-z 12559 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12214 |
| [Apostol] p. 22 | Definition of rationals | df-q 12940 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9390 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12467 |
| [Apostol] p. 26 | Theorem I.29 | arch 12468 archd 45688 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12666 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12469 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12938 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12937 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13192 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16349 zneo 12646 zneoALTV 48239 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26765 msqsqrtd 15446 resqrtth 15258 sqrtth 15368 sqrtthi 15374 sqsqrtd 15445 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12203 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12904 |
| [Apostol] p. 361 | Remark | crreczi 14231 |
| [Apostol] p. 363 | Remark | absgt0i 15403 |
| [Apostol] p. 363 | Example | abssubd 15459 abssubi 15407 |
| [ApostolNT] p. 7 | Remark | fmtno0 48097 fmtno1 48098 fmtno2 48107 fmtno3 48108 fmtno4 48109 fmtno5fac 48139 fmtnofz04prm 48134 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48085 |
| [ApostolNT] p. 8 | Definition | df-ppi 27134 |
| [ApostolNT] p. 14 | Definition | df-dvds 16263 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16279 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16304 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16299 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16292 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16294 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16280 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16281 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16286 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16321 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16323 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16325 |
| [ApostolNT] p. 15 | Definition | df-gcd 16505 dfgcd2 16556 |
| [ApostolNT] p. 16 | Definition | isprm2 16692 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16663 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16927 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16523 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16557 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16559 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16538 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16530 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16722 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16724 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16940 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16934 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16413 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16597 |
| [ApostolNT] p. 24 | Definition | df-mu 27135 |
| [ApostolNT] p. 25 | Definition | df-phi 16777 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27225 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16802 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16787 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16791 |
| [ApostolNT] p. 32 | Definition | df-vma 27132 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27227 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27250 |
| [ApostolNT] p. 38 | Remark | df-sgm 27136 |
| [ApostolNT] p. 38 | Definition | df-sgm 27136 |
| [ApostolNT] p. 75 | Definition | df-chp 27133 df-cht 27131 |
| [ApostolNT] p. 104 | Definition | congr 16674 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16266 |
| [ApostolNT] p. 106 | Definition | moddvds 16273 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16356 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16357 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13888 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13928 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14241 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16298 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16677 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17086 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16679 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16794 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16813 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16795 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27106 |
| [ApostolNT] p. 179 | Definition | df-lgs 27329 lgsprme0 27373 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27374 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27350 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27365 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27422 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27441 2lgsoddprm 27450 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27408 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27417 |
| [ApostolNT] p. 188 | Definition | df-lgs 27329 lgs1 27375 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27366 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27368 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27376 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27377 |
| [Baer] p. 40 | Property (b) | mapdord 42210 |
| [Baer] p. 40 | Property (c) | mapd11 42211 |
| [Baer] p. 40 | Property (e) | mapdin 42234 mapdlsm 42236 |
| [Baer] p. 40 | Property (f) | mapd0 42237 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42197 mapd1o 42220 |
| [Baer] p. 41 | Property (g) | mapdat 42239 |
| [Baer] p. 44 | Part (1) | mapdpg 42278 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42373 mapdheq 42300 mapdheq2 42301 mapdheq2biN 42302 |
| [Baer] p. 45 | Part (3) | baerlem3 42285 |
| [Baer] p. 46 | Part (4) | mapdheq4 42304 mapdheq4lem 42303 |
| [Baer] p. 46 | Part (5) | baerlem5a 42286 baerlem5abmN 42290 baerlem5amN 42288 baerlem5b 42287 baerlem5bmN 42289 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42393 hdmap1l6a 42381 hdmap1l6e 42386 hdmap1l6f 42387 hdmap1l6g 42388 hdmap1l6lem1 42379 hdmap1l6lem2 42380 mapdh6N 42319 mapdh6aN 42307 mapdh6eN 42312 mapdh6fN 42313 mapdh6gN 42314 mapdh6lem1N 42305 mapdh6lem2N 42306 |
| [Baer] p. 48 | Part 9 | hdmapval 42400 |
| [Baer] p. 48 | Part 10 | hdmap10 42412 |
| [Baer] p. 48 | Part 11 | hdmapadd 42415 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42389 mapdh6hN 42315 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42325 mapdh75d 42326 mapdh75e 42324 mapdh75fN 42327 mapdh7cN 42321 mapdh7dN 42322 mapdh7eN 42320 mapdh7fN 42323 |
| [Baer] p. 48 | Part (8) | mapdh8 42360 mapdh8a 42347 mapdh8aa 42348 mapdh8ab 42349 mapdh8ac 42350 mapdh8ad 42351 mapdh8b 42352 mapdh8c 42353 mapdh8d 42355 mapdh8d0N 42354 mapdh8e 42356 mapdh8g 42357 mapdh8i 42358 mapdh8j 42359 |
| [Baer] p. 48 | Part (9) | mapdh9a 42361 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42341 |
| [Baer] p. 49 | Part 12 | hdmap11 42420 hdmapeq0 42416 hdmapf1oN 42437 hdmapneg 42418 hdmaprnN 42436 hdmaprnlem1N 42421 hdmaprnlem3N 42422 hdmaprnlem3uN 42423 hdmaprnlem4N 42425 hdmaprnlem6N 42426 hdmaprnlem7N 42427 hdmaprnlem8N 42428 hdmaprnlem9N 42429 hdmapsub 42419 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42440 hdmap14lem10 42449 hdmap14lem1a 42438 hdmap14lem2N 42441 hdmap14lem2a 42439 hdmap14lem3 42442 hdmap14lem8 42447 hdmap14lem9 42448 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42450 hdmap14lem12 42451 hdmap14lem13 42452 hdmap14lem14 42453 hdmap14lem15 42454 hgmapval 42459 |
| [Baer] p. 50 | Part 15 | hgmapadd 42466 hgmapmul 42467 hgmaprnlem2N 42469 hgmapvs 42463 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42473 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42489 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42490 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42491 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42492 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42494 hgmapvv 42498 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42493 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42495 |
| [Baer] p. 111 | Line 15 | hdmapg 42502 hdmapglem7 42501 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26766 2irrexpqALT 26835 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2590 |
| [BellMachover] p. 460 | Notation | df-mo 2560 |
| [BellMachover] p. 460 | Definition | mo3 2585 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2728 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2732 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5229 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5240 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37497 sepex 5244 |
| [BellMachover] p. 466 | Problem | axpow2 5318 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5319 |
| [BellMachover] p. 466 | Axiom Union | axun2 7709 |
| [BellMachover] p. 468 | Definition | df-ord 6338 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6353 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6360 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6355 |
| [BellMachover] p. 471 | Definition of N | df-om 7836 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7773 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6340 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9587 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7851 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9712 |
| [BellMachover] p. 478 | Definition | rankval2 9766 rankval2b 35350 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9730 r1ord3g 9727 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9534 |
| [BellMachover] p. 488 | Axiom AC | ac5 10424 dfac4 10068 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10056 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 39891 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32495 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32537 chirredi 32536 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32525 |
| [Beran] p. 3 | Definition of join | sshjval3 31496 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31758 cmcm2i 31735 cmcm2ii 31740 cmt2N 39822 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31759 lecmi 31744 lecmii 31745 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31733 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31762 cm2ji 31767 cm2mi 31768 |
| [Beran] p. 95 | Definition | df-sh 31349 issh2 31351 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31228 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31241 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31232 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 31970 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 31972 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 31971 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 31973 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31224 his1i 31242 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31225 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31226 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31227 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31110 dfhnorm2 31264 normval 31266 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31326 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31115 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31383 |
| [Beran] p. 96 | Definition of converge | df-hlim 31114 hlimi 31330 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31275 norm-i 31271 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31279 norm-ii 31280 normlem0 31251 normlem1 31252 normlem2 31253 normlem3 31254 normlem4 31255 normlem5 31256 normlem6 31257 normlem7 31258 normlem7tALT 31261 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31281 norm-iii 31282 |
| [Beran] p. 98 | Remark 3.4 | bcs 31323 bcsiALT 31321 bcsiHIL 31322 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31263 normpar 31297 normpari 31296 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31288 normpyth 31287 normpythi 31284 |
| [Beran] p. 99 | Remark | lnfn0 32189 lnfn0i 32184 lnop0 32108 lnop0i 32112 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32168 nmcfnex 32195 nmcfnexi 32193 nmcopex 32171 nmcopexi 32169 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32196 nmcfnlbi 32194 nmcoplb 32172 nmcoplbi 32170 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32198 lnfnconi 32197 lnopcon 32177 lnopconi 32176 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31298 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31295 norm3adifii 31290 norm3dif 31292 norm3difi 31289 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31443 pjhth 31535 pjhtheu 31536 pjpjhth 31567 pjpjhthi 31568 pjth 25474 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31548 ococi 31547 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32203 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32204 riesz4 32206 riesz4i 32205 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32221 cnlnadjeu 32220 cnlnadjeui 32219 cnlnadji 32218 cnlnadjlem1 32209 nmopadjlei 32230 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32233 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32232 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32234 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32078 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32244 nmopcoadji 32243 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32235 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32245 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32242 pjadj2coi 32346 pjadjcoi 32303 |
| [Beran] p. 107 | Definition | df-ch 31363 isch2 31365 |
| [Beran] p. 107 | Remark 3.12 | choccl 31448 isch3 31383 occl 31446 ocsh 31425 shoccl 31447 shocsh 31426 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31550 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31474 |
| [Beran] p. 109 | Property (i) | pjadj2 32329 pjadj3 32330 pjadji 31827 pjadjii 31816 |
| [Beran] p. 109 | Property (ii) | pjidmco 32323 pjidmcoi 32319 pjidmi 31815 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32315 |
| [Beran] p. 111 | Remark | ho0val 31892 pjch1 31812 |
| [Beran] p. 111 | Definition | df-hfmul 31876 df-hfsum 31875 df-hodif 31874 df-homul 31873 df-hosum 31872 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 31813 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 31836 pjchi 31574 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31581 pjoc2i 31580 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 31822 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32307 pjssmii 31823 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32306 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32305 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32310 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32308 pjssge0ii 31824 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32309 pjdifnormii 31825 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1790 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1788 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1791 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1786 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34543 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34551 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34549 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34553 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34573 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34604 df-sitm 34582 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34604 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34581 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29188 isuhgrop 29210 isusgrop 29302 isuspgrop 29301 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48431 df-subgr 29408 uhgrspan1 29443 uhgrspansubgr 29431 |
| [Bollobas] p. 3 | Definition | df-gric 48451 gricuspgr 48488 isuspgrim 48466 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29594 df-clnbgr 48389 df-cusgr 29552 df-nbgr 29473 fusgrmaxsize 29604 |
| [Bollobas] p. 4 | Definition | df-upwlks 48704 df-wlks 29739 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29690 finsumvtxdgeven 29692 fusgr1th 29691 fusgrvtxdgonume 29694 vtxdgoddnumeven 29693 |
| [Bollobas] p. 5 | Notation | df-pths 29853 |
| [Bollobas] p. 5 | Definition | df-crcts 29925 df-cycls 29926 df-trls 29830 df-wlkson 29740 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29199 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48770 df-cllaw 48756 df-mgm 18650 df-mgm2 48789 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48771 df-asslaw 48758 df-sgrp 18729 df-sgrp2 48791 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 48790 df-comlaw 48757 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18745 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33158 mndlactf1o 33162 mndractf1 33160 mndractf1o 33163 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20257 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20175 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 33884 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 33888 assarrginv 33887 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 33929 fldextrspunfld 33927 fldextrspunlem1 33926 fldextrspunlem2 33928 fldextrspunlsp 33925 fldextrspunlsplem 33924 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33687 dfufd2 33700 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7260 fcofo 7261 |
| [BourbakiTop1] p. | Remark | xnegmnf 13203 xnegpnf 13202 |
| [BourbakiTop1] p. | Remark | rexneg 13204 |
| [BourbakiTop1] p. | Remark 3 | ust0 24253 ustfilxp 24246 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24123 |
| [BourbakiTop1] p. | Criterion | ishmeo 23792 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24316 iducn 24315 snfil 23897 |
| [BourbakiTop1] p. | Example 2 | neifil 23913 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24100 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24336 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34208 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23896 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24308 df-ust 24234 filintn0 23894 filn0 23895 istgp 24110 ucnprima 24314 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24319 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24330 df-usp 24290 df-utop 24264 trust 24262 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34107 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23149 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23302 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24239 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24242 |
| [BourbakiTop1] p. | Property V_ii | innei 23158 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23166 neissex 23160 |
| [BourbakiTop1] p. | Proposition 1 | neips 23146 neiss 23142 ucncn 24317 ustund 24255 ustuqtop 24279 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23300 neiptopreu 23166 utop2nei 24283 utop3cls 24284 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24324 uspreg 24306 utopreg 24285 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23724 imasncls 23725 imasnopn 23723 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24033 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24241 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24243 |
| [BourbakiTop1] p. | Property V_iii | elnei 23144 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24335 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24240 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24244 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23420 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23879 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22927 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34104 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46584 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46586 stoweid 46585 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46523 stoweidlem10 46532 stoweidlem14 46536 stoweidlem15 46537 stoweidlem35 46557 stoweidlem36 46558 stoweidlem37 46559 stoweidlem38 46560 stoweidlem40 46562 stoweidlem41 46563 stoweidlem43 46565 stoweidlem44 46566 stoweidlem46 46568 stoweidlem5 46527 stoweidlem50 46572 stoweidlem52 46574 stoweidlem53 46575 stoweidlem55 46577 stoweidlem56 46578 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46545 stoweidlem24 46546 stoweidlem27 46549 stoweidlem28 46550 stoweidlem30 46552 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46556 stoweidlem59 46581 stoweidlem60 46582 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46567 stoweidlem49 46571 stoweidlem7 46529 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46553 stoweidlem39 46561 stoweidlem42 46564 stoweidlem48 46570 stoweidlem51 46573 stoweidlem54 46576 stoweidlem57 46579 stoweidlem58 46580 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46547 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46539 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46533 stoweidlem13 46535 stoweidlem26 46548 stoweidlem61 46583 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46540 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48770 df-mgm 18650 df-mgm2 48789 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18729 df-sgrp2 48791 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19057 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5176 |
| [Church] p. 129 | Section II.24 | df-ifp 1072 dfifp2 1073 |
| [Clemente] p. 10 | Definition IT | natded 30544 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30544 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30544 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30544 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30544 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30544 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30544 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30544 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30544 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30544 |
| [Clemente] p. 14 | Proof 5.11 | natded 30544 |
| [Clemente] p. 14 | Definition E` `n | natded 30544 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30546 ex-natded5.2 30545 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30549 ex-natded5.3 30548 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30551 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30553 ex-natded5.7 30552 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30555 ex-natded5.8 30554 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30557 ex-natded5.13 30556 |
| [Clemente] p. 32 | Definition I` `n | natded 30544 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30544 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30544 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30544 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30558 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30559 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30561 ex-natded9.26 30560 |
| [Cohen] p. 301 | Remark | relogoprlem 26626 |
| [Cohen] p. 301 | Property 2 | relogmul 26627 relogmuld 26660 |
| [Cohen] p. 301 | Property 3 | relogdiv 26628 relogdivd 26661 |
| [Cohen] p. 301 | Property 4 | relogexp 26631 |
| [Cohen] p. 301 | Property 1a | log1 26620 |
| [Cohen] p. 301 | Property 1b | loge 26621 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26822 |
| [Cohen4] p. 349 | Property | relogbf 26826 |
| [Cohen4] p. 352 | Definition | elogb 26805 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26812 |
| [Cohen4] p. 361 | Property 3 | logbrec 26817 relogbdiv 26814 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26810 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26815 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26803 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26804 |
| [Cohen4] p. 367 | Property | logbchbase 26806 |
| [Cohen4] p. 377 | Property 2 | logblt 26819 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34536 sxbrsigalem4 34538 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18565 acsinfd 18564 acsinfdimd 18566 acsmap2d 18563 acsmapd 18562 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34541 |
| [Connell] p. 57 | Definition | df-scmat 22524 df-scmatalt 48969 |
| [Conway] p. 4 | Definition | lesrec 27862 lesrecd 27863 |
| [Conway] p. 5 | Definition | addsval 28025 addsval2 28026 df-adds 28023 df-muls 28170 df-negs 28084 |
| [Conway] p. 7 | Theorem | 0lt1s 27875 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28525 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 27924 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 27923 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27801 |
| [Conway] p. 17 | Theorem 3 | addsass 28068 addsassd 28069 addscom 28029 addscomd 28030 addsrid 28027 addsridd 28028 |
| [Conway] p. 17 | Definition | df-0s 27870 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28107 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28104 negsidd 28105 |
| [Conway] p. 18 | Theorem 5 | leadds1 28052 leadds1d 28058 |
| [Conway] p. 18 | Definition | df-1s 27871 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28099 negscld 28100 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28043 |
| [Conway] p. 19 | Note | mulsunif2 28233 |
| [Conway] p. 19 | Theorem 7 | addsdi 28218 addsdid 28219 addsdird 28220 mulnegs1d 28223 mulnegs2d 28224 mulsass 28229 mulsassd 28230 mulscom 28202 mulscomd 28203 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28197 mulscld 28198 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28201 ltmuls 28199 ltmulsd 28200 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28207 mulsgt0d 28208 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28281 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 27867 |
| [Conway] p. 24 | Definition | df-reno 28553 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28562 remulscl 28565 renegscl 28561 |
| [Conway] p. 27 | Definition | df-ons 28315 elons2 28321 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28325 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28327 onswe 28335 |
| [Conway] p. 29 | Remark | madebday 27963 newbday 27965 oldbday 27964 |
| [Conway] p. 29 | Definition | df-made 27890 df-new 27892 df-old 27891 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13861 |
| [Crawley] p. 1 | Definition of poset | df-poset 18321 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 39958 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40762 dalaw 40458 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42533 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40562 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40678 df-ldil 40676 isldil 40682 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40677 df-trnN 40679 isltrn 40691 ltrnu 40693 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40363 cdlema2N 40364 exatleN 39976 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40048 cdlemb 40366 cdlemb2 40613 cdlemb3 41178 idltrn 40722 l1cvat 39627 lhpat 40615 lhpat2 40617 lshpat 39628 ltrnel 40711 ltrnmw 40723 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40763 cdlemc2 40764 ltrnnidn 40746 trlat 40741 trljat1 40738 trljat2 40739 trljat3 40740 trlne 40757 trlnidat 40745 trlnle 40758 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40563 |
| [Crawley] p. 113 | Lemma C | cdlemc 40769 cdlemc3 40765 cdlemc4 40766 |
| [Crawley] p. 113 | Lemma D | cdlemd 40779 cdlemd1 40770 cdlemd2 40771 cdlemd3 40772 cdlemd4 40773 cdlemd5 40774 cdlemd6 40775 cdlemd7 40776 cdlemd8 40777 cdlemd9 40778 cdleme31sde 40957 cdleme31se 40954 cdleme31se2 40955 cdleme31snd 40958 cdleme32a 41013 cdleme32b 41014 cdleme32c 41015 cdleme32d 41016 cdleme32e 41017 cdleme32f 41018 cdleme32fva 41009 cdleme32fva1 41010 cdleme32fvcl 41012 cdleme32le 41019 cdleme48fv 41071 cdleme4gfv 41079 cdleme50eq 41113 cdleme50f 41114 cdleme50f1 41115 cdleme50f1o 41118 cdleme50laut 41119 cdleme50ldil 41120 cdleme50lebi 41112 cdleme50rn 41117 cdleme50rnlem 41116 cdlemeg49le 41083 cdlemeg49lebilem 41111 |
| [Crawley] p. 113 | Lemma E | cdleme 41132 cdleme00a 40781 cdleme01N 40793 cdleme02N 40794 cdleme0a 40783 cdleme0aa 40782 cdleme0b 40784 cdleme0c 40785 cdleme0cp 40786 cdleme0cq 40787 cdleme0dN 40788 cdleme0e 40789 cdleme0ex1N 40795 cdleme0ex2N 40796 cdleme0fN 40790 cdleme0gN 40791 cdleme0moN 40797 cdleme1 40799 cdleme10 40826 cdleme10tN 40830 cdleme11 40842 cdleme11a 40832 cdleme11c 40833 cdleme11dN 40834 cdleme11e 40835 cdleme11fN 40836 cdleme11g 40837 cdleme11h 40838 cdleme11j 40839 cdleme11k 40840 cdleme11l 40841 cdleme12 40843 cdleme13 40844 cdleme14 40845 cdleme15 40850 cdleme15a 40846 cdleme15b 40847 cdleme15c 40848 cdleme15d 40849 cdleme16 40857 cdleme16aN 40831 cdleme16b 40851 cdleme16c 40852 cdleme16d 40853 cdleme16e 40854 cdleme16f 40855 cdleme16g 40856 cdleme19a 40875 cdleme19b 40876 cdleme19c 40877 cdleme19d 40878 cdleme19e 40879 cdleme19f 40880 cdleme1b 40798 cdleme2 40800 cdleme20aN 40881 cdleme20bN 40882 cdleme20c 40883 cdleme20d 40884 cdleme20e 40885 cdleme20f 40886 cdleme20g 40887 cdleme20h 40888 cdleme20i 40889 cdleme20j 40890 cdleme20k 40891 cdleme20l 40894 cdleme20l1 40892 cdleme20l2 40893 cdleme20m 40895 cdleme20y 40874 cdleme20zN 40873 cdleme21 40909 cdleme21d 40902 cdleme21e 40903 cdleme22a 40912 cdleme22aa 40911 cdleme22b 40913 cdleme22cN 40914 cdleme22d 40915 cdleme22e 40916 cdleme22eALTN 40917 cdleme22f 40918 cdleme22f2 40919 cdleme22g 40920 cdleme23a 40921 cdleme23b 40922 cdleme23c 40923 cdleme26e 40931 cdleme26eALTN 40933 cdleme26ee 40932 cdleme26f 40935 cdleme26f2 40937 cdleme26f2ALTN 40936 cdleme26fALTN 40934 cdleme27N 40941 cdleme27a 40939 cdleme27cl 40938 cdleme28c 40944 cdleme3 40809 cdleme30a 40950 cdleme31fv 40962 cdleme31fv1 40963 cdleme31fv1s 40964 cdleme31fv2 40965 cdleme31id 40966 cdleme31sc 40956 cdleme31sdnN 40959 cdleme31sn 40952 cdleme31sn1 40953 cdleme31sn1c 40960 cdleme31sn2 40961 cdleme31so 40951 cdleme35a 41020 cdleme35b 41022 cdleme35c 41023 cdleme35d 41024 cdleme35e 41025 cdleme35f 41026 cdleme35fnpq 41021 cdleme35g 41027 cdleme35h 41028 cdleme35h2 41029 cdleme35sn2aw 41030 cdleme35sn3a 41031 cdleme36a 41032 cdleme36m 41033 cdleme37m 41034 cdleme38m 41035 cdleme38n 41036 cdleme39a 41037 cdleme39n 41038 cdleme3b 40801 cdleme3c 40802 cdleme3d 40803 cdleme3e 40804 cdleme3fN 40805 cdleme3fa 40808 cdleme3g 40806 cdleme3h 40807 cdleme4 40810 cdleme40m 41039 cdleme40n 41040 cdleme40v 41041 cdleme40w 41042 cdleme41fva11 41049 cdleme41sn3aw 41046 cdleme41sn4aw 41047 cdleme41snaw 41048 cdleme42a 41043 cdleme42b 41050 cdleme42c 41044 cdleme42d 41045 cdleme42e 41051 cdleme42f 41052 cdleme42g 41053 cdleme42h 41054 cdleme42i 41055 cdleme42k 41056 cdleme42ke 41057 cdleme42keg 41058 cdleme42mN 41059 cdleme42mgN 41060 cdleme43aN 41061 cdleme43bN 41062 cdleme43cN 41063 cdleme43dN 41064 cdleme5 40812 cdleme50ex 41131 cdleme50ltrn 41129 cdleme51finvN 41128 cdleme51finvfvN 41127 cdleme51finvtrN 41130 cdleme6 40813 cdleme7 40821 cdleme7a 40815 cdleme7aa 40814 cdleme7b 40816 cdleme7c 40817 cdleme7d 40818 cdleme7e 40819 cdleme7ga 40820 cdleme8 40822 cdleme8tN 40827 cdleme9 40825 cdleme9a 40823 cdleme9b 40824 cdleme9tN 40829 cdleme9taN 40828 cdlemeda 40870 cdlemedb 40869 cdlemednpq 40871 cdlemednuN 40872 cdlemefr27cl 40975 cdlemefr32fva1 40982 cdlemefr32fvaN 40981 cdlemefrs32fva 40972 cdlemefrs32fva1 40973 cdlemefs27cl 40985 cdlemefs32fva1 40995 cdlemefs32fvaN 40994 cdlemesner 40868 cdlemeulpq 40792 |
| [Crawley] p. 114 | Lemma E | 4atex 40648 4atexlem7 40647 cdleme0nex 40862 cdleme17a 40858 cdleme17c 40860 cdleme17d 41070 cdleme17d1 40861 cdleme17d2 41067 cdleme18a 40863 cdleme18b 40864 cdleme18c 40865 cdleme18d 40867 cdleme4a 40811 |
| [Crawley] p. 115 | Lemma E | cdleme21a 40897 cdleme21at 40900 cdleme21b 40898 cdleme21c 40899 cdleme21ct 40901 cdleme21f 40904 cdleme21g 40905 cdleme21h 40906 cdleme21i 40907 cdleme22gb 40866 |
| [Crawley] p. 116 | Lemma F | cdlemf 41135 cdlemf1 41133 cdlemf2 41134 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41139 cdlemg16 41229 cdlemg28 41276 cdlemg28a 41265 cdlemg28b 41275 cdlemg3a 41169 cdlemg42 41301 cdlemg43 41302 cdlemg44 41305 cdlemg44a 41303 cdlemg46 41307 cdlemg47 41308 cdlemg9 41206 ltrnco 41291 ltrncom 41310 tgrpabl 41323 trlco 41299 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41315 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41249 cdlemg17b 41234 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41328 df-edring 41329 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41332 |
| [Crawley] p. 118 | Remark | tendopltp 41352 |
| [Crawley] p. 118 | Lemma H | cdlemh 41389 cdlemh1 41387 cdlemh2 41388 |
| [Crawley] p. 118 | Lemma I | cdlemi 41392 cdlemi1 41390 cdlemi2 41391 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41393 cdlemj2 41394 cdlemj3 41395 tendocan 41396 |
| [Crawley] p. 118 | Lemma K | cdlemk 41546 cdlemk1 41403 cdlemk10 41415 cdlemk11 41421 cdlemk11t 41518 cdlemk11ta 41501 cdlemk11tb 41503 cdlemk11tc 41517 cdlemk11u-2N 41461 cdlemk11u 41443 cdlemk12 41422 cdlemk12u-2N 41462 cdlemk12u 41444 cdlemk13-2N 41448 cdlemk13 41424 cdlemk14-2N 41450 cdlemk14 41426 cdlemk15-2N 41451 cdlemk15 41427 cdlemk16-2N 41452 cdlemk16 41429 cdlemk16a 41428 cdlemk17-2N 41453 cdlemk17 41430 cdlemk18-2N 41458 cdlemk18-3N 41472 cdlemk18 41440 cdlemk19-2N 41459 cdlemk19 41441 cdlemk19u 41542 cdlemk1u 41431 cdlemk2 41404 cdlemk20-2N 41464 cdlemk20 41446 cdlemk21-2N 41463 cdlemk21N 41445 cdlemk22-3 41473 cdlemk22 41465 cdlemk23-3 41474 cdlemk24-3 41475 cdlemk25-3 41476 cdlemk26-3 41478 cdlemk26b-3 41477 cdlemk27-3 41479 cdlemk28-3 41480 cdlemk29-3 41483 cdlemk3 41405 cdlemk30 41466 cdlemk31 41468 cdlemk32 41469 cdlemk33N 41481 cdlemk34 41482 cdlemk35 41484 cdlemk36 41485 cdlemk37 41486 cdlemk38 41487 cdlemk39 41488 cdlemk39u 41540 cdlemk4 41406 cdlemk41 41492 cdlemk42 41513 cdlemk42yN 41516 cdlemk43N 41535 cdlemk45 41519 cdlemk46 41520 cdlemk47 41521 cdlemk48 41522 cdlemk49 41523 cdlemk5 41408 cdlemk50 41524 cdlemk51 41525 cdlemk52 41526 cdlemk53 41529 cdlemk54 41530 cdlemk55 41533 cdlemk55u 41538 cdlemk56 41543 cdlemk5a 41407 cdlemk5auN 41432 cdlemk5u 41433 cdlemk6 41409 cdlemk6u 41434 cdlemk7 41420 cdlemk7u-2N 41460 cdlemk7u 41442 cdlemk8 41410 cdlemk9 41411 cdlemk9bN 41412 cdlemki 41413 cdlemkid 41508 cdlemkj-2N 41454 cdlemkj 41435 cdlemksat 41418 cdlemksel 41417 cdlemksv 41416 cdlemksv2 41419 cdlemkuat 41438 cdlemkuel-2N 41456 cdlemkuel-3 41470 cdlemkuel 41437 cdlemkuv-2N 41455 cdlemkuv2-2 41457 cdlemkuv2-3N 41471 cdlemkuv2 41439 cdlemkuvN 41436 cdlemkvcl 41414 cdlemky 41498 cdlemkyyN 41534 tendoex 41547 |
| [Crawley] p. 120 | Remark | dva1dim 41557 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41548 cdleml2N 41549 cdleml3N 41550 cdleml4N 41551 cdleml5N 41552 cdleml6 41553 cdleml7 41554 cdleml8 41555 cdleml9 41556 dia1dim 41633 |
| [Crawley] p. 120 | Lemma M | dia11N 41620 diaf11N 41621 dialss 41618 diaord 41619 dibf11N 41733 djajN 41709 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41604 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41690 dia2dimlem1 41636 dia2dimlem2 41637 dia2dimlem3 41638 dia2dimlem4 41639 dia2dimlem5 41640 diaf1oN 41702 diarnN 41701 dvheveccl 41684 dvhopN 41688 |
| [Crawley] p. 121 | Lemma N | cdlemn 41784 cdlemn10 41778 cdlemn11 41783 cdlemn11a 41779 cdlemn11b 41780 cdlemn11c 41781 cdlemn11pre 41782 cdlemn2 41767 cdlemn2a 41768 cdlemn3 41769 cdlemn4 41770 cdlemn4a 41771 cdlemn5 41773 cdlemn5pre 41772 cdlemn6 41774 cdlemn7 41775 cdlemn8 41776 cdlemn9 41777 diclspsn 41766 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41745 |
| [Crawley] p. 122 | Lemma N | dih11 41837 dihf11 41839 dihjust 41789 dihjustlem 41788 dihord 41836 dihord1 41790 dihord10 41795 dihord11b 41794 dihord11c 41796 dihord2 41799 dihord2a 41791 dihord2b 41792 dihord2cN 41793 dihord2pre 41797 dihord2pre2 41798 dihordlem6 41785 dihordlem7 41786 dihordlem7b 41787 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 41802 dihfval 41803 dihval 41804 |
| [Diestel] p. 3 | Definition | df-gric 48451 df-grim 48448 isuspgrim 48466 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29552 df-nbgr 29473 |
| [Diestel] p. 3 | Definition by | df-grisom 48447 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48431 df-subgr 29408 uhgrspan1 29443 uhgrspansubgr 29431 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29694 vtxdgoddnumeven 29693 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29199 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34115 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34127 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34119 zarcls1 34120 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34130 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34133 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34136 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3902 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9592 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8798 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9600 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9928 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10502 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5249 |
| [Enderton] p. 19 | Definition | df-tp 4581 |
| [Enderton] p. 26 | Exercise 5 | unissb 4893 |
| [Enderton] p. 26 | Exercise 10 | pwel 5332 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5533 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5030 iinin2 5029 iinun2 5024 iunin1 5023 iunin1f 32699 iunin2 5022 uniin1 32693 uniin2 32694 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5028 iundif2 5025 |
| [Enderton] p. 32 | Exercise 20 | unineq 4235 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5049 |
| [Enderton] p. 33 | Exercise 25 | iununi 5050 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5057 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7743 iunpwss 5058 |
| [Enderton] p. 36 | Definition | opthwiener 5477 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5411 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4898 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5432 rnex 7880 rnexg 7872 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5883 rnuni 6123 |
| [Enderton] p. 42 | Definition of a function | dffun7 6537 dffun8 6538 |
| [Enderton] p. 43 | Definition of function value | funfv2 6944 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6579 |
| [Enderton] p. 44 | Definition (d) | dfima2 6041 dfima3 6042 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6953 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10420 ac7g 10421 df-ac 10062 dfac2 10078 dfac2a 10076 dfac2b 10077 dfac3 10067 dfac7 10079 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7219 |
| [Enderton] p. 52 | Definition | df-map 8798 |
| [Enderton] p. 53 | Exercise 21 | coass 6242 |
| [Enderton] p. 53 | Exercise 27 | dmco 6231 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6586 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6081 |
| [Enderton] p. 54 | Remark | ixpf 8891 ixpssmap 8903 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8869 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10430 ac9s 10440 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39141 erref 8687 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39144 erthi 8723 |
| [Enderton] p. 57 | Definition | df-ec 8668 |
| [Enderton] p. 58 | Definition | df-qs 8672 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8668 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5879 |
| [Enderton] p. 68 | Definition of successor | df-suc 6341 |
| [Enderton] p. 71 | Definition | df-tr 5202 dftr4 5207 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6416 unisucg 6415 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6416 unisucg 6415 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5217 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5219 trintALT 45404 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8562 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8564 onasuc 8485 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7388 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8563 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8565 onmsuc 8486 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8580 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8567 nnacom 8575 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8581 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8582 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8584 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8568 nnmsucr 8583 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8596 |
| [Enderton] p. 129 | Definition | df-en 8917 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7339 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9961 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16221 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9164 |
| [Enderton] p. 135 | Corollary 6C | php3 9166 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9163 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9195 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9197 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9126 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9130 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9102 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10126 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10127 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10122 dju1en 10118 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9276 unifi 9277 unifi2 9278 |
| [Enderton] p. 144 | Corollary 6K | undif2 4425 unfi 9128 unfi2 9243 |
| [Enderton] p. 145 | Figure 38 | ffoss 7916 |
| [Enderton] p. 145 | Definition | df-dom 8918 |
| [Enderton] p. 146 | Example 1 | domen 8931 domeng 8932 |
| [Enderton] p. 146 | Example 3 | nndomo 9175 nnsdom 9599 nnsdomg 9232 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10130 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9103 xpdom1 9037 xpdom1g 9035 xpdom2g 9034 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9109 |
| [Enderton] p. 151 | Theorem 6M | zorn 10454 zorng 10451 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10439 dfac5 10075 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10523 |
| [Enderton] p. 164 | Example | infdif 10154 |
| [Enderton] p. 168 | Definition | df-po 5548 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6450 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6382 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6449 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6390 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7808 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7753 |
| [Enderton] p. 194 | Remark | onprc 7750 |
| [Enderton] p. 194 | Exercise 16 | suc11 6444 |
| [Enderton] p. 197 | Definition | df-card 9887 |
| [Enderton] p. 197 | Theorem 7P | carden 10498 |
| [Enderton] p. 200 | Exercise 25 | tfis 7824 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9724 |
| [Enderton] p. 202 | Definition | df-r1 9712 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9734 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9815 rankval4b 35351 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9551 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9805 rankprb 9799 rankpw 9791 rankpwi 9771 rankuniss 9814 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9563 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9564 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10056 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10022 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10036 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8300 |
| [Enderton] p. 222 | Definition of kard | karden 9843 kardex 9842 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8555 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8557 |
| [Enderton] p. 240 | Exercise 25 | oarec 8519 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10196 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17650 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17592 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18561 mrieqv2d 17647 mrieqvd 17646 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17651 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17656 mreexexlem2d 17653 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18567 mreexfidimd 17658 |
| [Frege1879] p. 11 | Statement | df3or2 44292 |
| [Frege1879] p. 12 | Statement | df3an2 44293 dfxor4 44290 dfxor5 44291 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44314 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44315 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44319 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44323 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44324 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44330 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44332 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44333 axfrege8 44331 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 37887 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44336 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44344 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44338 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44337 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44346 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44347 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44350 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44340 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44345 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44342 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44348 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44352 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44351 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44343 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44349 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44339 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44341 rp-frege25 44329 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44334 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44354 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44335 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44355 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44358 axfrege31 44357 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44356 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44359 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44360 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44361 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44362 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44363 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44364 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44365 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44366 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44367 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44369 axfrege41 44368 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44370 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44371 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44372 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44373 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44374 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44375 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44376 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44377 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44378 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44381 ax-frege52c 44412 frege52aid 44382 frege52b 44413 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44386 ax-frege54c 44416 frege54b 44417 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44379 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3741 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44384 frege53aid 44383 frege53b 44414 frege53c 44438 |
| [Frege1879] p. 50 | Proposition 54 | biid 263 eqid 2756 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44392 frege55aid 44389 frege55b 44421 frege55c 44442 frege55cor1a 44393 frege55lem2a 44391 frege55lem2b 44420 frege55lem2c 44441 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44395 frege56aid 44394 frege56b 44422 frege56c 44443 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44399 ax-frege58b 44425 frege58bid 44426 frege58c 44445 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44397 frege57aid 44396 frege57b 44423 frege57c 44444 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3752 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44401 frege59b 44428 frege59c 44446 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44402 frege60b 44429 frege60c 44447 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44403 frege61b 44430 frege61c 44448 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44404 frege62b 44431 frege62c 44449 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44405 frege63b 44432 frege63c 44450 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44406 frege64b 44433 frege64c 44451 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44407 frege65b 44434 frege65c 44452 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44408 frege66b 44435 frege66c 44453 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44409 frege67b 44436 frege67c 44454 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44410 frege68b 44437 frege68c 44455 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44456 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44457 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44458 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44459 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44460 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44463 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44461 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44462 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44464 frege77d 44270 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44465 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44466 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44467 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44468 frege81d 44271 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44469 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44470 frege83d 44272 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44471 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44472 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44473 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44474 frege87d 44274 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44475 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44476 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44477 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44478 frege91d 44275 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44479 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44480 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44481 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44482 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44486 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44483 frege96d 44273 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44484 frege97d 44276 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44485 frege98d 44277 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44487 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44488 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44489 frege102d 44278 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44490 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44491 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44492 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44493 frege106d 44279 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44494 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44495 frege108d 44280 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44496 frege109d 44281 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44497 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44498 frege111d 44283 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44499 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44500 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44501 frege114d 44282 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44502 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44503 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44504 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44505 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44506 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44507 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44508 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44509 frege122d 44284 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44510 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44511 frege124d 44285 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44512 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44513 frege126d 44286 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44514 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44515 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44516 frege129d 44287 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44517 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44518 frege131d 44288 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44519 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44520 frege133d 44289 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 46835 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47158 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 46858 |
| [Fremlin1] p. 14 | Definition 112A | ismea 46973 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 46993 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 46984 meadjunre 46998 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 46985 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 46986 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 46982 meaiunle 46991 meaiunlelem 46990 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47003 meaiuninc2 47004 meaiuninc3 47007 meaiuninc3v 47006 meaiunincf 47005 meaiuninclem 47002 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47009 meaiininc2 47010 meaiininclem 47008 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47028 caragendifcl 47036 caratheodory 47050 omelesplit 47040 |
| [Fremlin1] p. 19 | Definition 113A | isome 47016 isomennd 47053 isomenndlem 47052 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47038 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47057 voncmpl 47143 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47020 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47045 carageniuncllem1 47043 carageniuncllem2 47044 caragenuncl 47035 caragenuncllem 47034 caragenunicl 47046 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47054 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47048 caratheodorylem2 47049 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47057 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47116 hoidmv1lelem1 47113 hoidmv1lelem2 47114 hoidmv1lelem3 47115 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47160 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47116 hoidmvle 47122 hoidmvlelem1 47117 hoidmvlelem2 47118 hoidmvlelem3 47119 hoidmvlelem4 47120 hoidmvlelem5 47121 hsphoidmvle2 47107 hsphoif 47098 hsphoival 47101 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47070 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47078 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47105 hoidmvn0val 47106 hoidmvval 47099 hoidmvval0 47109 hoidmvval0b 47112 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47110 hsphoidmvle 47108 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47059 df-voln 47061 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47126 ovn0 47088 ovn0lem 47087 ovnf 47085 ovnome 47095 ovnssle 47083 ovnsslelem 47082 ovnsupge0 47079 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47125 ovnhoilem1 47123 ovnhoilem2 47124 vonhoi 47189 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47142 hoidifhspf 47140 hoidifhspval 47130 hoidifhspval2 47137 hoidifhspval3 47141 hspmbl 47151 hspmbllem1 47148 hspmbllem2 47149 hspmbllem3 47150 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47143 vonmea 47096 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47094 ovnsubadd2 47168 ovnsubadd2lem 47167 ovnsubaddlem1 47092 ovnsubaddlem2 47093 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47153 hoimbl2 47187 hoimbllem 47152 hspdifhsp 47138 opnvonmbl 47156 opnvonmbllem2 47155 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47158 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47201 iccvonmbllem 47200 ioovonmbl 47199 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47207 vonicclem2 47206 vonioo 47204 vonioolem2 47203 vonn0icc 47210 vonn0icc2 47214 vonn0ioo 47209 vonn0ioo2 47212 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47211 snvonmbl 47208 vonct 47215 vonsn 47213 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 46881 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 46880 subsaliuncllem 46879 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47247 salpreimalegt 47231 salpreimaltle 47248 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47250 issmff 47256 issmflem 47249 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47267 issmflelem 47266 smfpreimale 47276 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47278 issmfgtlem 47277 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47218 issmf 47250 issmff 47256 issmfge 47292 issmfgelem 47291 issmfgt 47278 issmfgtlem 47277 issmfle 47267 issmflelem 47266 issmflem 47249 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47229 salpreimagtlt 47252 salpreimalelt 47251 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47292 issmfgelem 47291 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47275 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47273 cnfsmf 47262 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47289 decsmflem 47288 incsmf 47264 incsmflem 47263 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47223 pimconstlt1 47224 smfconst 47271 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47287 smfaddlem1 47285 smfaddlem2 47286 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47318 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47317 smfmullem1 47313 smfmullem2 47314 smfmullem3 47315 smfmullem4 47316 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47319 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47322 smfpimbor1lem2 47321 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47324 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47312 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47311 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47320 smfresal 47310 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47299 smflim2 47328 smflimlem1 47293 smflimlem2 47294 smflimlem3 47295 smflimlem4 47296 smflimlem5 47297 smflimlem6 47298 smflimmpt 47332 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47336 smfsuplem1 47333 smfsuplem2 47334 smfsuplem3 47335 smfsupmpt 47337 smfsupxr 47338 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47340 smfinflem 47339 smfinfmpt 47341 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47299 smflim2 47328 smflimmpt 47332 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47330 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47360 smfdivdmmbl2 47363 smfinfdmmbl 47371 smfinfdmmbllem 47370 smfsupdmmbl 47367 smfsupdmmbllem 47366 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47350 smflimsuplem2 47343 smflimsuplem6 47347 smflimsuplem7 47348 smflimsuplem8 47349 smflimsupmpt 47351 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47353 smfliminflem 47352 smfliminfmpt 47354 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47218 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47364 fsupdm2 47365 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47355 adddmmbl2 47356 finfdm 47368 finfdm2 47369 fsupdm 47364 fsupdm2 47365 muldmmbl 47357 muldmmbl2 47358 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47368 finfdm2 47369 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25571 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25614 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25624 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38145 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38148 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9583 inf1 9567 inf2 9568 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10859 enqer 10869 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10864 df-nq 10860 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10856 df-plq 10862 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7622 df-mpq 10857 df-mq 10863 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10865 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10923 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10924 ltbtwnnq 10926 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10919 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10920 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10927 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10929 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10941 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10943 |
| [Gleason] p. 122 | Definition | df-1p 10930 |
| [Gleason] p. 122 | Remark (1) | prub 10942 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10981 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10933 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10980 psslinpr 10979 supexpr 11002 suplem1pr 11000 suplem2pr 11001 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10966 addclprlem1 10964 addclprlem2 10965 df-plp 10931 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10970 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10969 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10982 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10991 ltexprlem1 10984 ltexprlem2 10985 ltexprlem3 10986 ltexprlem4 10987 ltexprlem5 10988 ltexprlem6 10989 ltexprlem7 10990 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10993 ltaprlem 10992 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10994 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10995 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10932 mulclpr 10968 mulclprlem 10967 reclem2pr 10996 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10977 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10972 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10971 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10976 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10999 reclem3pr 10997 reclem4pr 10998 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11003 enrer 11011 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11008 df-1r 11009 df-nr 11004 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11006 df-plr 11005 negexsr 11050 recexsr 11055 recexsrlem 11051 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11007 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12180 creur 12179 cru 12177 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11136 axcnre 11112 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15118 crimd 15235 crimi 15196 crre 15117 crred 15234 crrei 15195 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15120 remimd 15201 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15287 absval2d 15451 absval2i 15401 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15144 cjaddd 15223 cjaddi 15191 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15145 cjmuld 15224 cjmuli 15192 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15143 cjcjd 15202 cjcji 15174 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15142 cjreb 15126 cjrebd 15205 cjrebi 15177 cjred 15229 rere 15125 rereb 15123 rerebd 15204 rerebi 15176 rered 15227 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15151 addcjd 15215 addcji 15186 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15241 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15282 abscjd 15456 abscji 15405 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15292 abs00d 15452 abs00i 15402 absne0d 15453 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15325 releabsd 15457 releabsi 15406 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15297 absmuld 15460 absmuli 15408 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15285 sqabsaddi 15409 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15334 abstrid 15462 abstrii 15412 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14065 exp0 14068 expp1 14071 expp1d 14150 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26714 cxpaddd 26752 expadd 14107 expaddd 14151 expaddz 14109 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26723 cxpmuld 26772 expmul 14110 expmuld 14152 expmulz 14111 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26720 mulcxpd 26763 mulexp 14104 mulexpd 14164 mulexpz 14105 |
| [Gleason] p. 140 | Exercise 1 | znnen 16220 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13504 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15635 rlimadd 15646 rlimdiv 15649 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15637 rlimsub 15647 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15636 rlimmul 15648 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15640 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15586 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15607 climcj 15608 climim 15610 climre 15609 rlimabs 15612 rlimcj 15613 rlimim 15615 rlimre 15614 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11211 df-xr 11210 ltxr 13107 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15474 limsupval 15477 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15673 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15682 caucvgb 15683 caucvgbf 46011 caucvgr 15679 climcau 15674 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15820 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15889 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15339 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13828 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21391 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24376 xmet0 24375 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24392 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24383 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24385 mstri 24502 xmettri 24384 xmstri 24501 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24415 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23681 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25345 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24573 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24899 addcn2 15597 mulcn 24901 mulcn2 15599 subcn 24900 subcn2 15598 |
| [Gleason] p. 295 | Remark | bcval3 14309 bcval4 14310 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14324 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14307 df-bc 14306 |
| [Gleason] p. 296 | Remark | bcn0 14313 bcnn 14315 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15836 |
| [Gleason] p. 308 | Equation 2 | ef0 16097 |
| [Gleason] p. 308 | Equation 3 | efcj 16098 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16104 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16109 |
| [Gleason] p. 310 | Equation 14 | sinadd 16172 |
| [Gleason] p. 310 | Equation 15 | cosadd 16173 |
| [Gleason] p. 311 | Equation 17 | sincossq 16184 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16189 sinbnd 16188 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14219 sqeqori 14217 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16078 |
| [Godowski] p. 730 | Equation SF | goeqi 32415 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 31810 |
| [Golan] p. 1 | Remark | srgisid 20231 |
| [Golan] p. 1 | Definition | df-srg 20209 |
| [Golan] p. 149 | Definition | df-slmd 33335 |
| [Gonshor] p. 7 | Definition | df-cuts 27823 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 27862 lesrecd 27863 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27983 cofcut1d 27984 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27985 cofcut2d 27986 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27987 cofcutr1d 27988 cofcutr2d 27989 |
| [Gonshor] p. 13 | Definition | df-adds 28023 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28039 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28065 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28193 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28213 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28521 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28523 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28522 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28558 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28081 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36457 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17590 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17592 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48758 df-cllaw 48756 df-comlaw 48757 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48770 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 48791 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39315 dfmembpart2 39320 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32207 riesz2 32208 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32083 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32315 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32327 elpjidm 32326 pjnmopi 32290 |
| [Halmos] p. 44 | Remark | pjinormi 31829 pjinormii 31818 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32331 pjrn 31849 pjrni 31844 pjvec 31838 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 31869 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32296 hmopidmpji 32294 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32333 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32322 pjocvec 31839 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32311 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32314 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32317 pjssdif2i 32316 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 31997 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1809 |
| [Hatcher] p. 25 | Definition | df-phtpc 25027 df-phtpy 25006 |
| [Hatcher] p. 26 | Definition | df-pco 25040 df-pi1 25043 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25030 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25085 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22523 df-dmatalt 48968 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48387 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48372 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48384 bgoldbtbnd 48379 bgoldbtbnd 48379 tgblthelfgott 48385 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 34893 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 34894 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 34908 hgt750lemb 34907 hgt750leme 34909 hgt750lemf 34904 hgt750lemg 34905 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48381 tgoldbachgt 34914 tgoldbachgtALTV 48382 tgoldbachgtd 34913 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 34895 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30635 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18962 grpoideu 30651 mndideu 18755 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18992 grpoinveu 30661 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19023 grpo2inv 30673 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19036 grpoinvop 30675 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19058 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1782 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1783 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1785 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32562 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32575 cdj3i 32583 cdj3lem1 32576 cdjreui 32574 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32573 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42533 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42463 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42485 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42486 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42483 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42489 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42408 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42503 |
| [Holland95] p. 204 | Definition of involution | df-srng 20862 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40075 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42100 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42053 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40505 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 41949 poml4N 40525 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42040 pexmidALTN 40550 pexmidN 40541 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42105 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39696 ldualset 39697 |
| [Holland95] p. 222 | Item 1 | df-lines 40073 df-pointsN 40074 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40475 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40519 omllaw4 39818 pol1N 40482 polcon3N 40489 |
| [Holland95] p. 223 | Definition | df-psubclN 40507 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40478 |
| [Holmes] p. 40 | Definition | df-xrn 38827 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31226 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32324 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32105 eigre 31977 eigrei 31976 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32106 eigorth 31980 eigorthi 31979 |
| [Hughes] p. 137 | Remark (ii) | eigposi 31978 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30450 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30446 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30447 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30448 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30466 frgrregorufr0 30465 frgrregorufrg 30467 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30473 frrusgrord 30482 frrusgrord0 30481 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30229 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30456 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30459 frgrwopreg2 30460 frgrwopregasn 30457 frgrwopregbsn 30458 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30462 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30476 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30479 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30227 numclwlk1 30512 numclwlk1lem1 30510 numclwlk1lem2 30511 numclwwlk1 30502 numclwwlk8 30533 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30453 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 29910 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30488 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30514 numclwwlkovh0 30513 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30522 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30119 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30526 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30529 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30532 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30544 natded 30544 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30544 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30544 natded 30544 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30544 |
| [Jech] p. 4 | Definition of class | cv 1553 cvjust 2750 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10527 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10525 alephmul 10526 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10524 infmap2 10163 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9762 |
| [Jech] p. 72 | Equation 9.3 | scott0 9834 scottex 9833 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9815 rankval4b 35351 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9839 |
| [Jech] p. 78 | Note | opthprc 5704 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43440 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43528 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43529 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43452 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43456 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43457 rmyp1 43458 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43459 rmym1 43460 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43450 rmx1 43451 rmxluc 43461 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43454 rmy1 43455 rmyluc 43462 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43464 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43465 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43485 jm2.17b 43486 jm2.17c 43487 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43518 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43522 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43513 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43488 jm2.24nn 43484 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43527 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43533 rmygeid 43489 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43545 |
| [Juillerat] p. 11 | Section *5 | etransc 46805 etransclem47 46803 etransclem48 46804 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 46800 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 46802 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 46788 |
| [Juillerat] p. 13 | Proof | etransclem35 46791 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 46794 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 46780 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 46797 |
| [Juillerat] p. 14 | Proof | etransclem23 46779 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1981 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2026 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2031 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2021 cbvaliw 2020 wl-cbvmotv 37964 wl-motae 37966 wl-moteq 37965 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2000 spimw 1984 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2047 spw 2048 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31658 chabs1i 31660 chabs2 31659 chabs2i 31661 chjass 31675 chjassi 31628 latabs1 18483 latabs2 18484 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32480 ela 32481 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32425 cvrval2 39846 |
| [Kalmbach] p. 16 | Definition | df-ol 39750 df-oml 39751 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31726 cmbri 31732 cmtvalN 39783 df-cm 31725 df-cmtN 39749 |
| [Kalmbach] p. 22 | Remark | omllaw5N 39819 pjoml5 31755 pjoml5i 31730 |
| [Kalmbach] p. 22 | Definition | pjoml2 31753 pjoml2i 31727 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31756 cmcmi 31734 cmcmii 31739 cmtcomN 39821 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 39817 omlsi 31546 pjoml 31578 pjomli 31577 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 39816 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31738 cmcm3 31757 cmcm3i 31736 cmcm3ii 31741 cmcm4i 31737 cmt3N 39823 cmt4N 39824 cmtbr2N 39825 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31750 cmbr3i 31742 cmtbr3N 39826 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31760 fh1i 31763 fh2 31761 fh2i 31764 omlfh1N 39830 |
| [Kalmbach] p. 65 | Remark | chjatom 32499 chslej 31640 chsleji 31600 shslej 31522 shsleji 31512 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31637 chocini 31596 chsupcl 31482 chsupval2 31552 h0elch 31397 helch 31385 hsupval2 31551 ocin 31438 ococss 31435 shococss 31436 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31454 |
| [Kalmbach] p. 66 | Remark | df-pjh 31537 pjssmi 32307 pjssmii 31823 |
| [Kalmbach] p. 67 | Lemma 3 | osum 31787 osumi 31784 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32342 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32542 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32452 |
| [Kalmbach] p. 140 | Remark | hatomic 32502 hatomici 32501 hatomistici 32504 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 39891 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32523 lsatexch 39615 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32497 cvlcvr1 39911 cvr1 39982 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32516 cvexchi 32511 cvrexch 39992 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32506 hlrelat 39974 hlrelat5N 39973 lrelat 39586 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21184 lsmsatcv 39582 spansncv 31795 spansncvi 31794 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39601 spansncv2 32435 |
| [Kalmbach] p. 266 | Definition | df-st 32353 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 31991 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10594 fpwwe2 10591 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10595 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10602 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10597 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10599 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10612 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10616 gchxpidm 10617 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10628 gchhar 10627 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10161 unxpwdom 9527 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10618 |
| [Kreyszig] p. 3 | Property M1 | metcl 24365 xmetcl 24364 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24372 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24605 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11898 muleqadd 11821 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24471 |
| [Kreyszig] p. 19 | Remark | mopntopon 24472 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24531 mopnm 24477 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24529 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24534 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24575 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23291 lmmbr 25293 lmmbr2 25294 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23413 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25348 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25311 iscmet2 25329 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25351 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23494 metelcls 25340 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25341 metcld2 25342 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25134 lmodvneg1 20945 nvinv 30781 vcm 30718 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25130 lmod0vs 20935 slmd0vs 33358 vc0 30716 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20936 slmdvs0 33359 vcz 30717 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 30833 ngpmet 24636 nrmmetd 24607 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 30828 imsdval2 30829 ncvspds 25196 ngpds 24637 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24622 nvnd 30830 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24651 nmge0 24650 nvge0 30815 nvz 30811 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24657 nvabs 30814 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 30943 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 30887 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 30949 blocni 30947 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 30948 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25239 ipeq0 21663 ipz 30861 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25251 pythi 30992 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 30996 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25273 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15862 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25471 minveco 31026 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 30892 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25364 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31015 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32265 leopg 32264 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32283 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31060 |
| [Kulpa] p. 547 | Theorem | poimir 38100 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38099 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38098 |
| [Kulpa] p. 548 | Theorem | broucube 38101 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38093 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38094 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2408 axnul 5249 |
| [Kunen] p. 11 | Axiom 3 | axnul 5249 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5233 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8808 mapvalg 8806 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10469 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7910 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9712 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9754 r1elssi 9753 |
| [Kunen] p. 107 | Exercise 4 | rankop 9806 rankopb 9800 rankuni 9811 rankxplim 9827 rankxpsuc 9830 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45478 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45486 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45485 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45487 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45492 rexabso 45493 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45499 n0abso 45500 ssabso 45498 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45501 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45511 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45506 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45509 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45510 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45505 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45517 wfaxpr 45522 wfaxreg 45524 wfaxrep 45518 wfaxsep 45519 wfaxun 45523 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45508 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45521 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45517 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45516 omelaxinf2 45513 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45526 wfaxinf2 45525 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45539 permaxext 45529 permaxinf2 45537 permaxnul 45532 permaxpow 45533 permaxpr 45534 permaxrep 45530 permaxsep 45531 permaxun 45535 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45527 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45538 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4956 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 33916 |
| [Lang] p. | Definition | df-rn 5651 |
| [Lang] p. 3 | Statement | lidrideqd 18679 mndbn0 18760 |
| [Lang] p. 3 | Definition | df-mnd 18745 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18697 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18851 |
| [Lang] p. 5 | Equation | gsumreidx 19933 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48752 |
| [Lang] p. 6 | Example | nn0mnd 48749 |
| [Lang] p. 6 | Equation | gsumxp2 19996 |
| [Lang] p. 6 | Statement | cycsubm 19219 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19098 |
| [Lang] p. 6 | Observation | mndlsmidm 19686 |
| [Lang] p. 7 | Definition | dfgrp2e 18981 |
| [Lang] p. 30 | Definition | df-tocyc 33241 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33286 |
| [Lang] p. 32 | Property (b) | cyc3conja 33291 cycpmconjv 33276 |
| [Lang] p. 53 | Definition | df-cat 17676 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18106 cat1lem 18105 |
| [Lang] p. 54 | Definition | df-iso 17758 |
| [Lang] p. 57 | Definition | df-inito 17993 df-termo 17994 |
| [Lang] p. 58 | Example | irinitoringc 21504 |
| [Lang] p. 58 | Statement | initoeu1 18020 termoeu1 18027 |
| [Lang] p. 62 | Definition | df-func 17867 |
| [Lang] p. 65 | Definition | df-nat 17955 |
| [Lang] p. 91 | Note | df-ringc 20668 |
| [Lang] p. 92 | Statement | mxidlprm 33612 |
| [Lang] p. 92 | Definition | isprmidlc 33587 |
| [Lang] p. 128 | Remark | dsmmlmod 21770 |
| [Lang] p. 129 | Proof | lincscm 49000 lincscmcl 49002 lincsum 48999 lincsumcl 49001 |
| [Lang] p. 129 | Statement | lincolss 49004 |
| [Lang] p. 129 | Observation | dsmmfi 21763 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 33878 qusdimsum 33879 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 33859 |
| [Lang] p. 147 | Definition | snlindsntor 49041 |
| [Lang] p. 504 | Statement | mat1 22480 matring 22476 |
| [Lang] p. 504 | Definition | df-mamu 22424 |
| [Lang] p. 505 | Statement | mamuass 22435 mamutpos 22491 matassa 22477 mattposvs 22488 tposmap 22490 |
| [Lang] p. 513 | Definition | mdet1 22634 mdetf 22628 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22724 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22620 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22644 |
| [Lang] p. 515 | Definition | df-minmar1 22668 smadiadetr 22708 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22643 mdetralt 22641 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22656 |
| [Lang] p. 518 | Definition | df-madu 22667 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22678 madurid 22677 matinv 22710 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22923 |
| [Lang], p. 190 | Chapter 6 | vieta 33831 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 33945 finextalg 33949 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 33914 fedgmul 33882 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 33976 |
| [Lang], p. 561 | Remark | chpmatply1 22865 |
| [Lang], p. 561 | Definition | df-chpmat 22860 |
| [Lang2] p. 3 | Notations | df-ind 12186 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 44858 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 44853 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 44859 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5249 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2735 wl-df.clab 37949 |
| [Levy] p. 59 | Definition | df-ttrcl 9653 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9699 |
| [Levy] p. 338 | Axiom | df-clel 2831 df-cleq 2748 wl-df.cleq 37950 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 37953 |
| [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 37953 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2831 df-cleq 2748 wl-df.cleq 37950 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2735 wl-df.clab 37949 |
| [Levy] p. 358 | Axiom | df-clab 2735 wl-df.clab 37949 |
| [Levy58] p. 2 | Definition I | isfin1-3 10333 |
| [Levy58] p. 2 | Definition II | df-fin2 10233 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10232 |
| [Levy58] p. 2 | Definition III | df-fin3 10235 |
| [Levy58] p. 3 | Definition V | df-fin5 10236 |
| [Levy58] p. 3 | Definition IV | df-fin4 10234 |
| [Levy58] p. 4 | Definition VI | df-fin6 10237 |
| [Levy58] p. 4 | Definition VII | df-fin7 10238 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10362 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27720 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27731 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27763 nosupbnd1 27748 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27765 nosupbnd2 27750 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27769 noetasuplem4 27770 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27766 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1782 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1783 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1785 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32550 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32554 mdsymi 32553 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32548 mdsymlem6 32550 mdsymlem7 32551 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32552 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32455 ssdmd2 32456 ssmd1 32453 ssmd2 32454 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32451 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32423 df-md 32422 mdbr 32436 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32473 mdslj1i 32461 mdslj2i 32462 mdslle1i 32459 mdslle2i 32460 mdslmd1i 32471 mdslmd2i 32472 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32463 mdsl2bi 32465 mdsl2i 32464 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32477 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32474 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32475 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32452 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32457 mdsl3 32458 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32476 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32571 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 39893 hlrelat1 39972 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39611 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32478 cvmdi 32466 cvnbtwn4 32431 cvrnbtwn4 39851 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32479 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 39912 cvp 32517 cvrp 39988 lcvp 39612 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32541 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32540 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 39905 hlexch4N 39964 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32543 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40015 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40321 atpsubN 40325 df-pointsN 40074 pointpsubN 40323 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40076 pmap11 40334 pmaple 40333 pmapsub 40340 pmapval 40329 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40337 pmap1N 40339 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40342 pmapglb2N 40343 pmapglb2xN 40344 pmapglbx 40341 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40424 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40049 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40368 paddclN 40414 paddidm 40413 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40050 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40410 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40049 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40050 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19691 lsmmod2 19692 lssats 39584 shatomici 32500 shatomistici 32503 shmodi 31532 shmodsi 31531 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32442 mdsymlem7 32551 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31731 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31635 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32557 |
| [Margaris] p. 40 | Rule C | exlimiv 1944 |
| [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 399 df-ex 1794 df-or 857 dfbi2 477 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 30541 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45438 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45439 |
| [Margaris] p. 79 | Rule C | exinst01 45149 exinst11 45150 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1990 19.2g 2217 r19.2z 4447 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2231 rr19.3v 3621 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2187 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1840 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1795 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2210 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2234 19.9h 2314 exlimd 2247 exlimdh 2318 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2190 excomim 2191 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2353 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30542 conventions-labels 30542 conventions-labels 30542 conventions-labels 30542 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1841 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 44902 albi 1832 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2254 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2255 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 44904 exbi 1861 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2258 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 44901 2alimdv 1932 alimd 2241 alimdh 1831 alimdv 1930 ax-4 1823 ralimdaa 3257 ralimdv 3170 ralimdva 3168 ralimdvva 3203 sbcimdv 3807 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2236 19.21h 2315 19.21t 2235 19.21vv 44900 alrimd 2244 alrimdd 2243 alrimdh 1877 alrimdv 1943 alrimi 2242 alrimih 1838 alrimiv 1941 alrimivv 1942 bj-alrimdh 37015 hbralrimi 3146 r19.21be 3249 r19.21bi 3248 ralrimd 3261 ralrimdv 3154 ralrimdva 3156 ralrimdvv 3200 ralrimdvva 3211 ralrimi 3254 ralrimia 3255 ralrimiv 3147 ralrimiva 3148 ralrimivv 3197 ralrimivva 3199 ralrimivvva 3202 ralrimivw 3152 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 44903 2eximdv 1933 bj-exim 37030 exim 1848 eximd 2245 eximdh 1878 eximdv 1931 rexim 3097 reximd2a 3266 reximdai 3258 reximdd 45674 reximddv 3172 reximddv2 3215 reximddv3 3173 reximdv 3171 reximdv2 3166 reximdva 3169 reximdvai 3167 reximdvva 3204 reximi2 3089 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2240 19.23bi 2220 19.23h 2316 19.23t 2239 exlimdv 1947 exlimdvv 1948 exlimexi 45048 exlimiv 1944 exlimivv 1946 rexlimd3 45670 rexlimdv 3155 rexlimdv3a 3161 rexlimdva 3157 rexlimdva2 3159 rexlimdvaa 3158 rexlimdvv 3212 rexlimdvva 3213 rexlimdvvva 3214 rexlimdvw 3162 rexlimiv 3150 rexlimiva 3149 rexlimivv 3198 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2005 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1894 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1884 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2256 r19.27z 4458 r19.27zv 4459 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2257 19.28vv 44910 r19.28z 4450 r19.28zf 45685 r19.28zv 4454 rr19.28v 3622 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1887 r19.29d2r 3143 r19.29imd 3121 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1895 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2263 19.31vv 44908 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2262 r19.32 47640 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 44906 19.33 1898 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2006 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1891 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2259 19.36vv 44907 r19.36zv 4460 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2261 19.37vv 44909 r19.37zv 4455 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1853 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2004 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1901 19.40 1900 r19.40 3122 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2264 19.41rg 45074 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2265 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1896 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2266 r19.44zv 4457 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2267 r19.45zv 4456 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2631 |
| [Mayet] p. 370 | Remark | jpi 32412 largei 32409 stri 32399 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32354 ishst 32356 |
| [Mayet3] p. 10 | Theorem | hstrbi 32408 hstri 32407 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 31870 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 31871 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32420 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31474 chsupcl 31482 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32502 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32496 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32523 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40555 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18495 latj32 18493 latjass 18491 |
| [Megill] p. 444 | Axiom C5 | ax-5 1924 ax5ALT 39479 |
| [Megill] p. 444 | Section 7 | conventions 30541 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39473 ax-c11n 39460 axc11n 2451 |
| [Megill] p. 446 | Lemma L17 | equtrr 2036 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39468 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39500 hbnae 2457 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2506 sbid 2284 sbidd-misc 50288 sbidd 50287 |
| [Megill] p. 448 | Remark 9.6 | axc14 2488 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39456 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39455 sp 2212 |
| [Megill] p. 448 | Scheme C6' | ax-11 2185 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39457 |
| [Megill] p. 448 | Scheme C8' | ax-7 2022 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39462 |
| [Megill] p. 448 | Scheme C10' | ax-6 1981 ax-c10 39458 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39459 |
| [Megill] p. 448 | Scheme C12' | ax-8 2138 |
| [Megill] p. 448 | Scheme C13' | ax-9 2146 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39463 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39461 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39464 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39476 dral1 2464 dral2-o 39502 dral2 2463 drex1 2466 drex2 2467 drsb1 2520 drsb2 2295 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2200 sbequ 2110 sbid2v 2534 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39469 hba1 2321 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47434 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3827 rspsbca 3828 stdpc4 2092 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39456 ra4 3834 stdpc5 2237 |
| [Mendelson] p. 81 | Rule C | exlimiv 1944 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2042 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2279 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3737 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5477 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4346 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4347 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4224 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4281 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4225 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4089 |
| [Mendelson] p. 231 | Definition of union | dfun3 4223 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5412 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4856 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5531 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4567 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5532 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4883 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5792 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6245 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7747 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6341 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8553 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9101 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9022 xpsneng 9023 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9029 xpcomeng 9030 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9032 |
| [Mendelson] p. 255 | Definition | brsdom 8944 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9025 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8800 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9007 mapsnend 9006 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9107 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9106 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8853 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9010 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9026 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10125 djucomen 10124 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10129 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10123 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8488 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8515 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10506 |
| [Mendelson] p. 281 | Definition | df-r1 9712 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9761 |
| [Mendelson] p. 287 | Axiom system MK | ru 3737 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30400 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30435 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30437 vdgn1frgrv3 30438 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30439 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30432 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30425 2pthfrgrrn 30423 2pthfrgrrn2 30424 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31394 |
| [Monk1] p. 22 | Remark | conventions 30541 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30541 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4185 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5748 ssrelf 32760 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5749 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5157 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6239 coi2 6240 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5889 rn0 5895 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5850 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5658 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5898 rnxp 6145 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5739 xp0 5740 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6056 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6053 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7884 imaexg 7883 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6050 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7045 funfvop 7020 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6910 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6921 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6556 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7227 dff13f 7228 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7192 funrnex 7924 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7220 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6203 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4916 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7976 df-1st 7959 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7977 df-2nd 7960 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9802 ranksnb 9775 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9803 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9804 rankunb 9798 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9786 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9712 r1val2 9785 |
| [Monk1] p. 117 | Lemma | zorn2 10453 zorn2g 10450 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9934 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10508 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9929 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1823 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2022 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2206 ax-c15 39461 ax12v2 2208 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39456 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2185 |
| [Monk2] p. 109 | Lemma 15 | equvini 2480 equvinv 2043 eqvinop 5449 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1924 ax5ALT 39479 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2169 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2185 |
| [Monk2] p. 114 | Lemma 21 | sp 2212 |
| [Monk2] p. 114 | Lemma 22 | axc4 2347 hba1-o 39469 hba1 2321 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2181 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2203 nfra2 3357 nfra2w 3292 |
| [Moore] p. 53 | Part I | df-mre 17590 |
| [Munkres] p. 77 | Example 2 | distop 23028 indistop 23035 indistopon 23034 |
| [Munkres] p. 77 | Example 3 | fctop 23037 fctop2 23038 |
| [Munkres] p. 77 | Example 4 | cctop 23039 |
| [Munkres] p. 78 | Definition of basis | df-bases 22979 isbasis3g 22982 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17448 tgval2 22989 |
| [Munkres] p. 79 | Remark | tgcl 23002 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22996 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23020 tgss3 23019 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23021 basgen2 23022 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 37791 topdifinfeq 37792 topdifinffin 37790 topdifinfindis 37788 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23193 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23071 topcld 23068 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23072 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23074 |
| [Munkres] p. 94 | Definition of closure | clsval 23070 |
| [Munkres] p. 94 | Definition of interior | ntrval 23069 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23108 elcls 23106 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23116 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23181 neindisj 23150 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23183 |
| [Munkres] p. 97 | Definition of limit point | islp2 23178 lpval 23172 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23348 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23260 iscn 23268 iscn2 23271 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23313 cncnp2 23314 cncnpi 23311 df-cnp 23261 iscnp 23270 iscnp2 23272 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24576 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25346 |
| [Nathanson] p. 123 | Remark | reprgt 34872 reprinfz1 34873 reprlt 34870 |
| [Nathanson] p. 123 | Definition | df-repr 34860 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 34892 |
| [Nathanson] p. 123 | Proposition | breprexp 34884 breprexpnat 34885 itgexpif 34857 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32246 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48380 |
| [Pfenning] p. 17 | Definition XM | natded 30544 |
| [Pfenning] p. 17 | Definition NNC | natded 30544 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 30544 |
| [Pfenning] p. 18 | Rule" | natded 30544 |
| [Pfenning] p. 18 | Definition /\I | natded 30544 |
| [Pfenning] p. 18 | Definition ` `E | natded 30544 natded 30544 natded 30544 natded 30544 natded 30544 |
| [Pfenning] p. 18 | Definition ` `I | natded 30544 natded 30544 natded 30544 natded 30544 natded 30544 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30544 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30544 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30544 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30544 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30544 |
| [Pfenning] p. 127 | Definition =E | natded 30544 |
| [Pfenning] p. 127 | Definition =I | natded 30544 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25237 df-dip 30843 dip0l 30860 ip0l 21661 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25278 ipval 30845 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 30856 ipcj 21659 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25240 dipdir 30984 ipdir 21664 ipdiri 30972 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 30852 nmsq 25229 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 30967 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 30969 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 30970 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25246 dipass 30987 ipass 21670 ipassi 30983 |
| [Prugovecki] p. 186 | Definition of bra | braval 32086 df-bra 31992 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 31993 kbval 32096 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32524 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40460 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32538 atcvat4i 32539 cvrat3 40014 cvrat4 40015 lsatcvat3 39624 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32424 cvrval 39841 df-cv 32421 df-lcv 39591 lspsncv0 21189 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40472 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40473 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2735 rabid 3429 rabidd 45681 wl-df.clab 37949 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2307 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2748 wl-df.cleq 37950 |
| [Quine] p. 19 | Definition 2.9 | conventions 30541 df-v 3450 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2895 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2892 abid2f 2948 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2304 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2112 sbalex 2271 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2831 wl-df.clel 37953 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2756 eqid1 30608 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2763 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3740 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3741 dfsbcq2 3742 |
| [Quine] p. 43 | Theorem 6.8 | vex 3452 |
| [Quine] p. 43 | Theorem 6.9 | isset 3462 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3545 spcgv 3550 spcimgf 3512 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3752 spsbcd 3753 |
| [Quine] p. 44 | Theorem 6.12 | elex 3469 |
| [Quine] p. 44 | Theorem 6.13 | elab 3633 elabg 3630 elabgf 3628 |
| [Quine] p. 44 | Theorem 6.14 | noel 4285 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4670 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4579 df-sn 4577 |
| [Quine] p. 49 | Theorem 7.4 | snss 4737 snssg 4736 |
| [Quine] p. 49 | Theorem 7.5 | prss 4772 prssg 4771 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4715 prid1g 4713 prid2 4716 prid2g 4714 snid 4615 snidg 4613 |
| [Quine] p. 51 | Theorem 7.12 | snex 5390 |
| [Quine] p. 51 | Theorem 7.13 | prex 5389 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4878 unisnALT 45449 unisng 4877 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4882 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4891 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4888 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6480 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47628 dfiota2 6467 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47637 iotaval 6484 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6490 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6486 |
| [Quine] p. 58 | Definition 9.1 | df-op 4583 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5489 opabidw 5488 opelopab 5506 opelopaba 5500 opelopabaf 5508 opelopabf 5509 opelopabg 5502 opelopabga 5497 opelopabgf 5504 oprabid 7417 oprabidw 7416 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5646 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5648 |
| [Quine] p. 64 | Definition 9.15 | df-id 5535 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6575 |
| [Quine] p. 65 | Theorem 10.4 | funi 6542 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6563 funsng 6561 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6512 |
| [Quine] p. 65 | Definition 10.2 | args 6071 dffv4 6853 |
| [Quine] p. 68 | Definition 10.11 | conventions 30541 df-fv 6518 fv2 6851 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14275 nn0opth2i 14274 nn0opthi 14273 omopthi 8619 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8369 |
| [Quine] p. 232 | Equation i | carddom 10501 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6598 funimaexg 6597 |
| [Quine] p. 331 | Axiom system NF | ru 3737 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31226 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 30843 polid 31301 polid2i 31299 polidi 31300 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 30955 |
| [ReedSimon] p. 195 | Remark | lnophm 32161 lnophmi 32160 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32274 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32276 leopmuli 32275 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32279 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 31994 leoppos 32268 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32278 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32267 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48181 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48189 |
| [Roman] p. 4 | Definition | df-dmat 22523 df-dmatalt 48968 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20175 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20257 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49055 |
| [Roman] p. 112 | Note | isldepslvec2 49055 ldepsnlinc 49078 zlmodzxznm 49067 |
| [Roman] p. 112 | Example | zlmodzxzequa 49066 zlmodzxzequap 49069 zlmodzxzldep 49074 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22923 |
| [Rosenlicht] p. 80 | Theorem | heicant 38102 |
| [Rosser] p. 281 | Definition | df-op 4583 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 34896 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 34897 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 48936 pmtr3ncom 19491 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19487 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19430 cayleyth 19431 |
| [Rudin] p. 164 | Equation 27 | efcan 16102 |
| [Rudin] p. 164 | Equation 30 | efzval 16110 |
| [Rudin] p. 167 | Equation 48 | absefi 16204 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 199 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1785 |
| [Sanford] p. 39 | Rule 4 | mptxor 1783 |
| [Sanford] p. 40 | Rule 1 | mptnan 1782 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6092 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6095 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6091 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6089 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17590 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17591 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17591 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17593 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10083 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43587 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10393 axdc3 10401 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20259 isrngo 38344 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31684 |
| [Schechter] p. 276 | Definition of span | df-span 31451 spanval 31475 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23026 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6360 onelord 43776 ordelon 6359 ordelord 6357 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 43777 sucidg 6418 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6390 onsuc 7782 ord0 6389 ordsuci 7780 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 43778 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5205 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43553 elon2 6346 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6341 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5543 epelg 5541 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9538 epirron 43779 ordirr 6353 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 43781 oneptr 43780 ontr1 6382 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6378 oneptri 43782 ordtri3or 6367 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8458 ord0eln0 6391 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6404 onsucss 43791 trsucss 6425 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7787 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6431 ordnbtwn 6430 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 43793 ordnexbtwnsuc 43792 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10348 onsucf1lem 43794 onsucf1o 43797 onsucf1olem 43795 onsucrn 43796 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 43798 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7814 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 43787 ordne0gt0 43786 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 43789 limnsuc 43790 onsucelab 43788 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9588 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7829 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9591 ordom 7845 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9592 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8598 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7752 ssorduni 7751 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8488 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9595 limom 7851 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8425 df1o2 8432 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8473 oa0suclim 43800 oalim 8489 oasuc 8481 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8474 om0suclim 43801 omlim 8490 omsuc 8483 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8479 oe0m1 8478 oe0suclim 43802 oelim 8491 oesuc 8484 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43754 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 43804 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 43805 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 43806 limexissupab 43808 limiun 43807 limuni 6397 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8495 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8499 om1om1r 43809 om1r 8500 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8492 oaomoecl 43803 oecl 8494 omcl 8493 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43756 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8501 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8502 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 43810 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 43811 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8569 nnamecl 43812 nnecl 8571 nnmcl 8570 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 43813 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8509 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8510 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8517 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 43815 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 43816 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 43818 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8516 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 43822 omword1 8530 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 43821 oaordnrex 43820 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 43817 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 43823 omword2 8531 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 43824 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 43825 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 43826 omordi 8523 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8525 omord2com 43827 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 43828 df-2o 8426 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 43831 oewordi 8549 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 43832 oeworde 8551 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 43833 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 43834 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 43830 omnord1ex 43829 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 43835 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 43837 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 43841 oenord1ex 43840 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 43842 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8518 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 43836 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8536 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8537 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 43844 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8555 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 43845 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 43846 cantnfub2 43847 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 43850 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29054 axtgcgrrflx 28601 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29055 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29056 axtgcgrid 28602 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28587 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29067 axtgsegcon 28603 df-trkgcb 28589 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29078 axtg5seg 28604 df-trkgcb 28589 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29079 axtgbtwnid 28605 df-trkgb 28588 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29081 axtgpasch 28606 df-trkgb 28588 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29100 df-trkg2d 34916 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28609 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28610 df-trkg2d 34916 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29103 axtgeucl 28611 df-trkge 28590 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29116 axtgcont 28608 axtgcont1 28607 df-trkgb 28588 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36285 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36287 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36290 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36294 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36295 tgcgrcomimp 28616 tgcgrcoml 28618 tgcgrcomr 28617 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36300 tgcgrtriv 28623 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36304 tg5segofs 34927 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 34924 df-ofs 36281 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36306 tgcgrextend 28624 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36308 tgsegconeq 28625 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36320 btwntriv2 36310 tgbtwntriv2 28626 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36311 tgbtwncom 28627 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36314 tgbtwntriv1 28630 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36315 tgbtwnswapid 28631 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36321 btwnintr 36317 tgbtwnexch2 28635 tgbtwnintr 28632 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36323 btwnexch3 36318 tgbtwnexch 28637 tgbtwnexch3 28633 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36322 tgbtwnouttr 28636 tgbtwnouttr2 28634 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29099 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36325 tgbtwndiff 28645 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28638 trisegint 36326 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36342 tgifscgr 28647 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28697 colrot1 28698 colrot2 28699 lncom 28761 lnrot1 28762 lnrot2 28763 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36338 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36343 tgcgrsub 28648 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36353 tgcgrxfr 28657 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28656 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36339 df-cgrg 28650 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28650 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36354 tgbtwnxfr 28669 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36360 colinearperm2 36362 colinearperm3 36361 colinearperm4 36363 colinearperm5 36364 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28672 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36337 tgellng 28692 tglng 28685 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36365 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36373 lnxfr 28705 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36374 lnext 28706 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36378 tgfscgr 28707 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36379 lncgr 28708 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36340 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36381 lnid 28709 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36382 tgidinside 28710 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36399 tgbtwnconn1 28714 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36400 tgbtwnconn2 28715 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36401 tgbtwnconn3 28716 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36407 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36405 legov 28724 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28725 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28738 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36408 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36410 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36412 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36413 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36414 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36411 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36416 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28726 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28728 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28729 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28730 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28731 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36423 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36424 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36419 df-outsideof 36418 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36420 ishlg 28741 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28746 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28748 outsideofrflx 36425 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28742 hlcomd 28743 outsideofcom 36426 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28749 outsideoftr 36427 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 28757 outsideofeu 36429 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36436 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36437 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36430 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36445 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36446 tglineelsb2 28771 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36448 linerflx1 36447 linerflx2 36449 tglinecom 28774 tglinerflx1 28772 tglinerflx2 28773 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36451 tglinethru 28775 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36435 tglng 28685 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28733 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36454 tglinethrueu 28778 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36455 tglineineq 28782 tglineinteq 28784 tglineintmo 28781 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28788 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28789 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28790 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28805 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28801 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28793 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28792 ismir 28798 mirbtwn 28797 mircgr 28796 mirfv 28795 mirval 28794 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28803 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28804 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28805 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28808 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28809 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28814 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28811 mirbtwni 28810 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28812 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28824 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28828 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28825 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28826 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28827 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28830 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28831 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28837 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28833 israg 28836 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28838 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28839 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28841 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28842 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28843 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28844 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28845 ragncol 28848 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28846 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 28852 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 28856 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 28853 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28835 isperp 28851 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 28854 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 28861 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 28869 colperpexlem2 28870 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 28872 colperpexlem3 28871 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 28877 midex 28876 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 28874 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 28883 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 28878 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 28887 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 28890 opphllem6 28891 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 28893 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28606 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 28894 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 28902 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 28897 hpgbr 28899 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 28904 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 28903 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 28905 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 28906 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 28907 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 28908 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 28909 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 28923 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 28913 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 28927 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 28928 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 28929 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 28930 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 28931 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 28934 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 28936 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 28914 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 28937 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 28940 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 28941 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 28942 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 28943 trgcopyeu 28945 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 28969 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 28948 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 28957 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 28955 cgrahl2 28956 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 28958 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 28959 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 28961 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 28962 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 28965 cgrahl 28966 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 28970 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 28971 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 28972 acopyeu 28973 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 28980 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 28984 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 28977 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 28992 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 28985 isleag 28986 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 28994 tgsas1 28993 tgsas2 28995 tgsas3 28996 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 28998 tgasa1 28997 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 28999 tgsss2 29000 tgsss3 29001 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27305 dchrsum 27303 dchrsum2 27302 sumdchr 27306 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27307 sum2dchr 27308 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20084 ablfacrp2 20085 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27250 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27251 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27258 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27516 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27519 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27573 vmalogdivsum2 27572 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27563 dirith2 27562 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27561 rpvmasum 27560 rpvmasum2 27546 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27521 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27559 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27526 dchrisumlem1 27523 dchrisumlem2 27524 dchrisumlem3 27525 dchrisumlema 27522 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27529 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27558 dchrmusumlem 27556 dchrvmasumlem 27557 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27528 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27530 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27554 dchrisum0re 27547 dchrisumn0 27555 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27540 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27544 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27545 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27600 pntrsumbnd2 27601 pntrsumo1 27599 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27564 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27566 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27568 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27571 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27576 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27577 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27582 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27584 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27585 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27593 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27594 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27591 selberg3lem2 27592 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27595 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27589 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27602 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27603 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27604 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27618 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27630 pntlemb 27631 pntlemc 27629 pntlemd 27628 pntlemg 27632 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27630 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27622 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27627 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27630 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27643 pntleml 27645 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 33994 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 33981 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34013 constrinvcl 34024 constrmulcl 34022 constrnegcl 34014 constrsqrtcl 34030 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34000 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34010 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34032 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34042 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4253 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4353 dif0 4325 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4439 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4423 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4244 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4245 |
| [Stoll] p. 20 | Remark | invdif 4226 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4585 |
| [Stoll] p. 43 | Definition | uniiun 5010 |
| [Stoll] p. 44 | Definition | intiin 5011 |
| [Stoll] p. 45 | Definition | df-iin 4946 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4945 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 404 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4253 |
| [Strang] p. 242 | Section 6.3 | expgrowth 44859 |
| [Suppes] p. 22 | Theorem 2 | eq0 4297 eq0f 4294 |
| [Suppes] p. 22 | Theorem 4 | eqss 3946 eqssd 3948 eqssi 3947 |
| [Suppes] p. 23 | Theorem 5 | ss0 4350 ss0b 4349 |
| [Suppes] p. 23 | Theorem 6 | sstr 3939 sstrALT2 45358 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4051 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4053 |
| [Suppes] p. 23 | Theorem 9 | psstr 4056 |
| [Suppes] p. 23 | Theorem 10 | pssss 4046 |
| [Suppes] p. 25 | Theorem 12 | elin 3915 elun 4101 |
| [Suppes] p. 26 | Theorem 15 | inidm 4173 |
| [Suppes] p. 26 | Theorem 16 | in0 4343 |
| [Suppes] p. 27 | Theorem 23 | unidm 4105 |
| [Suppes] p. 27 | Theorem 24 | un0 4342 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4125 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4133 |
| [Suppes] p. 27 | Theorem 27 | unss 4137 |
| [Suppes] p. 27 | Theorem 28 | indir 4233 |
| [Suppes] p. 27 | Theorem 29 | undir 4234 |
| [Suppes] p. 28 | Theorem 32 | difid 4323 |
| [Suppes] p. 29 | Theorem 33 | difin 4219 |
| [Suppes] p. 29 | Theorem 34 | indif 4227 |
| [Suppes] p. 29 | Theorem 35 | undif1 4424 |
| [Suppes] p. 29 | Theorem 36 | difun2 4429 |
| [Suppes] p. 29 | Theorem 37 | difin0 4422 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4420 |
| [Suppes] p. 29 | Theorem 39 | difundi 4237 |
| [Suppes] p. 29 | Theorem 40 | difindi 4239 |
| [Suppes] p. 30 | Theorem 41 | nalset 5258 |
| [Suppes] p. 39 | Theorem 61 | uniss 4867 |
| [Suppes] p. 39 | Theorem 65 | uniop 5478 |
| [Suppes] p. 41 | Theorem 70 | intsn 4936 |
| [Suppes] p. 42 | Theorem 71 | intpr 4934 intprg 4933 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5433 |
| [Suppes] p. 42 | Theorem 78 | intun 4932 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4983 dfiun2g 4981 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4984 |
| [Suppes] p. 47 | Theorem 86 | elpw 4553 elpw2 5284 elpw2g 5283 elpwg 4552 elpwgdedVD 45440 |
| [Suppes] p. 47 | Theorem 87 | pwid 4572 |
| [Suppes] p. 47 | Theorem 89 | pw0 4764 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4765 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5655 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5798 xpindir 5799 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5709 xpundir 5710 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9535 |
| [Suppes] p. 58 | Theorem 2 | relss 5747 |
| [Suppes] p. 59 | Theorem 4 | eldm 5869 eldm2 5870 eldm2g 5868 eldmg 5867 |
| [Suppes] p. 59 | Definition 3 | df-dm 5650 |
| [Suppes] p. 60 | Theorem 6 | dmin 5880 |
| [Suppes] p. 60 | Theorem 8 | rnun 6119 |
| [Suppes] p. 60 | Theorem 9 | rnin 6120 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5857 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5847 brcnvg 5844 |
| [Suppes] p. 62 | Equation 5 | elcnv 5841 elcnv2 5842 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6083 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6118 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6116 |
| [Suppes] p. 63 | Definition | dftrrels2 39106 |
| [Suppes] p. 63 | Theorem 20 | co02 6237 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5944 |
| [Suppes] p. 63 | Definition 7 | df-co 5649 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5854 |
| [Suppes] p. 64 | Theorem 27 | coass 6242 |
| [Suppes] p. 65 | Theorem 31 | resundi 5972 |
| [Suppes] p. 65 | Theorem 34 | elima 6044 elima2 6045 elima3 6046 elimag 6043 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6124 |
| [Suppes] p. 66 | Theorem 40 | dminss 6128 |
| [Suppes] p. 66 | Theorem 41 | imainss 6129 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6132 |
| [Suppes] p. 81 | Definition 34 | dfec2 8669 |
| [Suppes] p. 82 | Theorem 72 | elec 8713 elecALTV 38718 elecg 8711 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39142 erth 8721 erth2 8722 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39145 erdisj 8724 |
| [Suppes] p. 83 | Definition 35, | df-parts 39315 dfmembpart2 39320 |
| [Suppes] p. 89 | Theorem 96 | map0b 8854 |
| [Suppes] p. 89 | Theorem 97 | map0 8858 map0g 8855 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8859 mapsnd 8857 |
| [Suppes] p. 89 | Theorem 99 | mapss 8860 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10014 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10013 |
| [Suppes] p. 92 | Theorem 1 | enref 8955 enrefg 8954 |
| [Suppes] p. 92 | Theorem 2 | ensym 8973 ensymb 8972 ensymi 8974 |
| [Suppes] p. 92 | Theorem 3 | entr 8976 |
| [Suppes] p. 92 | Theorem 4 | unen 9015 |
| [Suppes] p. 94 | Theorem 15 | endom 8949 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8970 |
| [Suppes] p. 94 | Theorem 17 | domtr 8977 |
| [Suppes] p. 95 | Theorem 18 | sbth 9058 |
| [Suppes] p. 97 | Theorem 23 | canth2 9091 canth2g 9092 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9062 df-sdom 8919 dfsdom2 9061 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9075 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9064 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9063 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9073 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8952 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9076 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9071 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9001 fundmeng 9002 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9036 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9072 |
| [Suppes] p. 104 | Theorem 37 | fofi 9246 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9252 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9252 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10498 |
| [Suppes] p. 130 | Definition 3 | df-tr 5202 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7752 |
| [Suppes] p. 134 | Definition 6 | df-suc 6341 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7870 finds 7866 finds1 7869 finds2 7868 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9597 isfinite2 9231 isfiniteg 9233 unbnn 9229 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10866 df-ltpq 10858 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7832 tfinds 7829 tfinds2 7833 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8508 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8510 |
| [Suppes] p. 211 | Theorem 25 | oaass 8518 |
| [Suppes] p. 225 | Definition 8 | iscard2 9924 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10510 |
| [Suppes] p. 228 | Theorem 59 | harcard 9926 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10012 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6387 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7765 onminsb 7766 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10520 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10016 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10023 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10017 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9888 |
| [Suppes] p. 242 | Theorem 6 | weth 10442 |
| [Suppes] p. 242 | Theorem 8 | entric 10504 |
| [Suppes] p. 242 | Theorem 9 | carden 10498 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 35994 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 35998 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2728 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2748 wl-df.cleq 37950 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2831 wl-df.clel 37953 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2750 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2776 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7389 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3737 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5372 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4601 elpr2 4603 elpr2g 4602 elprg 4599 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4591 elsn2 4618 elsn2g 4617 elsng 4590 velsn 4592 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5429 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4586 sneqr 4792 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4597 dfsn2 4589 dfsn2ALT 4598 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7713 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5438 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5425 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5409 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7716 unexg 7715 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4644 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4860 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3906 df-un 3904 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4876 uniprg 4875 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5328 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4642 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6407 elsucg 6405 sstr2 3938 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4106 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4156 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4119 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4174 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4231 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4232 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3919 df-ss 3916 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4551 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4134 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3917 sseqin2 4170 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3953 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4183 inss2 4184 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3995 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4870 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5410 sspwimp 45441 sspwimpALT 45448 sspwimpALT2 45451 sspwimpcf 45443 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5417 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5221 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3409 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5251 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3902 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 36961 dfnul2 4283 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4323 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4300 n0f 4296 neq0 4299 neq0f 4295 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9534 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9677 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9692 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3450 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5264 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4348 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5271 ssexg 5273 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5267 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9546 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9538 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4313 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4083 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4247 undif3VD 45405 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4084 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4091 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3071 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3081 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7725 xpexg 7722 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5647 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6581 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6760 fun11 6584 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6523 svrelfun 6582 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5856 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5858 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5652 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5653 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5649 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6169 dfrel2 6164 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5656 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5777 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5784 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5797 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5984 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5964 opelresi 5966 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5991 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5980 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5985 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6552 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6087 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6550 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6762 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2630 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30541 df-fv 6518 fv3 6874 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7895 cnvexg 7894 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7879 dmexg 7871 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7880 rnexg 7872 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 44977 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7890 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6869 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47716 tz6.12-1-afv2 47783 tz6.12-1 6879 tz6.12-afv 47715 tz6.12-afv2 47782 tz6.12 6880 tz6.12c-afv2 47784 tz6.12c 6878 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 47779 tz6.12-2 6843 tz6.12i-afv2 47785 tz6.12i 6882 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6513 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6514 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6516 wfo 6508 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6515 wf1 6507 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6517 wf1o 6509 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7000 eqfnfv2 7001 eqfnfv2f 7004 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6954 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7190 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7188 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6598 funimaexg 6597 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5095 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5549 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5601 dffr3 6078 eliniseg 6073 iniseg 6076 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5540 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5617 fr3nr 7744 frirr 5616 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5593 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7746 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5604 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5626 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6323 tz6.26i 6324 wefrc 5634 wereu2 5637 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6325 wfii 6326 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6519 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7302 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7303 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7309 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7310 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7311 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7315 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7322 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7324 |
| [TakeutiZaring] p. 35 | Notation | wtr 5201 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 44978 tz7.2 5623 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5206 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6348 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6356 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6357 ordelordALT 45061 ordelordALTVD 45390 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6363 ordelssne 6362 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6361 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6365 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7754 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7755 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6339 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6367 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45073 ordon 7749 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7750 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7822 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6383 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5203 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7764 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7800 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6441 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6440 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7751 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4891 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6341 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6417 sucidg 6418 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7782 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6431 ordnbtwn 6430 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7797 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6340 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7850 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7855 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7810 ordelsuc 7789 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7791 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7820 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7837 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7858 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7859 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7860 |
| [TakeutiZaring] p. 43 | Remark | omon 7847 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9580 omex 9588 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7845 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7865 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7862 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7863 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7840 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4914 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5220 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4915 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5294 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7767 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6386 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4900 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9605 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7762 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8334 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8356 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8357 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8358 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8365 tz7.44-2 8366 tz7.44-3 8367 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8326 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8321 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8305 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8404 tz7.49c 8405 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8402 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8401 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8403 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2676 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9957 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9958 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8489 oasuc 8481 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7830 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8492 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8473 oa0r 8495 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8493 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8505 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8577 nnaordi 8576 oaord 8504 oaordi 8503 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5001 uniss2 4894 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8507 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8512 oawordex 8514 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8569 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8606 |
| [TakeutiZaring] p. 60 | Remark | oancom 9596 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8517 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8574 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8509 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8476 omlim 8490 omsuc 8483 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8474 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8571 nnmcl 8570 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8590 nnmordi 8589 omord 8525 omordi 8523 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8526 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8594 omwordri 8529 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8496 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8499 om1r 8500 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8532 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8534 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8535 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8536 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8537 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8566 oe0 8479 oelim 8491 oesuc 8484 onesuc 8487 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8477 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8544 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8545 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8478 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8502 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8546 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8552 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8550 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8551 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8555 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8557 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9673 tz9.1 9674 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9712 r10 9716 r1lim 9720 r1limg 9719 r1suc 9718 r1sucg 9717 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9728 r1ord2 9729 r1ordg 9726 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9738 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9763 tz9.13 9739 tz9.13g 9740 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9713 rankval 9764 rankvalb 9745 rankvalg 9765 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9787 rankelb 9772 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9801 rankval3 9788 rankval3b 9774 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9777 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9743 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9782 rankr1c 9769 rankr1g 9780 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9783 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9797 rankssb 9796 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9790 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9789 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10422 dfac3 10067 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9976 numth 10419 numth2 10418 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10493 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10494 cardid2 9901 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9908 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10498 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9907 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9892 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9913 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9905 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9111 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8988 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9116 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9040 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9911 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10044 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9163 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9171 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10045 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9168 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10034 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10012 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9920 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10162 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9256 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8920 isfi 8945 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9172 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10481 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9033 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10473 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10132 unxpdom 9192 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9922 cardsdomelir 9921 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9194 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9960 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8798 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10509 infxpidm2 9963 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10153 infxp 10160 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9045 pw2f1o 9043 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9104 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10434 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10429 ac6s5 10438 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10490 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10491 uniimadomf 10492 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10221 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10216 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10200 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10197 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10204 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10211 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10220 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10530 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10198 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10223 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10043 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10042 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10054 alephfp2 10055 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10647 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10058 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10517 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10531 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10532 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39455 |
| [Tarski] p. 67 | Scheme B5 | sp 2212 |
| [Tarski] p. 68 | Lemma 6 | avril1 30604 equid 2026 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2031 |
| [Tarski] p. 70 | Lemma 14 | spim 2412 spime 2414 spimew 1985 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2206 ax-c15 39461 ax12i 1980 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2112 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1982 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1924 ax5ALT 39479 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2022 ax-8 2138 ax-9 2146 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28603 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28604 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28606 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28606 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28607 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16251 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38106 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38108 |
| [Weierstrass] p. 272 | Definition | df-mdet 22618 mdetuni 22655 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 912 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 877 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 878 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 928 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 978 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 189 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 37887 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44324 imim2 58 wl-luk-imim2 37882 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47561 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 905 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2683 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 911 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 37885 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 903 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 906 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 45450 wl-luk-notnotr 37886 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44354 axfrege28 44353 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 876 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 933 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 37879 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 898 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 950 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30542 pm2.27 42 wl-luk-pm2.27 37877 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 931 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 38818 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 932 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 980 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 981 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 979 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1096 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 915 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 916 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 953 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 890 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 892 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 893 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 894 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 860 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 861 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 908 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 951 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 952 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 900 pm2.67 901 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 907 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 983 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 909 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 205 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 984 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 985 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 942 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 940 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 982 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 986 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 941 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1002 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 472 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1003 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1004 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1005 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1006 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 474 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 462 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 405 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 810 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 451 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 452 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 485 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 487 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 772 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 773 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 815 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 630 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 817 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 495 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 496 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 971 pm3.44 970 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 816 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 476 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 974 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 263 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 321 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 355 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 317 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 814 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 841 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 224 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 813 bitr 812 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 570 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 913 pm4.25 914 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 463 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1018 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 879 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 471 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 930 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 641 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 926 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 645 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 987 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1097 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1016 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1062 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1033 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1007 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1009 pm4.45 1008 pm4.45im 836 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 993 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 862 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 552 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 992 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 995 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 996 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 994 pm4.56 999 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1000 pm4.57 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 407 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 865 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 400 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 858 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 408 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 859 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 401 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 564 pm4.71d 568 pm4.71i 566 pm4.71r 565 pm4.71rd 569 pm4.71ri 567 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 960 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 534 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 945 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 524 pm4.76 525 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 972 pm4.77 973 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 943 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1014 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 395 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 396 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1034 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1035 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 349 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 353 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 390 impexp 453 pm4.87 852 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 831 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 955 pm5.11g 954 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 956 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 957 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1023 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1024 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1022 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 385 pm5.18 383 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 389 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 832 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1025 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1058 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1059 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 910 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 579 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 391 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 363 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1012 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 964 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 839 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 580 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 844 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 833 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 842 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 392 pm5.41 393 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 550 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 549 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1015 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1028 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 959 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1011 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1029 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1030 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1038 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 368 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 272 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1039 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37012 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 44882 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 44883 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1884 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 44884 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 44885 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 44886 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1907 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 44887 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 44888 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 44889 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 44890 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 44891 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 44893 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 44894 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 44895 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 44892 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2117 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 44898 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 44899 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2095 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2188 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1843 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1844 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 44900 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 44901 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 44902 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 44903 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 44905 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 44904 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1901 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 44907 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 44908 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 44906 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1842 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 44909 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 44910 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1860 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 44911 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2371 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1874 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 44916 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 44912 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 44913 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 44914 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 44915 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 44920 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 44917 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 44918 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 44919 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 44921 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2590 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 44931 pm13.13b 44932 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 44933 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3032 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3033 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3620 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 44939 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 44940 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 44934 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45076 pm13.193 44935 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 44936 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 44937 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 44938 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 44945 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 44944 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 44943 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3801 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 44946 pm14.122b 44947 pm14.122c 44948 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 44949 pm14.123b 44950 pm14.123c 44951 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 44953 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 44952 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 44954 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6491 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 44955 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6492 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 44956 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 44958 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2654 eupickbi 2657 sbaniota 44959 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 44957 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2605 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 44960 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30541 df-fv 6518 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9949 pm54.43lem 9948 |
| [Young] p. 141 | Definition of operator ordering | leop2 32266 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32272 idleop 32273 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43353 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43360 pellexlem1 43354 |