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 17730 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17730 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18139 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17751 0funcg 49891 df-termc 50279 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50356 prsthinc 50270 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50384 df-mndtc 50384 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50380 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17774 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50372 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50397 oppgoppchom 50396 oppgoppcid 50398 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17844 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17832 invisoinvl 17853 |
| [Adamek] p. 28 | Example 3.13 | idinv 17852 idiso 17851 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17837 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17811 df-iso 17812 dfiso2 17835 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17818 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17869 cicerALT 49852 |
| [Adamek] p. 29 | Definition 3.15 | cic 17862 df-cic 17859 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17921 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17833 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17834 isoco 17840 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17921 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17944 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50110 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17937 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50380 discthing 50267 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50224 prsthinc 50270 thincciso 50259 thincciso2 50261 thincciso3 50262 thinccisod 50260 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50384 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17951 cofucla 49902 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 49968 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18174 catcisoi 50206 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18229 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17970 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17969 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18229 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17994 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18000 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17999 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18214 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18214 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 49938 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 49929 funcoppc 17938 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18162 elcatchom 50203 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17988 fthoppf 49970 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17987 fulloppf 49969 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18171 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 49891 df-catc 18162 |
| [Adamek] p. 45 | Exercise 3G | incat 50407 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50410 nelsubc3 49877 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 49957 imasubc2 49958 imasubc3 49962 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17901 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17902 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 49877 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17913 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17875 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 49966 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 49965 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 49967 ressffth 18003 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50408 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18009 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18030 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18034 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18010 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18036 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 49891 df-inito 18047 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 49891 df-termc 50279 initc 49897 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21640 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18048 oppctermo 50042 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18075 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18079 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50043 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18049 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21641 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18082 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17810 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50275 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50274 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50239 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17845 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17847 |
| [Adamek] p. 185 | Section 10.67 | updjud 9927 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50451 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50451 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50451 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50452 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50452 |
| [Adamek] p. 478 | Item Rng | df-ringc 20756 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49356 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49378 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14615 df-pfx 14716 df-substr 14686 df-word 14558 lencl 14577 wrd0 14583 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24876 df-nmoo 31108 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32516 hmopidmchi 32514 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32564 pjcmul2i 32565 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32281 unoplin 32283 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32282 unopadj2 32301 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32376 lnopunii 32375 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32449 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28131 |
| [Alling] p. 184 | Axiom B | bdayfo 27852 |
| [Alling] p. 184 | Axiom O | ltsso 27851 |
| [Alling] p. 184 | Axiom SD | nodense 27867 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27959 |
| [Alling] p. 185 | Theorem | conway 27983 |
| [Alling] p. 185 | Axiom FE | noeta 27918 |
| [Alling] p. 186 | Theorem 4 | lesrec 28003 lesrecd 28004 |
| [Alling], p. 2 | Definition | rp-brsslt 44177 |
| [Alling], p. 3 | Note | nla0001 44180 nla0002 44178 nla0003 44179 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11400 addcan2d 11420 addcan2i 11410 addcand 11419 addcani 11409 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11453 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11512 negsubd 11581 negsubi 11542 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11514 negnegd 11566 negnegi 11534 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11653 subdid 11676 subdii 11669 subdir 11654 subdird 11677 subdiri 11670 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11395 mul01d 11415 mul01i 11406 mul02 11394 mul02d 11414 mul02i 11405 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11857 mulcan2d 11854 mulcand 11853 mulcani 11859 |
| [Apostol] p. 18 | Theorem I.8 | receu 11865 xreceu 33252 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11894 divrecd 12000 divreci 11966 divreczi 11959 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11918 recreci 11953 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11860 mul0ord 11868 mul0ori 11867 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11659 mul2negd 11675 mul2negi 11668 mulneg1 11656 mulneg1d 11673 mulneg1i 11666 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11936 divadddivd 12041 divadddivi 11983 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11921 divmuldivd 12038 divmuldivi 11981 rdivmuldivd 20502 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11922 divdivdivd 12044 divdivdivi 11984 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13046 rpaddcld 13081 rpmulcl 13047 rpmulcld 13082 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13056 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13059 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11342 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11813 ltadd1dd 11831 ltadd1i 11774 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12071 ltmul1a 12070 ltmul1i 12139 ltmul1ii 12149 ltmul2 12072 ltmul2d 13108 ltmul2dd 13122 ltmul2i 12142 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11740 msqgt0d 11787 msqgt0i 11757 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11742 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11726 lt0neg1d 11789 ltneg 11720 ltnegd 11798 ltnegi 11764 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11705 lt2addd 11843 lt2addi 11782 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13023 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12067 recgt0d 12155 recgt0i 12126 recgt0ii 12127 |
| [Apostol] p. 22 | Definition of integers | df-z 12598 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12253 |
| [Apostol] p. 22 | Definition of rationals | df-q 12979 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9412 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12506 |
| [Apostol] p. 26 | Theorem I.29 | arch 12507 archd 45908 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12705 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12508 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12977 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12976 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13231 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16403 zneo 12685 zneoALTV 48462 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26906 msqsqrtd 15501 resqrtth 15313 sqrtth 15423 sqrtthi 15429 sqsqrtd 15500 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12242 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12943 |
| [Apostol] p. 361 | Remark | crreczi 14271 |
| [Apostol] p. 363 | Remark | absgt0i 15458 |
| [Apostol] p. 363 | Example | abssubd 15514 abssubi 15462 |
| [ApostolNT] p. 7 | Remark | fmtno0 48320 fmtno1 48321 fmtno2 48330 fmtno3 48331 fmtno4 48332 fmtno5fac 48362 fmtnofz04prm 48357 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48308 |
| [ApostolNT] p. 8 | Definition | df-ppi 27275 |
| [ApostolNT] p. 14 | Definition | df-dvds 16317 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16333 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16358 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16353 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16346 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16348 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16334 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16335 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16340 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16375 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16377 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16379 |
| [ApostolNT] p. 15 | Definition | df-gcd 16559 dfgcd2 16610 |
| [ApostolNT] p. 16 | Definition | isprm2 16746 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16717 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16981 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16577 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16611 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16613 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16592 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16584 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16776 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16778 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16994 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16988 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16467 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16651 |
| [ApostolNT] p. 24 | Definition | df-mu 27276 |
| [ApostolNT] p. 25 | Definition | df-phi 16831 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27366 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16856 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16841 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16845 |
| [ApostolNT] p. 32 | Definition | df-vma 27273 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27368 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27391 |
| [ApostolNT] p. 38 | Remark | df-sgm 27277 |
| [ApostolNT] p. 38 | Definition | df-sgm 27277 |
| [ApostolNT] p. 75 | Definition | df-chp 27274 df-cht 27272 |
| [ApostolNT] p. 104 | Definition | congr 16728 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16320 |
| [ApostolNT] p. 106 | Definition | moddvds 16327 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16410 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16411 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13928 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13968 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14281 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16352 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16731 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17140 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16733 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16848 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16867 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16849 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27247 |
| [ApostolNT] p. 179 | Definition | df-lgs 27470 lgsprme0 27514 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27515 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27491 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27506 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27563 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27582 2lgsoddprm 27591 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27549 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27558 |
| [ApostolNT] p. 188 | Definition | df-lgs 27470 lgs1 27516 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27507 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27509 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27517 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27518 |
| [Baer] p. 40 | Property (b) | mapdord 42440 |
| [Baer] p. 40 | Property (c) | mapd11 42441 |
| [Baer] p. 40 | Property (e) | mapdin 42464 mapdlsm 42466 |
| [Baer] p. 40 | Property (f) | mapd0 42467 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42427 mapd1o 42450 |
| [Baer] p. 41 | Property (g) | mapdat 42469 |
| [Baer] p. 44 | Part (1) | mapdpg 42508 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42603 mapdheq 42530 mapdheq2 42531 mapdheq2biN 42532 |
| [Baer] p. 45 | Part (3) | baerlem3 42515 |
| [Baer] p. 46 | Part (4) | mapdheq4 42534 mapdheq4lem 42533 |
| [Baer] p. 46 | Part (5) | baerlem5a 42516 baerlem5abmN 42520 baerlem5amN 42518 baerlem5b 42517 baerlem5bmN 42519 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42623 hdmap1l6a 42611 hdmap1l6e 42616 hdmap1l6f 42617 hdmap1l6g 42618 hdmap1l6lem1 42609 hdmap1l6lem2 42610 mapdh6N 42549 mapdh6aN 42537 mapdh6eN 42542 mapdh6fN 42543 mapdh6gN 42544 mapdh6lem1N 42535 mapdh6lem2N 42536 |
| [Baer] p. 48 | Part 9 | hdmapval 42630 |
| [Baer] p. 48 | Part 10 | hdmap10 42642 |
| [Baer] p. 48 | Part 11 | hdmapadd 42645 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42619 mapdh6hN 42545 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42555 mapdh75d 42556 mapdh75e 42554 mapdh75fN 42557 mapdh7cN 42551 mapdh7dN 42552 mapdh7eN 42550 mapdh7fN 42553 |
| [Baer] p. 48 | Part (8) | mapdh8 42590 mapdh8a 42577 mapdh8aa 42578 mapdh8ab 42579 mapdh8ac 42580 mapdh8ad 42581 mapdh8b 42582 mapdh8c 42583 mapdh8d 42585 mapdh8d0N 42584 mapdh8e 42586 mapdh8g 42587 mapdh8i 42588 mapdh8j 42589 |
| [Baer] p. 48 | Part (9) | mapdh9a 42591 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42571 |
| [Baer] p. 49 | Part 12 | hdmap11 42650 hdmapeq0 42646 hdmapf1oN 42667 hdmapneg 42648 hdmaprnN 42666 hdmaprnlem1N 42651 hdmaprnlem3N 42652 hdmaprnlem3uN 42653 hdmaprnlem4N 42655 hdmaprnlem6N 42656 hdmaprnlem7N 42657 hdmaprnlem8N 42658 hdmaprnlem9N 42659 hdmapsub 42649 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42670 hdmap14lem10 42679 hdmap14lem1a 42668 hdmap14lem2N 42671 hdmap14lem2a 42669 hdmap14lem3 42672 hdmap14lem8 42677 hdmap14lem9 42678 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42680 hdmap14lem12 42681 hdmap14lem13 42682 hdmap14lem14 42683 hdmap14lem15 42684 hgmapval 42689 |
| [Baer] p. 50 | Part 15 | hgmapadd 42696 hgmapmul 42697 hgmaprnlem2N 42699 hgmapvs 42693 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42703 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42719 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42720 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42721 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42722 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42724 hgmapvv 42728 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42723 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42725 |
| [Baer] p. 111 | Line 15 | hdmapg 42732 hdmapglem7 42731 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26907 2irrexpqALT 26976 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2596 |
| [BellMachover] p. 460 | Notation | df-mo 2566 |
| [BellMachover] p. 460 | Definition | mo3 2591 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2734 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2738 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5245 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5256 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37728 sepex 5262 |
| [BellMachover] p. 466 | Problem | axpow2 5337 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5338 |
| [BellMachover] p. 466 | Axiom Union | axun2 7736 |
| [BellMachover] p. 468 | Definition | df-ord 6363 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6378 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6385 onelond 36699 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6380 |
| [BellMachover] p. 471 | Definition of N | df-om 7861 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7798 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6365 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9609 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7876 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9734 |
| [BellMachover] p. 478 | Definition | rankval2 9788 rankval2b 35501 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9752 r1ord3g 9749 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9556 |
| [BellMachover] p. 488 | Axiom AC | ac5 10467 dfac4 10113 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10101 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40121 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32716 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32758 chirredi 32757 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32746 |
| [Beran] p. 3 | Definition of join | sshjval3 31717 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 31979 cmcm2i 31956 cmcm2ii 31961 cmt2N 40052 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 31980 lecmi 31965 lecmii 31966 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 31954 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 31983 cm2ji 31988 cm2mi 31989 |
| [Beran] p. 95 | Definition | df-sh 31570 issh2 31572 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31449 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31462 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31453 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32191 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32193 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32192 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32194 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31445 his1i 31463 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31446 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31447 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31448 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31331 dfhnorm2 31485 normval 31487 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31547 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31336 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31604 |
| [Beran] p. 96 | Definition of converge | df-hlim 31335 hlimi 31551 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31496 norm-i 31492 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31500 norm-ii 31501 normlem0 31472 normlem1 31473 normlem2 31474 normlem3 31475 normlem4 31476 normlem5 31477 normlem6 31478 normlem7 31479 normlem7tALT 31482 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31502 norm-iii 31503 |
| [Beran] p. 98 | Remark 3.4 | bcs 31544 bcsiALT 31542 bcsiHIL 31543 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31484 normpar 31518 normpari 31517 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31509 normpyth 31508 normpythi 31505 |
| [Beran] p. 99 | Remark | lnfn0 32410 lnfn0i 32405 lnop0 32329 lnop0i 32333 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32389 nmcfnex 32416 nmcfnexi 32414 nmcopex 32392 nmcopexi 32390 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32417 nmcfnlbi 32415 nmcoplb 32393 nmcoplbi 32391 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32419 lnfnconi 32418 lnopcon 32398 lnopconi 32397 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31519 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31516 norm3adifii 31511 norm3dif 31513 norm3difi 31510 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31664 pjhth 31756 pjhtheu 31757 pjpjhth 31788 pjpjhthi 31789 pjth 25609 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 31769 ococi 31768 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32424 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32425 riesz4 32427 riesz4i 32426 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32442 cnlnadjeu 32441 cnlnadjeui 32440 cnlnadji 32439 cnlnadjlem1 32430 nmopadjlei 32451 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32454 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32453 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32455 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32299 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32465 nmopcoadji 32464 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32456 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32466 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32463 pjadj2coi 32567 pjadjcoi 32524 |
| [Beran] p. 107 | Definition | df-ch 31584 isch2 31586 |
| [Beran] p. 107 | Remark 3.12 | choccl 31669 isch3 31604 occl 31667 ocsh 31646 shoccl 31668 shocsh 31647 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 31771 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31695 |
| [Beran] p. 109 | Property (i) | pjadj2 32550 pjadj3 32551 pjadji 32048 pjadjii 32037 |
| [Beran] p. 109 | Property (ii) | pjidmco 32544 pjidmcoi 32540 pjidmi 32036 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32536 |
| [Beran] p. 111 | Remark | ho0val 32113 pjch1 32033 |
| [Beran] p. 111 | Definition | df-hfmul 32097 df-hfsum 32096 df-hodif 32095 df-homul 32094 df-hosum 32093 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32034 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32057 pjchi 31795 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 31802 pjoc2i 31801 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32043 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32528 pjssmii 32044 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32527 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32526 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32531 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32529 pjssge0ii 32045 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32530 pjdifnormii 32046 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1805 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1803 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1806 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1801 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34691 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34699 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34697 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34701 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34721 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34752 df-sitm 34730 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34752 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34729 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29409 isuhgrop 29431 isusgrop 29523 isuspgrop 29522 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48654 df-subgr 29629 uhgrspan1 29664 uhgrspansubgr 29652 |
| [Bollobas] p. 3 | Definition | df-gric 48674 gricuspgr 48711 isuspgrim 48689 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 29815 df-clnbgr 48612 df-cusgr 29773 df-nbgr 29694 fusgrmaxsize 29825 |
| [Bollobas] p. 4 | Definition | df-upwlks 48927 df-wlks 29960 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 29911 finsumvtxdgeven 29913 fusgr1th 29912 fusgrvtxdgonume 29915 vtxdgoddnumeven 29914 |
| [Bollobas] p. 5 | Notation | df-pths 30074 |
| [Bollobas] p. 5 | Definition | df-crcts 30146 df-cycls 30147 df-trls 30051 df-wlkson 29961 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29420 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 48993 df-cllaw 48979 df-mgm 18704 df-mgm2 49012 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 48994 df-asslaw 48981 df-sgrp 18783 df-sgrp2 49014 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49013 df-comlaw 48980 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18799 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33355 mndlactf1o 33359 mndractf1 33357 mndractf1o 33360 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20323 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20237 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34032 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34036 assarrginv 34035 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34077 fldextrspunfld 34075 fldextrspunlem1 34074 fldextrspunlem2 34076 fldextrspunlsp 34073 fldextrspunlsplem 34072 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 33836 dfufd2 33849 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7285 fcofo 7286 |
| [BourbakiTop1] p. | Remark | xnegmnf 13242 xnegpnf 13241 |
| [BourbakiTop1] p. | Remark | rexneg 13243 |
| [BourbakiTop1] p. | Remark 3 | ust0 24388 ustfilxp 24381 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24258 |
| [BourbakiTop1] p. | Criterion | ishmeo 23927 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24451 iducn 24450 snfil 24032 |
| [BourbakiTop1] p. | Example 2 | neifil 24048 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24235 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24471 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34356 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24031 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24443 df-ust 24369 filintn0 24029 filn0 24030 istgp 24245 ucnprima 24449 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24454 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24465 df-usp 24425 df-utop 24399 trust 24397 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34255 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23284 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23437 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24374 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24377 |
| [BourbakiTop1] p. | Property V_ii | innei 23293 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23301 neissex 23295 |
| [BourbakiTop1] p. | Proposition 1 | neips 23281 neiss 23277 ucncn 24452 ustund 24390 ustuqtop 24414 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23435 neiptopreu 23301 utop2nei 24418 utop3cls 24419 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24459 uspreg 24441 utopreg 24420 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23859 imasncls 23860 imasnopn 23858 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24168 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24376 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24378 |
| [BourbakiTop1] p. | Property V_iii | elnei 23279 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24470 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24375 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24379 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23555 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24014 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23062 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34252 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 46804 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 46806 stoweid 46805 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 46743 stoweidlem10 46752 stoweidlem14 46756 stoweidlem15 46757 stoweidlem35 46777 stoweidlem36 46778 stoweidlem37 46779 stoweidlem38 46780 stoweidlem40 46782 stoweidlem41 46783 stoweidlem43 46785 stoweidlem44 46786 stoweidlem46 46788 stoweidlem5 46747 stoweidlem50 46792 stoweidlem52 46794 stoweidlem53 46795 stoweidlem55 46797 stoweidlem56 46798 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 46765 stoweidlem24 46766 stoweidlem27 46769 stoweidlem28 46770 stoweidlem30 46772 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 46776 stoweidlem59 46801 stoweidlem60 46802 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 46787 stoweidlem49 46791 stoweidlem7 46749 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 46773 stoweidlem39 46781 stoweidlem42 46784 stoweidlem48 46790 stoweidlem51 46793 stoweidlem54 46796 stoweidlem57 46799 stoweidlem58 46800 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 46767 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 46759 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 46753 stoweidlem13 46755 stoweidlem26 46768 stoweidlem61 46803 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 46760 |
| [Bruck] p. 1 | Section I.1 | df-clintop 48993 df-mgm 18704 df-mgm2 49012 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18783 df-sgrp2 49014 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19111 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5192 |
| [Church] p. 129 | Section II.24 | df-ifp 1078 dfifp2 1079 |
| [Clemente] p. 10 | Definition IT | natded 30765 |
| [Clemente] p. 10 | Definition I` `m,n | natded 30765 |
| [Clemente] p. 11 | Definition E=>m,n | natded 30765 |
| [Clemente] p. 11 | Definition I=>m,n | natded 30765 |
| [Clemente] p. 11 | Definition E` `(1) | natded 30765 |
| [Clemente] p. 11 | Definition E` `(2) | natded 30765 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 30765 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 30765 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 30765 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 30765 |
| [Clemente] p. 14 | Proof 5.11 | natded 30765 |
| [Clemente] p. 14 | Definition E` `n | natded 30765 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 30767 ex-natded5.2 30766 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 30770 ex-natded5.3 30769 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 30772 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 30774 ex-natded5.7 30773 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 30776 ex-natded5.8 30775 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 30778 ex-natded5.13 30777 |
| [Clemente] p. 32 | Definition I` `n | natded 30765 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 30765 |
| [Clemente] p. 32 | Definition E` `n,t | natded 30765 |
| [Clemente] p. 32 | Definition I` `n,t | natded 30765 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 30779 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 30780 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 30782 ex-natded9.26 30781 |
| [Cohen] p. 301 | Remark | relogoprlem 26767 |
| [Cohen] p. 301 | Property 2 | relogmul 26768 relogmuld 26801 |
| [Cohen] p. 301 | Property 3 | relogdiv 26769 relogdivd 26802 |
| [Cohen] p. 301 | Property 4 | relogexp 26772 |
| [Cohen] p. 301 | Property 1a | log1 26761 |
| [Cohen] p. 301 | Property 1b | loge 26762 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26963 |
| [Cohen4] p. 349 | Property | relogbf 26967 |
| [Cohen4] p. 352 | Definition | elogb 26946 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26953 |
| [Cohen4] p. 361 | Property 3 | logbrec 26958 relogbdiv 26955 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26951 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26956 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26944 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26945 |
| [Cohen4] p. 367 | Property | logbchbase 26947 |
| [Cohen4] p. 377 | Property 2 | logblt 26960 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34684 sxbrsigalem4 34686 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18619 acsinfd 18618 acsinfdimd 18620 acsmap2d 18617 acsmapd 18616 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34689 |
| [Connell] p. 57 | Definition | df-scmat 22659 df-scmatalt 49207 |
| [Conway] p. 4 | Definition | lesrec 28003 lesrecd 28004 |
| [Conway] p. 5 | Definition | addsval 28166 addsval2 28167 df-adds 28164 df-muls 28311 df-negs 28225 |
| [Conway] p. 7 | Theorem | 0lt1s 28016 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28666 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28065 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28064 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 27942 |
| [Conway] p. 17 | Theorem 3 | addsass 28209 addsassd 28210 addscom 28170 addscomd 28171 addsrid 28168 addsridd 28169 |
| [Conway] p. 17 | Definition | df-0s 28011 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28248 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28245 negsidd 28246 |
| [Conway] p. 18 | Theorem 5 | leadds1 28193 leadds1d 28199 |
| [Conway] p. 18 | Definition | df-1s 28012 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28240 negscld 28241 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28184 |
| [Conway] p. 19 | Note | mulsunif2 28374 |
| [Conway] p. 19 | Theorem 7 | addsdi 28359 addsdid 28360 addsdird 28361 mulnegs1d 28364 mulnegs2d 28365 mulsass 28370 mulsassd 28371 mulscom 28343 mulscomd 28344 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28338 mulscld 28339 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28342 ltmuls 28340 ltmulsd 28341 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28348 mulsgt0d 28349 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28422 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28008 |
| [Conway] p. 24 | Definition | df-reno 28694 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28703 remulscl 28706 renegscl 28702 |
| [Conway] p. 27 | Definition | df-ons 28456 elons2 28462 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28466 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28468 onswe 28476 |
| [Conway] p. 29 | Remark | madebday 28104 newbday 28106 oldbday 28105 |
| [Conway] p. 29 | Definition | df-made 28031 df-new 28033 df-old 28032 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13901 |
| [Crawley] p. 1 | Definition of poset | df-poset 18375 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40188 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 40992 dalaw 40688 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 42763 |
| [Crawley] p. 111 | Definition of set W | df-watsN 40792 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 40908 df-ldil 40906 isldil 40912 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 40907 df-trnN 40909 isltrn 40921 ltrnu 40923 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40593 cdlema2N 40594 exatleN 40206 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40278 cdlemb 40596 cdlemb2 40843 cdlemb3 41408 idltrn 40952 l1cvat 39857 lhpat 40845 lhpat2 40847 lshpat 39858 ltrnel 40941 ltrnmw 40953 |
| [Crawley] p. 112 | Lemma C | cdlemc1 40993 cdlemc2 40994 ltrnnidn 40976 trlat 40971 trljat1 40968 trljat2 40969 trljat3 40970 trlne 40987 trlnidat 40975 trlnle 40988 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 40793 |
| [Crawley] p. 113 | Lemma C | cdlemc 40999 cdlemc3 40995 cdlemc4 40996 |
| [Crawley] p. 113 | Lemma D | cdlemd 41009 cdlemd1 41000 cdlemd2 41001 cdlemd3 41002 cdlemd4 41003 cdlemd5 41004 cdlemd6 41005 cdlemd7 41006 cdlemd8 41007 cdlemd9 41008 cdleme31sde 41187 cdleme31se 41184 cdleme31se2 41185 cdleme31snd 41188 cdleme32a 41243 cdleme32b 41244 cdleme32c 41245 cdleme32d 41246 cdleme32e 41247 cdleme32f 41248 cdleme32fva 41239 cdleme32fva1 41240 cdleme32fvcl 41242 cdleme32le 41249 cdleme48fv 41301 cdleme4gfv 41309 cdleme50eq 41343 cdleme50f 41344 cdleme50f1 41345 cdleme50f1o 41348 cdleme50laut 41349 cdleme50ldil 41350 cdleme50lebi 41342 cdleme50rn 41347 cdleme50rnlem 41346 cdlemeg49le 41313 cdlemeg49lebilem 41341 |
| [Crawley] p. 113 | Lemma E | cdleme 41362 cdleme00a 41011 cdleme01N 41023 cdleme02N 41024 cdleme0a 41013 cdleme0aa 41012 cdleme0b 41014 cdleme0c 41015 cdleme0cp 41016 cdleme0cq 41017 cdleme0dN 41018 cdleme0e 41019 cdleme0ex1N 41025 cdleme0ex2N 41026 cdleme0fN 41020 cdleme0gN 41021 cdleme0moN 41027 cdleme1 41029 cdleme10 41056 cdleme10tN 41060 cdleme11 41072 cdleme11a 41062 cdleme11c 41063 cdleme11dN 41064 cdleme11e 41065 cdleme11fN 41066 cdleme11g 41067 cdleme11h 41068 cdleme11j 41069 cdleme11k 41070 cdleme11l 41071 cdleme12 41073 cdleme13 41074 cdleme14 41075 cdleme15 41080 cdleme15a 41076 cdleme15b 41077 cdleme15c 41078 cdleme15d 41079 cdleme16 41087 cdleme16aN 41061 cdleme16b 41081 cdleme16c 41082 cdleme16d 41083 cdleme16e 41084 cdleme16f 41085 cdleme16g 41086 cdleme19a 41105 cdleme19b 41106 cdleme19c 41107 cdleme19d 41108 cdleme19e 41109 cdleme19f 41110 cdleme1b 41028 cdleme2 41030 cdleme20aN 41111 cdleme20bN 41112 cdleme20c 41113 cdleme20d 41114 cdleme20e 41115 cdleme20f 41116 cdleme20g 41117 cdleme20h 41118 cdleme20i 41119 cdleme20j 41120 cdleme20k 41121 cdleme20l 41124 cdleme20l1 41122 cdleme20l2 41123 cdleme20m 41125 cdleme20y 41104 cdleme20zN 41103 cdleme21 41139 cdleme21d 41132 cdleme21e 41133 cdleme22a 41142 cdleme22aa 41141 cdleme22b 41143 cdleme22cN 41144 cdleme22d 41145 cdleme22e 41146 cdleme22eALTN 41147 cdleme22f 41148 cdleme22f2 41149 cdleme22g 41150 cdleme23a 41151 cdleme23b 41152 cdleme23c 41153 cdleme26e 41161 cdleme26eALTN 41163 cdleme26ee 41162 cdleme26f 41165 cdleme26f2 41167 cdleme26f2ALTN 41166 cdleme26fALTN 41164 cdleme27N 41171 cdleme27a 41169 cdleme27cl 41168 cdleme28c 41174 cdleme3 41039 cdleme30a 41180 cdleme31fv 41192 cdleme31fv1 41193 cdleme31fv1s 41194 cdleme31fv2 41195 cdleme31id 41196 cdleme31sc 41186 cdleme31sdnN 41189 cdleme31sn 41182 cdleme31sn1 41183 cdleme31sn1c 41190 cdleme31sn2 41191 cdleme31so 41181 cdleme35a 41250 cdleme35b 41252 cdleme35c 41253 cdleme35d 41254 cdleme35e 41255 cdleme35f 41256 cdleme35fnpq 41251 cdleme35g 41257 cdleme35h 41258 cdleme35h2 41259 cdleme35sn2aw 41260 cdleme35sn3a 41261 cdleme36a 41262 cdleme36m 41263 cdleme37m 41264 cdleme38m 41265 cdleme38n 41266 cdleme39a 41267 cdleme39n 41268 cdleme3b 41031 cdleme3c 41032 cdleme3d 41033 cdleme3e 41034 cdleme3fN 41035 cdleme3fa 41038 cdleme3g 41036 cdleme3h 41037 cdleme4 41040 cdleme40m 41269 cdleme40n 41270 cdleme40v 41271 cdleme40w 41272 cdleme41fva11 41279 cdleme41sn3aw 41276 cdleme41sn4aw 41277 cdleme41snaw 41278 cdleme42a 41273 cdleme42b 41280 cdleme42c 41274 cdleme42d 41275 cdleme42e 41281 cdleme42f 41282 cdleme42g 41283 cdleme42h 41284 cdleme42i 41285 cdleme42k 41286 cdleme42ke 41287 cdleme42keg 41288 cdleme42mN 41289 cdleme42mgN 41290 cdleme43aN 41291 cdleme43bN 41292 cdleme43cN 41293 cdleme43dN 41294 cdleme5 41042 cdleme50ex 41361 cdleme50ltrn 41359 cdleme51finvN 41358 cdleme51finvfvN 41357 cdleme51finvtrN 41360 cdleme6 41043 cdleme7 41051 cdleme7a 41045 cdleme7aa 41044 cdleme7b 41046 cdleme7c 41047 cdleme7d 41048 cdleme7e 41049 cdleme7ga 41050 cdleme8 41052 cdleme8tN 41057 cdleme9 41055 cdleme9a 41053 cdleme9b 41054 cdleme9tN 41059 cdleme9taN 41058 cdlemeda 41100 cdlemedb 41099 cdlemednpq 41101 cdlemednuN 41102 cdlemefr27cl 41205 cdlemefr32fva1 41212 cdlemefr32fvaN 41211 cdlemefrs32fva 41202 cdlemefrs32fva1 41203 cdlemefs27cl 41215 cdlemefs32fva1 41225 cdlemefs32fvaN 41224 cdlemesner 41098 cdlemeulpq 41022 |
| [Crawley] p. 114 | Lemma E | 4atex 40878 4atexlem7 40877 cdleme0nex 41092 cdleme17a 41088 cdleme17c 41090 cdleme17d 41300 cdleme17d1 41091 cdleme17d2 41297 cdleme18a 41093 cdleme18b 41094 cdleme18c 41095 cdleme18d 41097 cdleme4a 41041 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41127 cdleme21at 41130 cdleme21b 41128 cdleme21c 41129 cdleme21ct 41131 cdleme21f 41134 cdleme21g 41135 cdleme21h 41136 cdleme21i 41137 cdleme22gb 41096 |
| [Crawley] p. 116 | Lemma F | cdlemf 41365 cdlemf1 41363 cdlemf2 41364 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41369 cdlemg16 41459 cdlemg28 41506 cdlemg28a 41495 cdlemg28b 41505 cdlemg3a 41399 cdlemg42 41531 cdlemg43 41532 cdlemg44 41535 cdlemg44a 41533 cdlemg46 41537 cdlemg47 41538 cdlemg9 41436 ltrnco 41521 ltrncom 41540 tgrpabl 41553 trlco 41529 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41545 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41479 cdlemg17b 41464 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41558 df-edring 41559 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41562 |
| [Crawley] p. 118 | Remark | tendopltp 41582 |
| [Crawley] p. 118 | Lemma H | cdlemh 41619 cdlemh1 41617 cdlemh2 41618 |
| [Crawley] p. 118 | Lemma I | cdlemi 41622 cdlemi1 41620 cdlemi2 41621 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41623 cdlemj2 41624 cdlemj3 41625 tendocan 41626 |
| [Crawley] p. 118 | Lemma K | cdlemk 41776 cdlemk1 41633 cdlemk10 41645 cdlemk11 41651 cdlemk11t 41748 cdlemk11ta 41731 cdlemk11tb 41733 cdlemk11tc 41747 cdlemk11u-2N 41691 cdlemk11u 41673 cdlemk12 41652 cdlemk12u-2N 41692 cdlemk12u 41674 cdlemk13-2N 41678 cdlemk13 41654 cdlemk14-2N 41680 cdlemk14 41656 cdlemk15-2N 41681 cdlemk15 41657 cdlemk16-2N 41682 cdlemk16 41659 cdlemk16a 41658 cdlemk17-2N 41683 cdlemk17 41660 cdlemk18-2N 41688 cdlemk18-3N 41702 cdlemk18 41670 cdlemk19-2N 41689 cdlemk19 41671 cdlemk19u 41772 cdlemk1u 41661 cdlemk2 41634 cdlemk20-2N 41694 cdlemk20 41676 cdlemk21-2N 41693 cdlemk21N 41675 cdlemk22-3 41703 cdlemk22 41695 cdlemk23-3 41704 cdlemk24-3 41705 cdlemk25-3 41706 cdlemk26-3 41708 cdlemk26b-3 41707 cdlemk27-3 41709 cdlemk28-3 41710 cdlemk29-3 41713 cdlemk3 41635 cdlemk30 41696 cdlemk31 41698 cdlemk32 41699 cdlemk33N 41711 cdlemk34 41712 cdlemk35 41714 cdlemk36 41715 cdlemk37 41716 cdlemk38 41717 cdlemk39 41718 cdlemk39u 41770 cdlemk4 41636 cdlemk41 41722 cdlemk42 41743 cdlemk42yN 41746 cdlemk43N 41765 cdlemk45 41749 cdlemk46 41750 cdlemk47 41751 cdlemk48 41752 cdlemk49 41753 cdlemk5 41638 cdlemk50 41754 cdlemk51 41755 cdlemk52 41756 cdlemk53 41759 cdlemk54 41760 cdlemk55 41763 cdlemk55u 41768 cdlemk56 41773 cdlemk5a 41637 cdlemk5auN 41662 cdlemk5u 41663 cdlemk6 41639 cdlemk6u 41664 cdlemk7 41650 cdlemk7u-2N 41690 cdlemk7u 41672 cdlemk8 41640 cdlemk9 41641 cdlemk9bN 41642 cdlemki 41643 cdlemkid 41738 cdlemkj-2N 41684 cdlemkj 41665 cdlemksat 41648 cdlemksel 41647 cdlemksv 41646 cdlemksv2 41649 cdlemkuat 41668 cdlemkuel-2N 41686 cdlemkuel-3 41700 cdlemkuel 41667 cdlemkuv-2N 41685 cdlemkuv2-2 41687 cdlemkuv2-3N 41701 cdlemkuv2 41669 cdlemkuvN 41666 cdlemkvcl 41644 cdlemky 41728 cdlemkyyN 41764 tendoex 41777 |
| [Crawley] p. 120 | Remark | dva1dim 41787 |
| [Crawley] p. 120 | Lemma L | cdleml1N 41778 cdleml2N 41779 cdleml3N 41780 cdleml4N 41781 cdleml5N 41782 cdleml6 41783 cdleml7 41784 cdleml8 41785 cdleml9 41786 dia1dim 41863 |
| [Crawley] p. 120 | Lemma M | dia11N 41850 diaf11N 41851 dialss 41848 diaord 41849 dibf11N 41963 djajN 41939 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 41834 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 41920 dia2dimlem1 41866 dia2dimlem2 41867 dia2dimlem3 41868 dia2dimlem4 41869 dia2dimlem5 41870 diaf1oN 41932 diarnN 41931 dvheveccl 41914 dvhopN 41918 |
| [Crawley] p. 121 | Lemma N | cdlemn 42014 cdlemn10 42008 cdlemn11 42013 cdlemn11a 42009 cdlemn11b 42010 cdlemn11c 42011 cdlemn11pre 42012 cdlemn2 41997 cdlemn2a 41998 cdlemn3 41999 cdlemn4 42000 cdlemn4a 42001 cdlemn5 42003 cdlemn5pre 42002 cdlemn6 42004 cdlemn7 42005 cdlemn8 42006 cdlemn9 42007 diclspsn 41996 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 41975 |
| [Crawley] p. 122 | Lemma N | dih11 42067 dihf11 42069 dihjust 42019 dihjustlem 42018 dihord 42066 dihord1 42020 dihord10 42025 dihord11b 42024 dihord11c 42026 dihord2 42029 dihord2a 42021 dihord2b 42022 dihord2cN 42023 dihord2pre 42027 dihord2pre2 42028 dihordlem6 42015 dihordlem7 42016 dihordlem7b 42017 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42032 dihfval 42033 dihval 42034 |
| [Diestel] p. 3 | Definition | df-gric 48674 df-grim 48671 isuspgrim 48689 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29773 df-nbgr 29694 |
| [Diestel] p. 3 | Definition by | df-grisom 48670 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48654 df-subgr 29629 uhgrspan1 29664 uhgrspansubgr 29652 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 29915 vtxdgoddnumeven 29914 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29420 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34263 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34275 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34267 zarcls1 34268 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34278 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34281 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34284 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3907 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9614 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8824 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9622 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9973 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10545 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5267 |
| [Enderton] p. 19 | Definition | df-tp 4593 |
| [Enderton] p. 26 | Exercise 5 | unissb 4905 |
| [Enderton] p. 26 | Exercise 10 | pwel 5351 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5553 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5044 iinin2 5043 iinun2 5036 iunin1 5035 iunin1f 32913 iunin2 5034 uniin1 5038 uniin2 5039 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5042 iundif2 5037 |
| [Enderton] p. 32 | Exercise 20 | unineq 4240 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5063 |
| [Enderton] p. 33 | Exercise 25 | iununi 5064 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5071 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7768 iunpwss 5072 |
| [Enderton] p. 36 | Definition | opthwiener 5496 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5430 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4910 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5451 rnex 7905 rnexg 7897 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5903 rnuni 6145 |
| [Enderton] p. 42 | Definition of a function | dffun7 6563 dffun8 6564 |
| [Enderton] p. 43 | Definition of function value | funfv2 6969 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6605 |
| [Enderton] p. 44 | Definition (d) | dfima2 6063 dfima3 6064 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6978 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10463 ac7g 10464 df-ac 10107 dfac2 10122 dfac2a 10120 dfac2b 10121 dfac3 10112 dfac7 10123 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7244 |
| [Enderton] p. 52 | Definition | df-map 8824 |
| [Enderton] p. 53 | Exercise 21 | coass 6266 |
| [Enderton] p. 53 | Exercise 27 | dmco 6255 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6612 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6103 |
| [Enderton] p. 54 | Remark | ixpf 8916 ixpssmap 8928 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8894 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10473 ac9s 10483 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39371 erref 8713 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39374 erthi 8749 |
| [Enderton] p. 57 | Definition | df-ec 8694 |
| [Enderton] p. 58 | Definition | df-qs 8698 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8694 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5899 |
| [Enderton] p. 68 | Definition of successor | df-suc 6366 |
| [Enderton] p. 71 | Definition | df-tr 5218 dftr4 5223 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6442 unisucg 6441 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5233 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5235 trintALT 45617 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8588 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8590 onasuc 8511 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7415 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8589 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8591 onmsuc 8512 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8606 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8593 nnacom 8601 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8607 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8608 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8610 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8594 nnmsucr 8609 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8622 |
| [Enderton] p. 129 | Definition | df-en 8942 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7366 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10006 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16275 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9189 |
| [Enderton] p. 135 | Corollary 6C | php3 9191 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9188 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9220 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9222 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9151 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9155 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9127 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10170 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10171 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10166 dju1en 10162 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9298 unifi 9299 unifi2 9300 |
| [Enderton] p. 144 | Corollary 6K | undif2 4437 unfi 9153 unfi2 9268 |
| [Enderton] p. 145 | Figure 38 | ffoss 7941 |
| [Enderton] p. 145 | Definition | df-dom 8943 |
| [Enderton] p. 146 | Example 1 | domen 8956 domeng 8957 |
| [Enderton] p. 146 | Example 3 | nndomo 9200 nnsdom 9621 nnsdomg 9257 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10174 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9128 xpdom1 9062 xpdom1g 9060 xpdom2g 9059 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9134 |
| [Enderton] p. 151 | Theorem 6M | zorn 10497 zorng 10494 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10482 dfac5 10119 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10566 |
| [Enderton] p. 164 | Example | infdif 10198 |
| [Enderton] p. 168 | Definition | df-po 5568 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6476 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6408 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6475 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6416 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7833 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7778 |
| [Enderton] p. 194 | Remark | onprc 7775 |
| [Enderton] p. 194 | Exercise 16 | suc11 6470 |
| [Enderton] p. 197 | Definition | df-card 9932 |
| [Enderton] p. 197 | Theorem 7P | carden 10541 |
| [Enderton] p. 200 | Exercise 25 | tfis 7849 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9746 |
| [Enderton] p. 202 | Definition | df-r1 9734 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9756 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9837 rankval4b 35502 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9573 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9827 rankprb 9821 rankpw 9813 rankpwi 9793 rankuniss 9836 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9585 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9586 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10101 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10067 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10081 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8326 |
| [Enderton] p. 222 | Definition | df-kard 35571 |
| [Enderton] p. 222 | Definition of kard | karden 9886 kardex 9884 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8581 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8583 |
| [Enderton] p. 240 | Exercise 25 | oarec 8545 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10239 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17704 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17646 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18615 mrieqv2d 17701 mrieqvd 17700 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17705 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17710 mreexexlem2d 17707 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18621 mreexfidimd 17712 |
| [Frege1879] p. 11 | Statement | df3or2 44522 |
| [Frege1879] p. 12 | Statement | df3an2 44523 dfxor4 44520 dfxor5 44521 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44544 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44545 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44549 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44553 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44554 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44560 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44562 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44563 axfrege8 44561 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38119 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44566 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44574 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44568 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44567 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44576 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44577 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44580 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44570 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44575 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44572 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44578 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44582 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44581 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44573 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44579 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44569 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44571 rp-frege25 44559 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44564 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44584 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44565 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44585 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44588 axfrege31 44587 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44586 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44589 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44590 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44591 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44592 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44593 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44594 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44595 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44596 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44597 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44599 axfrege41 44598 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44600 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44601 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44602 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44603 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44604 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44605 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44606 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44607 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44608 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44611 ax-frege52c 44642 frege52aid 44612 frege52b 44643 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44616 ax-frege54c 44646 frege54b 44647 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44609 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3745 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44614 frege53aid 44613 frege53b 44644 frege53c 44668 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2762 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44622 frege55aid 44619 frege55b 44651 frege55c 44672 frege55cor1a 44623 frege55lem2a 44621 frege55lem2b 44650 frege55lem2c 44671 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44625 frege56aid 44624 frege56b 44652 frege56c 44673 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44629 ax-frege58b 44655 frege58bid 44656 frege58c 44675 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44627 frege57aid 44626 frege57b 44653 frege57c 44674 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3756 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44631 frege59b 44658 frege59c 44676 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44632 frege60b 44659 frege60c 44677 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44633 frege61b 44660 frege61c 44678 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44634 frege62b 44661 frege62c 44679 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44635 frege63b 44662 frege63c 44680 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44636 frege64b 44663 frege64c 44681 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44637 frege65b 44664 frege65c 44682 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44638 frege66b 44665 frege66c 44683 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44639 frege67b 44666 frege67c 44684 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44640 frege68b 44667 frege68c 44685 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44686 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44687 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44688 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44689 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44690 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44693 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44691 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44692 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44694 frege77d 44500 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44695 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44696 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44697 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44698 frege81d 44501 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44699 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44700 frege83d 44502 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44701 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44702 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44703 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44704 frege87d 44504 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44705 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44706 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44707 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44708 frege91d 44505 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44709 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44710 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44711 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44712 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44716 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44713 frege96d 44503 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44714 frege97d 44506 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44715 frege98d 44507 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44717 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44718 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44719 frege102d 44508 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44720 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44721 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44722 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44723 frege106d 44509 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44724 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44725 frege108d 44510 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44726 frege109d 44511 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44727 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44728 frege111d 44513 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44729 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44730 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44731 frege114d 44512 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44732 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44733 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44734 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44735 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44736 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44737 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44738 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44739 frege122d 44514 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44740 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44741 frege124d 44515 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44742 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44743 frege126d 44516 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44744 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44745 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44746 frege129d 44517 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44747 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44748 frege131d 44518 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44749 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44750 frege133d 44519 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47055 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47378 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47078 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47193 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47213 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47204 meadjunre 47218 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47205 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47206 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47202 meaiunle 47211 meaiunlelem 47210 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47223 meaiuninc2 47224 meaiuninc3 47227 meaiuninc3v 47226 meaiunincf 47225 meaiuninclem 47222 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47229 meaiininc2 47230 meaiininclem 47228 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47248 caragendifcl 47256 caratheodory 47270 omelesplit 47260 |
| [Fremlin1] p. 19 | Definition 113A | isome 47236 isomennd 47273 isomenndlem 47272 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47258 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47277 voncmpl 47363 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47240 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47265 carageniuncllem1 47263 carageniuncllem2 47264 caragenuncl 47255 caragenuncllem 47254 caragenunicl 47266 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47274 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47268 caratheodorylem2 47269 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47277 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47336 hoidmv1lelem1 47333 hoidmv1lelem2 47334 hoidmv1lelem3 47335 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47380 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47336 hoidmvle 47342 hoidmvlelem1 47337 hoidmvlelem2 47338 hoidmvlelem3 47339 hoidmvlelem4 47340 hoidmvlelem5 47341 hsphoidmvle2 47327 hsphoif 47318 hsphoival 47321 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47290 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47298 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47325 hoidmvn0val 47326 hoidmvval 47319 hoidmvval0 47329 hoidmvval0b 47332 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47330 hsphoidmvle 47328 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47279 df-voln 47281 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47346 ovn0 47308 ovn0lem 47307 ovnf 47305 ovnome 47315 ovnssle 47303 ovnsslelem 47302 ovnsupge0 47299 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47345 ovnhoilem1 47343 ovnhoilem2 47344 vonhoi 47409 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47362 hoidifhspf 47360 hoidifhspval 47350 hoidifhspval2 47357 hoidifhspval3 47361 hspmbl 47371 hspmbllem1 47368 hspmbllem2 47369 hspmbllem3 47370 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47363 vonmea 47316 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47314 ovnsubadd2 47388 ovnsubadd2lem 47387 ovnsubaddlem1 47312 ovnsubaddlem2 47313 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47373 hoimbl2 47407 hoimbllem 47372 hspdifhsp 47358 opnvonmbl 47376 opnvonmbllem2 47375 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47378 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47421 iccvonmbllem 47420 ioovonmbl 47419 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47427 vonicclem2 47426 vonioo 47424 vonioolem2 47423 vonn0icc 47430 vonn0icc2 47434 vonn0ioo 47429 vonn0ioo2 47432 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47431 snvonmbl 47428 vonct 47435 vonsn 47433 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47101 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47100 subsaliuncllem 47099 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47467 salpreimalegt 47451 salpreimaltle 47468 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47470 issmff 47476 issmflem 47469 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47487 issmflelem 47486 smfpreimale 47496 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47498 issmfgtlem 47497 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47438 issmf 47470 issmff 47476 issmfge 47512 issmfgelem 47511 issmfgt 47498 issmfgtlem 47497 issmfle 47487 issmflelem 47486 issmflem 47469 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47449 salpreimagtlt 47472 salpreimalelt 47471 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47512 issmfgelem 47511 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47495 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47493 cnfsmf 47482 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47509 decsmflem 47508 incsmf 47484 incsmflem 47483 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47443 pimconstlt1 47444 smfconst 47491 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47507 smfaddlem1 47505 smfaddlem2 47506 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47538 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47537 smfmullem1 47533 smfmullem2 47534 smfmullem3 47535 smfmullem4 47536 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47539 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47542 smfpimbor1lem2 47541 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47544 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47532 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47531 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47540 smfresal 47530 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47519 smflim2 47548 smflimlem1 47513 smflimlem2 47514 smflimlem3 47515 smflimlem4 47516 smflimlem5 47517 smflimlem6 47518 smflimmpt 47552 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47556 smfsuplem1 47553 smfsuplem2 47554 smfsuplem3 47555 smfsupmpt 47557 smfsupxr 47558 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47560 smfinflem 47559 smfinfmpt 47561 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47519 smflim2 47548 smflimmpt 47552 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47550 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47580 smfdivdmmbl2 47583 smfinfdmmbl 47591 smfinfdmmbllem 47590 smfsupdmmbl 47587 smfsupdmmbllem 47586 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47570 smflimsuplem2 47563 smflimsuplem6 47567 smflimsuplem7 47568 smflimsuplem8 47569 smflimsupmpt 47571 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47573 smfliminflem 47572 smfliminfmpt 47574 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47438 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47584 fsupdm2 47585 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47575 adddmmbl2 47576 finfdm 47588 finfdm2 47589 fsupdm 47584 fsupdm2 47585 muldmmbl 47577 muldmmbl2 47578 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47588 finfdm2 47589 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25706 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25749 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25759 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38377 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38380 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9605 inf1 9589 inf2 9590 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10902 enqer 10912 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10907 df-nq 10903 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10899 df-plq 10905 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7649 df-mpq 10900 df-mq 10906 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10908 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10966 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10967 ltbtwnnq 10969 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10962 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10963 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10970 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10972 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10984 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10986 |
| [Gleason] p. 122 | Definition | df-1p 10973 |
| [Gleason] p. 122 | Remark (1) | prub 10985 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11024 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10976 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11023 psslinpr 11022 supexpr 11045 suplem1pr 11043 suplem2pr 11044 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11009 addclprlem1 11007 addclprlem2 11008 df-plp 10974 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11013 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11012 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11025 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11034 ltexprlem1 11027 ltexprlem2 11028 ltexprlem3 11029 ltexprlem4 11030 ltexprlem5 11031 ltexprlem6 11032 ltexprlem7 11033 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11036 ltaprlem 11035 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11037 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11038 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10975 mulclpr 11011 mulclprlem 11010 reclem2pr 11039 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11020 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11015 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11014 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11019 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11042 reclem3pr 11040 reclem4pr 11041 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11046 enrer 11054 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11051 df-1r 11052 df-nr 11047 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11049 df-plr 11048 negexsr 11093 recexsr 11098 recexsrlem 11094 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11050 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12219 creur 12218 cru 12216 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11179 axcnre 11155 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15173 crimd 15290 crimi 15251 crre 15172 crred 15289 crrei 15250 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15175 remimd 15256 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15342 absval2d 15506 absval2i 15456 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15199 cjaddd 15278 cjaddi 15246 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15200 cjmuld 15279 cjmuli 15247 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15198 cjcjd 15257 cjcji 15229 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15197 cjreb 15181 cjrebd 15260 cjrebi 15232 cjred 15284 rere 15180 rereb 15178 rerebd 15259 rerebi 15231 rered 15282 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15206 addcjd 15270 addcji 15241 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15296 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15337 abscjd 15511 abscji 15460 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15347 abs00d 15507 abs00i 15457 absne0d 15508 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15380 releabsd 15512 releabsi 15461 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15352 absmuld 15515 absmuli 15463 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15340 sqabsaddi 15464 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15389 abstrid 15517 abstrii 15467 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14105 exp0 14108 expp1 14111 expp1d 14190 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26855 cxpaddd 26893 expadd 14147 expaddd 14191 expaddz 14149 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26864 cxpmuld 26913 expmul 14150 expmuld 14192 expmulz 14151 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26861 mulcxpd 26904 mulexp 14144 mulexpd 14204 mulexpz 14145 |
| [Gleason] p. 140 | Exercise 1 | znnen 16274 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13543 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15690 rlimadd 15701 rlimdiv 15704 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15692 rlimsub 15702 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15691 rlimmul 15703 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15695 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15641 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15662 climcj 15663 climim 15665 climre 15664 rlimabs 15667 rlimcj 15668 rlimim 15670 rlimre 15669 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11254 df-xr 11253 ltxr 13146 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15529 limsupval 15532 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15728 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15737 caucvgb 15738 caucvgbf 46231 caucvgr 15734 climcau 15729 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15875 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15944 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15394 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13868 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21527 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24511 xmet0 24510 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24527 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24518 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24520 mstri 24637 xmettri 24519 xmstri 24636 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24550 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23816 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25480 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24708 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25034 addcn2 15652 mulcn 25036 mulcn2 15654 subcn 25035 subcn2 15653 |
| [Gleason] p. 295 | Remark | bcval3 14349 bcval4 14350 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14364 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14347 df-bc 14346 |
| [Gleason] p. 296 | Remark | bcn0 14353 bcnn 14355 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15891 |
| [Gleason] p. 308 | Equation 2 | ef0 16151 |
| [Gleason] p. 308 | Equation 3 | efcj 16152 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16158 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16163 |
| [Gleason] p. 310 | Equation 14 | sinadd 16226 |
| [Gleason] p. 310 | Equation 15 | cosadd 16227 |
| [Gleason] p. 311 | Equation 17 | sincossq 16238 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16243 sinbnd 16242 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14259 sqeqori 14257 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16132 |
| [Godowski] p. 730 | Equation SF | goeqi 32636 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32031 |
| [Golan] p. 1 | Remark | srgisid 20297 |
| [Golan] p. 1 | Definition | df-srg 20275 |
| [Golan] p. 149 | Definition | df-slmd 33530 |
| [Gonshor] p. 7 | Definition | df-cuts 27964 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28003 lesrecd 28004 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28124 cofcut1d 28125 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28126 cofcut2d 28127 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28128 cofcutr1d 28129 cofcutr2d 28130 |
| [Gonshor] p. 13 | Definition | df-adds 28164 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28180 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28206 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28334 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28354 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28662 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28664 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28663 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28699 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28222 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36659 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17644 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17646 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 48981 df-cllaw 48979 df-comlaw 48980 |
| [Hall] p. 2 | Section 1.2 | df-clintop 48993 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49014 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39545 dfmembpart2 39550 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32428 riesz2 32429 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32304 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32536 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32548 elpjidm 32547 pjnmopi 32511 |
| [Halmos] p. 44 | Remark | pjinormi 32050 pjinormii 32039 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32552 pjrn 32070 pjrni 32065 pjvec 32059 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32090 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32517 hmopidmpji 32515 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32554 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32543 pjocvec 32060 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32532 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32535 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32538 pjssdif2i 32537 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32218 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 24 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1824 |
| [Hatcher] p. 25 | Definition | df-phtpc 25162 df-phtpy 25141 |
| [Hatcher] p. 26 | Definition | df-pco 25175 df-pi1 25178 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25165 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25220 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22658 df-dmatalt 49206 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48610 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48595 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48607 bgoldbtbnd 48602 bgoldbtbnd 48602 tgblthelfgott 48608 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35038 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35039 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35053 hgt750lemb 35052 hgt750leme 35054 hgt750lemf 35049 hgt750lemg 35050 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48604 tgoldbachgt 35059 tgoldbachgtALTV 48605 tgoldbachgtd 35058 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35040 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 30856 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19017 grpoideu 30872 mndideu 18809 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19047 grpoinveu 30882 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19078 grpo2inv 30894 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19090 grpoinvop 30896 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19112 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1797 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1798 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1800 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 32783 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 32796 cdj3i 32804 cdj3lem1 32797 cdjreui 32795 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 32794 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 42763 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42693 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42715 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42716 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42713 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42719 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42638 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42733 |
| [Holland95] p. 204 | Definition of involution | df-srng 20954 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40305 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42330 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42283 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40735 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42179 poml4N 40755 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42270 pexmidALTN 40780 pexmidN 40771 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42335 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 39926 ldualset 39927 |
| [Holland95] p. 222 | Item 1 | df-lines 40303 df-pointsN 40304 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40705 |
| [Holland95] p. 223 | Remark | ispsubcl2N 40749 omllaw4 40048 pol1N 40712 polcon3N 40719 |
| [Holland95] p. 223 | Definition | df-psubclN 40737 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40708 |
| [Holmes] p. 40 | Definition | df-xrn 39057 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31447 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32545 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32326 eigre 32198 eigrei 32197 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32327 eigorth 32201 eigorthi 32200 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32199 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30671 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30667 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30668 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30669 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30687 frgrregorufr0 30686 frgrregorufrg 30688 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30694 frrusgrord 30703 frrusgrord0 30702 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30450 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30677 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30680 frgrwopreg2 30681 frgrwopregasn 30678 frgrwopregbsn 30679 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30683 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30697 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30700 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30448 numclwlk1 30733 numclwlk1lem1 30731 numclwlk1lem2 30732 numclwwlk1 30723 numclwwlk8 30754 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30674 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30131 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30709 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30735 numclwwlkovh0 30734 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30743 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30340 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30747 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30750 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30753 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 30765 natded 30765 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 30765 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 30765 natded 30765 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 30765 |
| [Jech] p. 4 | Definition of class | cv 1568 cvjust 2756 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10570 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10568 alephmul 10569 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10567 infmap2 10207 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9784 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9856 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9837 rankval4b 35502 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9881 |
| [Jech] p. 78 | Note | opthprc 5724 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43670 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 43758 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 43759 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43682 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43686 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43687 rmyp1 43688 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43689 rmym1 43690 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43680 rmx1 43681 rmxluc 43691 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43684 rmy1 43685 rmyluc 43692 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43694 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43695 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43715 jm2.17b 43716 jm2.17c 43717 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 43748 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 43752 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43743 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43718 jm2.24nn 43714 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 43757 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 43763 rmygeid 43719 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 43775 |
| [Juillerat] p. 11 | Section *5 | etransc 47025 etransclem47 47023 etransclem48 47024 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47020 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47022 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47008 |
| [Juillerat] p. 13 | Proof | etransclem35 47011 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47014 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47000 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47017 |
| [Juillerat] p. 14 | Proof | etransclem23 46999 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1996 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2041 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2046 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2036 cbvaliw 2035 wl-cbvmotv 38196 wl-motae 38198 wl-moteq 38197 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2015 spimw 1999 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2062 spw 2063 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 31879 chabs1i 31881 chabs2 31880 chabs2i 31882 chjass 31896 chjassi 31849 latabs1 18537 latabs2 18538 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32701 ela 32702 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32646 cvrval2 40076 |
| [Kalmbach] p. 16 | Definition | df-ol 39980 df-oml 39981 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 31947 cmbri 31953 cmtvalN 40013 df-cm 31946 df-cmtN 39979 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40049 pjoml5 31976 pjoml5i 31951 |
| [Kalmbach] p. 22 | Definition | pjoml2 31974 pjoml2i 31948 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 31977 cmcmi 31955 cmcmii 31960 cmtcomN 40051 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40047 omlsi 31767 pjoml 31799 pjomli 31798 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40046 |
| [Kalmbach] p. 23 | Remark | cmbr2i 31959 cmcm3 31978 cmcm3i 31957 cmcm3ii 31962 cmcm4i 31958 cmt3N 40053 cmt4N 40054 cmtbr2N 40055 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 31971 cmbr3i 31963 cmtbr3N 40056 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 31981 fh1i 31984 fh2 31982 fh2i 31985 omlfh1N 40060 |
| [Kalmbach] p. 65 | Remark | chjatom 32720 chslej 31861 chsleji 31821 shslej 31743 shsleji 31733 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 31858 chocini 31817 chsupcl 31703 chsupval2 31773 h0elch 31618 helch 31606 hsupval2 31772 ocin 31659 ococss 31656 shococss 31657 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31675 |
| [Kalmbach] p. 66 | Remark | df-pjh 31758 pjssmi 32528 pjssmii 32044 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32008 osumi 32005 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32563 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 32763 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32673 |
| [Kalmbach] p. 140 | Remark | hatomic 32723 hatomici 32722 hatomistici 32725 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40121 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32744 lsatexch 39845 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32718 cvlcvr1 40141 cvr1 40212 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32737 cvexchi 32732 cvrexch 40222 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32727 hlrelat 40204 hlrelat5N 40203 lrelat 39816 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21276 lsmsatcv 39812 spansncv 32016 spansncvi 32015 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 39831 spansncv2 32656 |
| [Kalmbach] p. 266 | Definition | df-st 32574 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32212 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10637 fpwwe2 10634 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10638 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10645 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10640 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10642 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10655 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10659 gchxpidm 10660 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10671 gchhar 10670 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10205 unxpwdom 9549 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10661 |
| [Kreyszig] p. 3 | Property M1 | metcl 24500 xmetcl 24499 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24507 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24740 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11938 muleqadd 11864 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24606 |
| [Kreyszig] p. 19 | Remark | mopntopon 24607 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24666 mopnm 24612 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24664 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24669 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24710 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23426 lmmbr 25428 lmmbr2 25429 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23548 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25483 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25446 iscmet2 25464 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25486 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23629 metelcls 25475 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25476 metcld2 25477 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25269 lmodvneg1 21037 nvinv 31002 vcm 30939 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25265 lmod0vs 21027 slmd0vs 33553 vc0 30937 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21028 slmdvs0 33554 vcz 30938 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31054 ngpmet 24771 nrmmetd 24742 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31049 imsdval2 31050 ncvspds 25331 ngpds 24772 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24757 nvnd 31051 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24786 nmge0 24785 nvge0 31036 nvz 31032 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24792 nvabs 31035 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31164 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31108 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31170 blocni 31168 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31169 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25374 ipeq0 21799 ipz 31082 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25386 pythi 31213 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31217 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25408 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15917 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25606 minveco 31247 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31113 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25499 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31236 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32486 leopg 32485 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32504 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31281 |
| [Kulpa] p. 547 | Theorem | poimir 38332 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38331 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38330 |
| [Kulpa] p. 548 | Theorem | broucube 38333 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38325 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38326 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2414 axnul 5267 |
| [Kunen] p. 11 | Axiom 3 | axnul 5267 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5249 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8833 mapvalg 8831 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10512 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7935 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9734 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9776 r1elssi 9775 |
| [Kunen] p. 107 | Exercise 4 | rankop 9828 rankopb 9822 rankuni 9833 rankxplim 9849 rankxpsuc 9852 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45691 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45699 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45698 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45700 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45705 rexabso 45706 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45712 n0abso 45713 ssabso 45711 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45714 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45724 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45719 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45722 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45723 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45718 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45730 wfaxpr 45735 wfaxreg 45737 wfaxrep 45731 wfaxsep 45732 wfaxun 45736 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45721 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45734 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45730 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45729 omelaxinf2 45726 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45739 wfaxinf2 45738 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 45752 permaxext 45742 permaxinf2 45750 permaxnul 45745 permaxpow 45746 permaxpr 45747 permaxrep 45743 permaxsep 45744 permaxun 45748 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45740 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 45751 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4968 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34064 |
| [Lang] p. | Definition | df-rn 5671 |
| [Lang] p. 3 | Statement | lidrideqd 18733 mndbn0 18814 |
| [Lang] p. 3 | Definition | df-mnd 18799 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18751 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18906 |
| [Lang] p. 5 | Equation | gsumreidx 19993 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 48975 |
| [Lang] p. 6 | Example | nn0mnd 48972 |
| [Lang] p. 6 | Equation | gsumxp2 20056 |
| [Lang] p. 6 | Statement | cycsubm 19279 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19152 |
| [Lang] p. 6 | Observation | mndlsmidm 19746 |
| [Lang] p. 7 | Definition | dfgrp2e 19036 |
| [Lang] p. 30 | Definition | df-tocyc 33436 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33481 |
| [Lang] p. 32 | Property (b) | cyc3conja 33486 cycpmconjv 33471 |
| [Lang] p. 53 | Definition | df-cat 17730 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18160 cat1lem 18159 |
| [Lang] p. 54 | Definition | df-iso 17812 |
| [Lang] p. 57 | Definition | df-inito 18047 df-termo 18048 |
| [Lang] p. 58 | Example | irinitoringc 21640 |
| [Lang] p. 58 | Statement | initoeu1 18074 termoeu1 18081 |
| [Lang] p. 62 | Definition | df-func 17921 |
| [Lang] p. 65 | Definition | df-nat 18009 |
| [Lang] p. 91 | Note | df-ringc 20756 |
| [Lang] p. 92 | Statement | mxidlprm 33762 |
| [Lang] p. 92 | Definition | isprmidlc 21483 |
| [Lang] p. 128 | Remark | dsmmlmod 21906 |
| [Lang] p. 129 | Proof | lincscm 49238 lincscmcl 49240 lincsum 49237 lincsumcl 49239 |
| [Lang] p. 129 | Statement | lincolss 49242 |
| [Lang] p. 129 | Observation | dsmmfi 21899 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34026 qusdimsum 34027 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34007 |
| [Lang] p. 147 | Definition | snlindsntor 49279 |
| [Lang] p. 504 | Statement | mat1 22615 matring 22611 |
| [Lang] p. 504 | Definition | df-mamu 22559 |
| [Lang] p. 505 | Statement | mamuass 22570 mamutpos 22626 matassa 22612 mattposvs 22623 tposmap 22625 |
| [Lang] p. 513 | Definition | mdet1 22769 mdetf 22763 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22859 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22755 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22779 |
| [Lang] p. 515 | Definition | df-minmar1 22803 smadiadetr 22843 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22778 mdetralt 22776 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22791 |
| [Lang] p. 518 | Definition | df-madu 22802 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22813 madurid 22812 matinv 22845 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23058 |
| [Lang], p. 190 | Chapter 6 | vieta 33979 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34093 finextalg 34097 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34062 fedgmul 34030 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34124 |
| [Lang], p. 561 | Remark | chpmatply1 23000 |
| [Lang], p. 561 | Definition | df-chpmat 22995 |
| [Lang2] p. 3 | Notations | df-ind 12225 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45072 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45067 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45073 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5267 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2741 wl-df.clab 38181 |
| [Levy] p. 59 | Definition | df-ttrcl 9675 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9721 |
| [Levy] p. 338 | Axiom | df-clel 2837 df-cleq 2754 wl-df.cleq 38182 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38185 |
| [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 38185 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2837 df-cleq 2754 wl-df.cleq 38182 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2741 wl-df.clab 38181 |
| [Levy] p. 358 | Axiom | df-clab 2741 wl-df.clab 38181 |
| [Levy58] p. 2 | Definition I | isfin1-3 10376 |
| [Levy58] p. 2 | Definition II | df-fin2 10276 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10275 |
| [Levy58] p. 2 | Definition III | df-fin3 10278 |
| [Levy58] p. 3 | Definition V | df-fin5 10279 |
| [Levy58] p. 3 | Definition IV | df-fin4 10277 |
| [Levy58] p. 4 | Definition VI | df-fin6 10280 |
| [Levy58] p. 4 | Definition VII | df-fin7 10281 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10405 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27861 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27872 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27904 nosupbnd1 27889 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27906 nosupbnd2 27891 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27910 noetasuplem4 27911 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27907 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1797 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1798 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1800 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 32771 |
| [Maeda] p. 168 | Lemma 5 | mdsym 32775 mdsymi 32774 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 32769 mdsymlem6 32771 mdsymlem7 32772 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 32773 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32676 ssdmd2 32677 ssmd1 32674 ssmd2 32675 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32672 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32644 df-md 32643 mdbr 32657 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32694 mdslj1i 32682 mdslj2i 32683 mdslle1i 32680 mdslle2i 32681 mdslmd1i 32692 mdslmd2i 32693 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32684 mdsl2bi 32686 mdsl2i 32685 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32698 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32695 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32696 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32673 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32678 mdsl3 32679 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32697 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 32792 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40123 hlrelat1 40202 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 39841 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32699 cvmdi 32687 cvnbtwn4 32652 cvrnbtwn4 40081 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32700 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40142 cvp 32738 cvrp 40218 lcvp 39842 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 32762 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 32761 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40135 hlexch4N 40194 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 32764 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40245 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40551 atpsubN 40555 df-pointsN 40304 pointpsubN 40553 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40306 pmap11 40564 pmaple 40563 pmapsub 40570 pmapval 40559 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40567 pmap1N 40569 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40572 pmapglb2N 40573 pmapglb2xN 40574 pmapglbx 40571 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40654 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40279 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40598 paddclN 40644 paddidm 40643 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40280 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40640 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40279 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40280 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19751 lsmmod2 19752 lssats 39814 shatomici 32721 shatomistici 32724 shmodi 31753 shmodsi 31752 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32663 mdsymlem7 32772 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 31952 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 31856 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 32778 |
| [Margaris] p. 40 | Rule C | exlimiv 1959 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | ax-3 8 |
| [Margaris] p. 49 | Definition | df-an 401 df-ex 1809 df-or 861 dfbi2 479 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 30762 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45651 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45652 |
| [Margaris] p. 79 | Rule C | exinst01 45362 exinst11 45363 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2005 19.2g 2223 r19.2z 4459 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2237 rr19.3v 3625 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2193 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1855 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1810 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2216 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2240 19.9h 2320 exlimd 2253 exlimdh 2324 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2196 excomim 2197 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2359 |
| [Margaris] p. 90 | Section 19 | conventions-labels 30763 conventions-labels 30763 conventions-labels 30763 conventions-labels 30763 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1856 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45116 albi 1847 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2260 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2261 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45118 exbi 1876 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2264 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45115 2alimdv 1947 alimd 2247 alimdh 1846 alimdv 1945 ax-4 1838 ralimdaa 3265 ralimdv 3178 ralimdva 3176 ralimdvva 3211 sbcimdv 3811 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2242 19.21h 2321 19.21t 2241 19.21vv 45114 alrimd 2250 alrimdd 2249 alrimdh 1892 alrimdv 1958 alrimi 2248 alrimih 1853 alrimiv 1956 alrimivv 1957 bj-alrimdh 37245 hbralrimi 3154 r19.21be 3257 r19.21bi 3256 ralrimd 3269 ralrimdv 3162 ralrimdva 3164 ralrimdvv 3208 ralrimdvva 3219 ralrimi 3262 ralrimia 3263 ralrimiv 3155 ralrimiva 3156 ralrimivv 3205 ralrimivva 3207 ralrimivvva 3210 ralrimivw 3160 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45117 2eximdv 1948 bj-exim 37260 exim 1863 eximd 2251 eximdh 1893 eximdv 1946 rexim 3105 reximd2a 3274 reximdai 3266 reximdd 45894 reximddv 3180 reximddv2 3223 reximddv3 3181 reximdv 3179 reximdv2 3174 reximdva 3177 reximdvai 3175 reximdvva 3212 reximi2 3097 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2246 19.23bi 2226 19.23h 2322 19.23t 2245 exlimdv 1962 exlimdvv 1963 exlimexi 45261 exlimiv 1959 exlimivv 1961 rexlimd3 45890 rexlimdv 3163 rexlimdv3a 3169 rexlimdva 3165 rexlimdva2 3167 rexlimdvaa 3166 rexlimdvv 3220 rexlimdvva 3221 rexlimdvvva 3222 rexlimdvw 3170 rexlimiv 3158 rexlimiva 3157 rexlimivv 3206 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2020 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1909 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1899 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2262 r19.27z 4470 r19.27zv 4471 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2263 19.28vv 45124 r19.28z 4462 r19.28zf 45905 r19.28zv 4466 rr19.28v 3626 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1902 r19.29d2r 3151 r19.29imd 3129 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1910 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2269 19.31vv 45122 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2268 r19.32 47863 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45120 19.33 1913 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2021 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1906 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2265 19.36vv 45121 r19.36zv 4472 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2267 19.37vv 45123 r19.37zv 4467 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1868 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2019 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1916 19.40 1915 r19.40 3130 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2270 19.41rg 45287 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2271 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1911 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2272 r19.44zv 4469 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2273 r19.45zv 4468 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2637 |
| [Mayet] p. 370 | Remark | jpi 32633 largei 32630 stri 32620 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32575 ishst 32577 |
| [Mayet3] p. 10 | Theorem | hstrbi 32629 hstri 32628 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32091 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32092 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32641 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31695 chsupcl 31703 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32723 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32717 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32744 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 40785 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18549 latj32 18547 latjass 18545 |
| [Megill] p. 444 | Axiom C5 | ax-5 1939 ax5ALT 39709 |
| [Megill] p. 444 | Section 7 | conventions 30762 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39703 ax-c11n 39690 axc11n 2457 |
| [Megill] p. 446 | Lemma L17 | equtrr 2051 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39698 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39730 hbnae 2463 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2512 sbid 2290 sbidd-misc 50525 sbidd 50524 |
| [Megill] p. 448 | Remark 9.6 | axc14 2494 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39686 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39685 sp 2218 |
| [Megill] p. 448 | Scheme C6' | ax-11 2191 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39687 |
| [Megill] p. 448 | Scheme C8' | ax-7 2037 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39692 |
| [Megill] p. 448 | Scheme C10' | ax-6 1996 ax-c10 39688 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39689 |
| [Megill] p. 448 | Scheme C12' | ax-8 2144 |
| [Megill] p. 448 | Scheme C13' | ax-9 2152 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39693 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39691 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39694 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39706 dral1 2470 dral2-o 39732 dral2 2469 drex1 2472 drex2 2473 drsb1 2526 drsb2 2301 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2206 sbequ 2116 sbid2v 2540 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39699 hba1 2327 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47657 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3831 rspsbca 3832 stdpc4 2101 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39686 ra4 3838 stdpc5 2243 |
| [Mendelson] p. 81 | Rule C | exlimiv 1959 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2057 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2285 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3742 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5496 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4354 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4355 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4229 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4286 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4230 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4094 |
| [Mendelson] p. 231 | Definition of union | dfun3 4228 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5431 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4868 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5551 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4579 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5552 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4895 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5812 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6270 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7772 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6366 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8579 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9126 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9047 xpsneng 9048 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9054 xpcomeng 9055 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9057 |
| [Mendelson] p. 255 | Definition | brsdom 8969 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9050 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8826 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9032 mapsnend 9031 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9132 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9131 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8878 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9035 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9051 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10169 djucomen 10168 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10173 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10167 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8514 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8541 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10549 |
| [Mendelson] p. 281 | Definition | df-r1 9734 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9783 |
| [Mendelson] p. 287 | Axiom system MK | ru 3742 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30621 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30656 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30658 vdgn1frgrv3 30659 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30660 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30653 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30646 2pthfrgrrn 30644 2pthfrgrrn2 30645 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31615 |
| [Monk1] p. 22 | Remark | conventions 30762 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 30762 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4190 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5768 ssrelf 32971 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5769 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5173 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6263 coi2 6264 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5909 rn0 5915 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5870 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5678 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5918 rnxp 6167 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5759 xp0 5760 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6078 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6075 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7909 imaexg 7908 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6072 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7070 funfvop 7045 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6935 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6946 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6582 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7252 dff13f 7253 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7217 funrnex 7949 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7245 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6227 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4928 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8001 df-1st 7984 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8002 df-2nd 7985 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9824 ranksnb 9797 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9825 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9826 rankunb 9820 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9808 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9734 r1val2 9807 |
| [Monk1] p. 117 | Lemma | zorn2 10496 zorn2g 10493 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9979 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10551 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9974 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1838 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2037 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2212 ax-c15 39691 ax12v2 2214 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39686 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2191 |
| [Monk2] p. 109 | Lemma 15 | equvini 2486 equvinv 2058 eqvinop 5468 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1939 ax5ALT 39709 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2175 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2191 |
| [Monk2] p. 114 | Lemma 21 | sp 2218 |
| [Monk2] p. 114 | Lemma 22 | axc4 2353 hba1-o 39699 hba1 2327 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2187 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2209 nfra2 3364 nfra2w 3300 |
| [Moore] p. 53 | Part I | df-mre 17644 |
| [Munkres] p. 77 | Example 2 | distop 23163 indistop 23170 indistopon 23169 |
| [Munkres] p. 77 | Example 3 | fctop 23172 fctop2 23173 |
| [Munkres] p. 77 | Example 4 | cctop 23174 |
| [Munkres] p. 78 | Definition of basis | df-bases 23114 isbasis3g 23117 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17502 tgval2 23124 |
| [Munkres] p. 79 | Remark | tgcl 23137 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23131 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23155 tgss3 23154 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23156 basgen2 23157 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38023 topdifinfeq 38024 topdifinffin 38022 topdifinfindis 38020 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23328 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23206 topcld 23203 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23207 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23209 |
| [Munkres] p. 94 | Definition of closure | clsval 23205 |
| [Munkres] p. 94 | Definition of interior | ntrval 23204 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23243 elcls 23241 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23251 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23316 neindisj 23285 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23318 |
| [Munkres] p. 97 | Definition of limit point | islp2 23313 lpval 23307 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23483 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23395 iscn 23403 iscn2 23406 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23448 cncnp2 23449 cncnpi 23446 df-cnp 23396 iscnp 23405 iscnp2 23407 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24711 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25481 |
| [Nathanson] p. 123 | Remark | reprgt 35017 reprinfz1 35018 reprlt 35015 |
| [Nathanson] p. 123 | Definition | df-repr 35005 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35037 |
| [Nathanson] p. 123 | Proposition | breprexp 35029 breprexpnat 35030 itgexpif 35002 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32467 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48603 |
| [Pfenning] p. 17 | Definition XM | natded 30765 |
| [Pfenning] p. 17 | Definition NNC | natded 30765 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 30765 |
| [Pfenning] p. 18 | Rule" | natded 30765 |
| [Pfenning] p. 18 | Definition /\I | natded 30765 |
| [Pfenning] p. 18 | Definition ` `E | natded 30765 natded 30765 natded 30765 natded 30765 natded 30765 |
| [Pfenning] p. 18 | Definition ` `I | natded 30765 natded 30765 natded 30765 natded 30765 natded 30765 |
| [Pfenning] p. 18 | Definition ` `EL | natded 30765 |
| [Pfenning] p. 18 | Definition ` `ER | natded 30765 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 30765 |
| [Pfenning] p. 18 | Definition ` `IR | natded 30765 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 30765 |
| [Pfenning] p. 127 | Definition =E | natded 30765 |
| [Pfenning] p. 127 | Definition =I | natded 30765 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25372 df-dip 31064 dip0l 31081 ip0l 21797 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25413 ipval 31066 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31077 ipcj 21795 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25375 dipdir 31205 ipdir 21800 ipdiri 31193 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31073 nmsq 25364 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31188 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31190 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31191 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25381 dipass 31208 ipass 21806 ipassi 31204 |
| [Prugovecki] p. 186 | Definition of bra | braval 32307 df-bra 32213 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32214 kbval 32317 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32745 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40690 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32759 atcvat4i 32760 cvrat3 40244 cvrat4 40245 lsatcvat3 39854 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32645 cvrval 40071 df-cv 32642 df-lcv 39821 lspsncv0 21281 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40702 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40703 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2741 rabid 3436 rabidd 45901 wl-df.clab 38181 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2313 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2754 wl-df.cleq 38182 |
| [Quine] p. 19 | Definition 2.9 | conventions 30762 df-v 3456 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2901 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2898 abid2f 2954 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2310 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2118 sbalex 2277 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2837 wl-df.clel 38185 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2762 eqid1 30829 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2769 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3744 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3745 dfsbcq2 3746 |
| [Quine] p. 43 | Theorem 6.8 | vex 3458 |
| [Quine] p. 43 | Theorem 6.9 | isset 3468 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3549 spcgv 3554 spcimgf 3517 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3756 spsbcd 3757 |
| [Quine] p. 44 | Theorem 6.12 | elex 3475 |
| [Quine] p. 44 | Theorem 6.13 | elab 3637 elabg 3634 elabgf 3632 |
| [Quine] p. 44 | Theorem 6.14 | noel 4290 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4682 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4591 df-sn 4589 |
| [Quine] p. 49 | Theorem 7.4 | snss 4749 snssg 4748 |
| [Quine] p. 49 | Theorem 7.5 | prss 4785 prssg 4784 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4727 prid1g 4725 prid2 4728 prid2g 4726 snid 4627 snidg 4625 |
| [Quine] p. 51 | Theorem 7.12 | snex 5409 |
| [Quine] p. 51 | Theorem 7.13 | prex 5408 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4890 unisnALT 45662 unisng 4889 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4894 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4903 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4900 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6506 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 47851 dfiota2 6493 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 47860 iotaval 6510 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6516 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6512 |
| [Quine] p. 58 | Definition 9.1 | df-op 4595 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5508 opabidw 5507 opelopab 5526 opelopaba 5519 opelopabaf 5528 opelopabf 5529 opelopabg 5522 opelopabga 5516 opelopabgf 5524 oprabid 7444 oprabidw 7443 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5666 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5668 |
| [Quine] p. 64 | Definition 9.15 | df-id 5555 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6601 |
| [Quine] p. 65 | Theorem 10.4 | funi 6568 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6589 funsng 6587 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6538 |
| [Quine] p. 65 | Definition 10.2 | args 6093 dffv4 6878 |
| [Quine] p. 68 | Definition 10.11 | conventions 30762 df-fv 6544 fv2 6876 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14315 nn0opth2i 14314 nn0opthi 14313 omopthi 8645 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8395 |
| [Quine] p. 232 | Equation i | carddom 10544 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6623 funimaexg 6622 |
| [Quine] p. 331 | Axiom system NF | ru 3742 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31447 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31064 polid 31522 polid2i 31520 polidi 31521 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31176 |
| [ReedSimon] p. 195 | Remark | lnophm 32382 lnophmi 32381 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32495 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32497 leopmuli 32496 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32500 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32215 leoppos 32489 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32499 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32488 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48404 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48412 |
| [Roman] p. 4 | Definition | df-dmat 22658 df-dmatalt 49206 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20237 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20323 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49293 |
| [Roman] p. 112 | Note | isldepslvec2 49293 ldepsnlinc 49316 zlmodzxznm 49305 |
| [Roman] p. 112 | Example | zlmodzxzequa 49304 zlmodzxzequap 49307 zlmodzxzldep 49312 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23058 |
| [Rosenlicht] p. 80 | Theorem | heicant 38334 |
| [Rosser] p. 281 | Definition | df-op 4595 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35041 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35042 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49174 pmtr3ncom 19551 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19547 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19490 cayleyth 19491 |
| [Rudin] p. 164 | Equation 27 | efcan 16156 |
| [Rudin] p. 164 | Equation 30 | efzval 16164 |
| [Rudin] p. 167 | Equation 48 | absefi 16258 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 50642 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1800 |
| [Sanford] p. 39 | Rule 4 | mptxor 1798 |
| [Sanford] p. 40 | Rule 1 | mptnan 1797 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6114 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6117 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6113 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6111 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17644 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17645 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17645 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17647 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10127 |
| [Schechter] p. 141 | Definition (MC) | dfac11 43817 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10436 axdc3 10444 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20325 isrngo 38576 |
| [Schechter] p. 276 | Remark 11.6.e | span0 31905 |
| [Schechter] p. 276 | Definition of span | df-span 31672 spanval 31696 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23161 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6385 onelond 36699 onelord 44006 ordelon 6384 ordelord 6382 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44007 sucidg 6444 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6416 onsuc 7807 ord0 6415 ordsuci 7805 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44008 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5221 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 43783 elon2 6371 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6366 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5563 epelg 5561 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9560 epirron 44009 ordirr 6378 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44011 oneptr 44010 ontr1 6408 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6404 oneptri 44012 ordtri3or 6393 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8484 ord0eln0 6417 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6430 onsucss 44021 trsucss 6451 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7812 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6457 ordnbtwn 6456 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44023 ordnexbtwnsuc 44022 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10391 onsucf1lem 44024 onsucf1o 44027 onsucf1olem 44025 onsucrn 44026 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44028 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7839 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44017 ordne0gt0 44016 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44019 limnsuc 44020 onsucelab 44018 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9610 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7854 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9613 ordom 7870 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9614 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8624 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7777 ssorduni 7776 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8514 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9617 limom 7876 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8451 df1o2 8458 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8499 oa0suclim 44030 oalim 8515 oasuc 8507 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8500 om0suclim 44031 omlim 8516 omsuc 8509 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8505 oe0m1 8504 oe0suclim 44032 oelim 8517 oesuc 8510 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 43984 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44034 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44035 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44036 limexissupab 44038 limiun 44037 limuni 6423 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8521 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8525 om1om1r 44039 om1r 8526 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8518 oaomoecl 44033 oecl 8520 omcl 8519 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 43986 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8527 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8528 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44040 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44041 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8595 nnamecl 44042 nnecl 8597 nnmcl 8596 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44043 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8535 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8536 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8543 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44045 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44046 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44048 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8542 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44052 omword1 8556 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44051 oaordnrex 44050 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44047 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44053 omword2 8557 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44054 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44055 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44056 omordi 8549 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8551 omord2com 44057 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44058 df-2o 8452 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44061 oewordi 8575 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44062 oeworde 8577 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44063 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44064 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44060 omnord1ex 44059 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44065 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44067 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44071 oenord1ex 44070 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44072 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8544 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44066 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8562 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8563 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44074 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8581 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44075 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44076 cantnfub2 44077 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44080 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29275 axtgcgrrflx 28742 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29276 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29277 axtgcgrid 28743 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28728 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29288 axtgsegcon 28744 df-trkgcb 28730 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29299 axtg5seg 28745 df-trkgcb 28730 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29300 axtgbtwnid 28746 df-trkgb 28729 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29302 axtgpasch 28747 df-trkgb 28729 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29321 df-trkg2d 35061 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28750 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28751 df-trkg2d 35061 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29324 axtgeucl 28752 df-trkge 28731 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29337 axtgcont 28749 axtgcont1 28748 df-trkgb 28729 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29215 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36487 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36489 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36492 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36496 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36497 tgcgrcomimp 28757 tgcgrcoml 28759 tgcgrcomr 28758 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36502 tgcgrtriv 28764 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36506 tg5segofs 35072 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35069 df-ofs 36483 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36508 tgcgrextend 28765 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36510 tgsegconeq 28766 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36522 btwntriv2 36512 tgbtwntriv2 28767 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36513 tgbtwncom 28768 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36516 tgbtwntriv1 28771 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36517 tgbtwnswapid 28772 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36523 btwnintr 36519 tgbtwnexch2 28776 tgbtwnintr 28773 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36525 btwnexch3 36520 tgbtwnexch 28778 tgbtwnexch3 28774 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36524 tgbtwnouttr 28777 tgbtwnouttr2 28775 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29320 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36527 tgbtwndiff 28786 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28779 trisegint 36528 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36544 tgifscgr 28788 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 28838 colrot1 28839 colrot2 28840 lncom 28906 lnrot1 28907 lnrot2 28908 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36540 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36545 tgcgrsub 28789 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36555 tgcgrxfr 28798 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28797 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36541 df-cgrg 28791 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28791 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36556 tgbtwnxfr 28810 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36562 colinearperm2 36564 colinearperm3 36563 colinearperm4 36565 colinearperm5 36566 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28813 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36539 tgellng 28833 tglng 28826 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36567 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36575 lnxfr 28846 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36576 lnext 28847 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36580 tgfscgr 28848 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36581 lncgr 28849 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36542 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36583 lnid 28850 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36584 tgidinside 28851 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36601 tgbtwnconn1 28855 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36602 tgbtwnconn2 28856 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36603 tgbtwnconn3 28857 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36609 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36607 legov 28865 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 28866 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 28879 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36610 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36612 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36614 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36615 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36616 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36613 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36618 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 28867 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 28869 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 28870 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 28871 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 28872 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36625 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36626 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36621 df-outsideof 36620 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36622 ishlg 28885 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 28890 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 28892 outsideofrflx 36627 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 28886 hlcomd 28887 outsideofcom 36628 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 28893 outsideoftr 36629 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 28902 hlcgreu 28901 outsideofeu 36631 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36638 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36639 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36632 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36647 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36648 tglineelsb2 28916 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36650 linerflx1 36649 linerflx2 36651 tglinecom 28919 tglinerflx1 28917 tglinerflx2 28918 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36653 tglinethru 28920 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36637 tglng 28826 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 28874 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36656 tglinethrueu 28923 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36657 tglineineq 28927 tglineinsn 28928 tglineinteq 28930 tglineintmo 28926 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 28934 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 28935 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 28936 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 28954 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 28950 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 28942 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 28941 ismir 28947 mirbtwn 28946 mircgr 28945 mirfv 28944 mirval 28943 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 28952 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 28953 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 28954 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 28957 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 28958 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 28963 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 28960 mirbtwni 28959 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 28961 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 28973 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 28977 symquadmid 29119 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 28974 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 28975 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 28976 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 28979 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 28980 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 28989 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 28985 israg 28988 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 28990 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 28991 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 28993 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 28994 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 28995 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 28996 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 28997 ragncol 29000 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 28998 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29004 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29008 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29005 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 28987 isperp 29003 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29006 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29013 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29022 colperpexlem2 29023 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29025 colperpexlem3 29024 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29030 midex 29029 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29027 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29036 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29031 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29040 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29043 opphllem6 29044 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29046 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28747 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29048 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29056 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29051 hpgbr 29053 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29058 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29057 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29059 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29060 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29061 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29062 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29063 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29077 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29079 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29083 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29067 elplng 29073 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29085 lnssplng1 29086 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29090 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29104 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29094 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29108 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29109 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29110 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29111 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29112 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29115 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29117 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29095 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29118 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29122 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29123 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29124 lnperpexs 29125 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29126 trgcopyeu 29128 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29152 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29131 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29140 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29138 cgrahl2 29139 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29141 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29142 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29144 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29145 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29148 cgrahl 29149 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29153 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29154 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29155 acopyeu 29156 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29157 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29158 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29159 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29160 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29162 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29169 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29173 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29166 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29181 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29174 isleag 29175 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29183 tgsas1 29182 tgsas2 29184 tgsas3 29185 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29187 tgasa1 29186 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29188 tgsss2 29189 tgsss3 29190 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29198 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29201 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29202 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29207 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29208 dfprlng3 29209 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29211 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29212 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29215 prlngmo2 29217 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29216 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29219 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29220 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29221 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29222 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29223 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29225 prlngsymquadopp 29226 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29227 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29228 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27446 dchrsum 27444 dchrsum2 27443 sumdchr 27447 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27448 sum2dchr 27449 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20144 ablfacrp2 20145 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27391 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27392 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27399 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27657 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27660 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27714 vmalogdivsum2 27713 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27704 dirith2 27703 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27702 rpvmasum 27701 rpvmasum2 27687 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27662 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27700 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27667 dchrisumlem1 27664 dchrisumlem2 27665 dchrisumlem3 27666 dchrisumlema 27663 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27670 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27699 dchrmusumlem 27697 dchrvmasumlem 27698 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27669 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27671 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27695 dchrisum0re 27688 dchrisumn0 27696 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27681 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27685 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27686 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27741 pntrsumbnd2 27742 pntrsumo1 27740 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27705 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27707 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27709 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27712 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27717 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27718 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27723 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27725 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27726 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27734 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27735 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27732 selberg3lem2 27733 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27736 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27730 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27743 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27744 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27745 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27759 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27771 pntlemb 27772 pntlemc 27770 pntlemd 27769 pntlemg 27773 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27771 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27763 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27768 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27771 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27784 pntleml 27786 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34142 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34129 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34161 constrinvcl 34172 constrmulcl 34170 constrnegcl 34162 constrsqrtcl 34178 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34148 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34158 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34180 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34190 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4258 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4362 dif0 4333 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4451 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4435 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4249 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4250 |
| [Stoll] p. 20 | Remark | invdif 4231 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4597 |
| [Stoll] p. 43 | Definition | uniiun 5022 |
| [Stoll] p. 44 | Definition | intiin 5023 |
| [Stoll] p. 45 | Definition | df-iin 4958 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4957 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 406 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4258 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45073 |
| [Suppes] p. 22 | Theorem 2 | eq0 4303 eq0f 4300 |
| [Suppes] p. 22 | Theorem 4 | eqss 3951 eqssd 3953 eqssi 3952 |
| [Suppes] p. 23 | Theorem 5 | ss0 4358 ss0b 4357 |
| [Suppes] p. 23 | Theorem 6 | sstr 3944 sstrALT2 45571 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4056 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4058 |
| [Suppes] p. 23 | Theorem 9 | psstr 4061 |
| [Suppes] p. 23 | Theorem 10 | pssss 4051 |
| [Suppes] p. 25 | Theorem 12 | elin 3920 elun 4106 |
| [Suppes] p. 26 | Theorem 15 | inidm 4178 |
| [Suppes] p. 26 | Theorem 16 | in0 4351 |
| [Suppes] p. 27 | Theorem 23 | unidm 4110 |
| [Suppes] p. 27 | Theorem 24 | un0 4350 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4130 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4138 |
| [Suppes] p. 27 | Theorem 27 | unss 4142 |
| [Suppes] p. 27 | Theorem 28 | indir 4238 |
| [Suppes] p. 27 | Theorem 29 | undir 4239 |
| [Suppes] p. 28 | Theorem 32 | difid 4331 |
| [Suppes] p. 29 | Theorem 33 | difin 4224 |
| [Suppes] p. 29 | Theorem 34 | indif 4232 |
| [Suppes] p. 29 | Theorem 35 | undif1 4436 |
| [Suppes] p. 29 | Theorem 36 | difun2 4441 |
| [Suppes] p. 29 | Theorem 37 | difin0 4434 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4432 |
| [Suppes] p. 29 | Theorem 39 | difundi 4242 |
| [Suppes] p. 29 | Theorem 40 | difindi 4244 |
| [Suppes] p. 30 | Theorem 41 | nalset 5276 |
| [Suppes] p. 39 | Theorem 61 | uniss 4879 |
| [Suppes] p. 39 | Theorem 65 | uniop 5497 |
| [Suppes] p. 41 | Theorem 70 | intsn 4948 |
| [Suppes] p. 42 | Theorem 71 | intpr 4946 intprg 4945 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5452 |
| [Suppes] p. 42 | Theorem 78 | intun 4944 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4995 dfiun2g 4993 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4996 |
| [Suppes] p. 47 | Theorem 86 | elpw 4565 elpw2 5304 elpw2g 5303 elpwg 4564 elpwgdedVD 45653 |
| [Suppes] p. 47 | Theorem 87 | pwid 4584 |
| [Suppes] p. 47 | Theorem 89 | pw0 4777 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4778 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5675 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5818 xpindir 5819 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5729 xpundir 5730 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9557 |
| [Suppes] p. 58 | Theorem 2 | relss 5767 |
| [Suppes] p. 59 | Theorem 4 | eldm 5889 eldm2 5890 eldm2g 5888 eldmg 5887 |
| [Suppes] p. 59 | Definition 3 | df-dm 5670 |
| [Suppes] p. 60 | Theorem 6 | dmin 5900 |
| [Suppes] p. 60 | Theorem 8 | rnun 6141 |
| [Suppes] p. 60 | Theorem 9 | rnin 6142 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5877 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5867 brcnvg 5864 |
| [Suppes] p. 62 | Equation 5 | elcnv 5861 elcnv2 5862 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6105 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6140 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6138 |
| [Suppes] p. 63 | Definition | dftrrels2 39336 |
| [Suppes] p. 63 | Theorem 20 | co02 6261 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5964 |
| [Suppes] p. 63 | Definition 7 | df-co 5669 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5874 |
| [Suppes] p. 64 | Theorem 27 | coass 6266 |
| [Suppes] p. 65 | Theorem 31 | resundi 5991 |
| [Suppes] p. 65 | Theorem 34 | elima 6066 elima2 6067 elima3 6068 elimag 6065 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6146 |
| [Suppes] p. 66 | Theorem 40 | dminss 6149 |
| [Suppes] p. 66 | Theorem 41 | imainss 6150 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6153 |
| [Suppes] p. 81 | Definition 34 | dfec2 8695 |
| [Suppes] p. 82 | Theorem 72 | elec 8739 elecALTV 38948 elecg 8737 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39372 erth 8747 erth2 8748 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39375 erdisj 8750 |
| [Suppes] p. 83 | Definition 35, | df-parts 39545 dfmembpart2 39550 |
| [Suppes] p. 89 | Theorem 96 | map0b 8879 |
| [Suppes] p. 89 | Theorem 97 | map0 8883 map0g 8880 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8884 mapsnd 8882 |
| [Suppes] p. 89 | Theorem 99 | mapss 8885 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10059 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10058 |
| [Suppes] p. 92 | Theorem 1 | enref 8980 enrefg 8979 |
| [Suppes] p. 92 | Theorem 2 | ensym 8998 ensymb 8997 ensymi 8999 |
| [Suppes] p. 92 | Theorem 3 | entr 9001 |
| [Suppes] p. 92 | Theorem 4 | unen 9040 |
| [Suppes] p. 94 | Theorem 15 | endom 8974 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8995 |
| [Suppes] p. 94 | Theorem 17 | domtr 9002 |
| [Suppes] p. 95 | Theorem 18 | sbth 9083 |
| [Suppes] p. 97 | Theorem 23 | canth2 9116 canth2g 9117 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9087 df-sdom 8944 dfsdom2 9086 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9100 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9089 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9088 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9098 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8977 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9101 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9096 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9026 fundmeng 9027 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9061 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9097 |
| [Suppes] p. 104 | Theorem 37 | fofi 9271 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9276 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9276 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10541 |
| [Suppes] p. 130 | Definition 3 | df-tr 5218 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7777 |
| [Suppes] p. 134 | Definition 6 | df-suc 6366 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7895 finds 7891 finds1 7894 finds2 7893 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9619 isfinite2 9256 isfiniteg 9258 unbnn 9254 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10909 df-ltpq 10901 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7857 tfinds 7854 tfinds2 7858 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8534 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8536 |
| [Suppes] p. 211 | Theorem 25 | oaass 8544 |
| [Suppes] p. 225 | Definition 8 | iscard2 9969 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10553 |
| [Suppes] p. 228 | Theorem 59 | harcard 9971 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10057 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6413 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7790 onminsb 7791 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10563 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10061 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10068 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10062 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9933 |
| [Suppes] p. 242 | Theorem 6 | weth 10485 |
| [Suppes] p. 242 | Theorem 8 | entric 10547 |
| [Suppes] p. 242 | Theorem 9 | carden 10541 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36196 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36200 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2734 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2754 wl-df.cleq 38182 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2837 wl-df.clel 38185 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2756 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2782 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7416 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3742 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5391 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4613 elpr2 4615 elpr2g 4614 elprg 4611 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4603 elsn2 4630 elsn2g 4629 elsng 4602 velsn 4604 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5448 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4598 sneqr 4804 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4609 dfsn2 4601 dfsn2ALT 4610 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7741 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5457 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5444 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5428 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7744 unexg 7743 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4656 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4872 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3911 df-un 3909 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4888 uniprg 4887 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5347 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4654 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6433 elsucg 6431 sstr2 3943 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4111 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4161 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4124 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4179 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4236 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4237 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3924 df-ss 3921 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4563 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4139 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3922 sseqin2 4175 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3958 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4188 inss2 4189 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4000 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4882 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5429 sspwimp 45654 sspwimpALT 45661 sspwimpALT2 45664 sspwimpcf 45656 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5436 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5237 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3416 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5269 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3907 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37191 dfnul2 4288 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4331 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4306 n0f 4302 neq0 4305 neq0f 4301 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9556 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9699 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9714 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3456 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5282 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4356 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5290 ssexg 5289 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5285 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9568 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9560 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4320 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4088 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4252 undif3VD 45618 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4089 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4096 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3079 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3089 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7750 xpexg 7747 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5667 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6607 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6785 fun11 6610 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6549 svrelfun 6608 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5876 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5878 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5672 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5673 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5669 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6191 dfrel2 6186 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5676 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5797 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5804 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5817 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 6003 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5983 opelresi 5985 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6010 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5999 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 6004 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6578 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6109 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6576 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6787 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2636 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 30762 df-fv 6544 fv3 6899 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7920 cnvexg 7919 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7904 dmexg 7896 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7905 rnexg 7897 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45190 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7915 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6894 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 47939 tz6.12-1-afv2 48006 tz6.12-1 6904 tz6.12-afv 47938 tz6.12-afv2 48005 tz6.12 6905 tz6.12c-afv2 48007 tz6.12c 6903 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48002 tz6.12-2 6868 tz6.12i-afv2 48008 tz6.12i 6907 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6539 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6540 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6542 wfo 6534 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6541 wf1 6533 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6543 wf1o 6535 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7025 eqfnfv2 7026 eqfnfv2f 7029 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6979 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7215 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7213 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6623 funimaexg 6622 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5109 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5569 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5621 dffr3 6100 eliniseg 6095 iniseg 6098 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5560 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5637 fr3nr 7769 frirr 5636 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5613 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7771 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5624 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5646 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6348 tz6.26i 6349 wefrc 5654 wereu2 5657 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6350 wfii 6351 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6545 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7327 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7328 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7334 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7335 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7336 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7340 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7347 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7349 |
| [TakeutiZaring] p. 35 | Notation | wtr 5217 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45191 tz7.2 5643 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5222 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6373 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6381 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6382 ordelordALT 45274 ordelordALTVD 45603 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6388 ordelssne 6387 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6386 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6391 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7779 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7780 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6364 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6393 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45286 ordon 7774 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7775 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7847 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6409 ontr2d 36700 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5219 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7789 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7825 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6467 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6466 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7776 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4903 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6366 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6443 sucidg 6444 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7807 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6457 ordnbtwn 6456 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7822 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6365 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7875 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7880 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7835 ordelsuc 7814 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7816 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7845 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7862 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7883 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7884 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7885 |
| [TakeutiZaring] p. 43 | Remark | omon 7872 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9602 omex 9610 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7870 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7890 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7887 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7888 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7865 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4926 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5236 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4927 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5313 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7792 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6412 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4912 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9627 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7787 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8360 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8382 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8383 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8384 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8391 tz7.44-2 8392 tz7.44-3 8393 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8352 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8347 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8331 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8430 tz7.49c 8431 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8428 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8427 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8429 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2682 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10002 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10003 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8515 oasuc 8507 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7855 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8518 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8499 oa0r 8521 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8519 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8531 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8603 nnaordi 8602 oaord 8530 oaordi 8529 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5013 uniss2 4906 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8533 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8538 oawordex 8540 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8595 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8632 |
| [TakeutiZaring] p. 60 | Remark | oancom 9618 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8543 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8600 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8535 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8502 omlim 8516 omsuc 8509 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8500 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8597 nnmcl 8596 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8616 nnmordi 8615 omord 8551 omordi 8549 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8552 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8620 omwordri 8555 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8522 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8525 om1r 8526 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8558 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8560 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8561 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8562 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8563 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8592 oe0 8505 oelim 8517 oesuc 8510 onesuc 8513 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8503 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8570 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8571 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8504 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8528 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8572 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8578 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8576 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8577 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8581 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8583 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9695 tz9.1 9696 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9734 r10 9738 r1lim 9742 r1limg 9741 r1suc 9740 r1sucg 9739 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9750 r1ord2 9751 r1ordg 9748 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9760 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9785 tz9.13 9761 tz9.13g 9762 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9735 rankval 9786 rankvalb 9767 rankvalg 9787 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9809 rankelb 9794 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9823 rankval3 9810 rankval3b 9796 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9799 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9765 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9804 rankr1c 9791 rankr1g 9802 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9805 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9819 rankssb 9818 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9812 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9811 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10465 dfac3 10112 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10021 numth 10462 numth2 10461 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10536 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10537 cardid2 9946 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9953 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10541 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9952 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9937 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9958 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9950 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9136 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9013 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9141 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9065 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9956 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10089 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9188 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9196 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10090 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9193 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10079 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10057 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9965 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10206 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9280 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8945 isfi 8970 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9197 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10524 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9058 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10516 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10176 unxpdom 9217 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9967 cardsdomelir 9966 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9219 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10005 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8824 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10552 infxpidm2 10008 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10197 infxp 10204 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9070 pw2f1o 9068 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9129 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10477 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10472 ac6s5 10481 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10533 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10534 uniimadomf 10535 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10264 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10259 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10243 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10240 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10247 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10254 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10263 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10573 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10241 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10266 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10088 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10087 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10099 alephfp2 10100 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10690 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10103 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10560 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10574 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10575 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39685 |
| [Tarski] p. 67 | Scheme B5 | sp 2218 |
| [Tarski] p. 68 | Lemma 6 | avril1 30825 equid 2041 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2046 |
| [Tarski] p. 70 | Lemma 14 | spim 2418 spime 2420 spimew 2000 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2212 ax-c15 39691 ax12i 1995 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2118 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1997 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1939 ax5ALT 39709 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2037 ax-8 2144 ax-9 2152 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28744 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28745 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28747 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28747 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28748 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16305 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38338 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38340 |
| [Weierstrass] p. 272 | Definition | df-mdet 22753 mdetuni 22790 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 916 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 881 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 932 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 982 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38119 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44554 imim2 59 wl-luk-imim2 38114 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 47784 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 909 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2689 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 915 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38117 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 907 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 910 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45663 wl-luk-notnotr 38118 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44584 axfrege28 44583 con3 154 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 129 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 880 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 937 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38111 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 902 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 953 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 30763 pm2.27 43 wl-luk-pm2.27 38109 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 935 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 39048 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 936 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 984 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 983 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1103 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 919 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 956 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 894 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 895 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 170 pm2.5g 169 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 193 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 896 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 864 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 901 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 903 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 912 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 954 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 904 pm2.67 905 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 911 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 913 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 944 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 986 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1006 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 474 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 476 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 464 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 407 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 814 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 453 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 487 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 489 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 776 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 819 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 633 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 497 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 974 pm3.44 973 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 820 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 478 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 977 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 818 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 845 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 817 bitr 816 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 573 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 917 pm4.25 918 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 465 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1024 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 883 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 473 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 934 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 644 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 930 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 648 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 991 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1104 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1022 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1068 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1039 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1011 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1013 pm4.45 1012 pm4.45im 840 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 866 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 554 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 996 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 999 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 998 pm4.56 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1004 pm4.57 1005 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 409 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 869 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 402 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 862 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 566 pm4.71d 570 pm4.71i 568 pm4.71r 567 pm4.71rd 571 pm4.71ri 569 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 963 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 536 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 949 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 526 pm4.76 527 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 975 pm4.77 976 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 947 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1020 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 397 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1040 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1041 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 350 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 354 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 391 impexp 455 pm4.87 856 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 835 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 958 pm5.11g 957 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 959 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 961 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 960 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1028 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 390 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 836 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1031 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1064 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1065 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 914 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 582 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 392 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 967 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 843 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 848 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 837 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 846 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 393 pm5.41 394 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 551 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1021 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1034 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 962 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1015 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1036 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1044 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 369 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 273 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1045 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37242 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45096 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45097 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1899 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45098 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45099 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45100 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1922 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45101 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45102 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45103 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45104 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45105 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45107 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45108 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45109 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45106 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2123 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45112 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45113 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2103 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2194 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1858 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1859 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45114 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45115 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45116 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45117 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45119 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45118 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1916 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45121 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45122 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45120 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1857 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45123 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45124 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1875 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45125 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2377 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1889 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45130 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45126 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45127 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45128 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45129 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45134 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45131 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45132 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45133 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45135 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2596 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45145 pm13.13b 45146 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45147 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3038 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3039 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3624 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45153 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45154 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45148 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45289 pm13.193 45149 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45150 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45151 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45152 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45159 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45158 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45157 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3805 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45160 pm14.122b 45161 pm14.122c 45162 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45163 pm14.123b 45164 pm14.123c 45165 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45167 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45166 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45168 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6517 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45169 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6518 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45170 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45172 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2660 eupickbi 2663 sbaniota 45173 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45171 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2611 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45174 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 30762 df-fv 6544 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9994 pm54.43lem 9993 |
| [Young] p. 141 | Definition of operator ordering | leop2 32487 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32493 idleop 32494 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43583 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43590 pellexlem1 43584 |