Bibliographic Cross-References
|
|
Metamath Proof Explorer Bibliographic Cross-References |
|
| Mirrors > Home > MPE Home > Bibliographic Cross-References | ||
| Color key: |
Metamath Proof Explorer |
Hilbert Space Explorer |
 User Mathboxes |
| Bibliographic Reference | Description | Metamath Proof Explorer Page(s) |
|---|---|---|
| [Adamek] p. 21 | Definition 3.1 | df-cat 17842 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17842 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 18251 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17863 0funcg 50193 df-termc 50581 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 50658 prsthinc 50572 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 50686 df-mndtc 50686 |
| [Adamek] p. 24 | Example 3.3(4)(c) | discsnterm 50682 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17886 |
| [Adamek] p. 25 | Example 3.6(1) | oduoppcciso 50674 |
| [Adamek] p. 25 | Example 3.6(2) | oppgoppcco 50699 oppgoppchom 50698 oppgoppcid 50700 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17956 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17944 invisoinvl 17965 |
| [Adamek] p. 28 | Example 3.13 | idinv 17964 idiso 17963 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17949 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17923 df-iso 17924 dfiso2 17947 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17930 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17981 cicerALT 50154 |
| [Adamek] p. 29 | Definition 3.15 | cic 17974 df-cic 17971 |
| [Adamek] p. 29 | Definition 3.17 | df-func 18033 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17945 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17946 isoco 17952 |
| [Adamek] p. 30 | Remark 3.19 | df-func 18033 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 18056 |
| [Adamek] p. 30 | Example 3.20(2) | diag1 50412 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 18049 |
| [Adamek] p. 33 | Example 3.26(1) | discsnterm 50682 discthing 50569 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 50526 prsthinc 50572 thincciso 50561 thincciso2 50563 thincciso3 50564 thinccisod 50562 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 50686 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 18063 cofucla 50204 |
| [Adamek] p. 34 | Remark 3.28(1) | cofidfth 50270 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 18286 catcisoi 50508 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18341 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 18082 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 18081 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18341 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 18106 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 18112 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 18111 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18326 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18326 |
| [Adamek] p. 39 | Remark 3.42 | 2oppf 50240 |
| [Adamek] p. 39 | Definition 3.41 | df-oppf 50231 funcoppc 18050 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 18274 elcatchom 50505 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 18100 fthoppf 50272 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 18099 fulloppf 50271 |
| [Adamek] p. 40 | Remark 3.48 | catccat 18283 |
| [Adamek] p. 40 | Definition 3.47 | 0funcg 50193 df-catc 18274 |
| [Adamek] p. 45 | Exercise 3G | incat 50709 |
| [Adamek] p. 48 | Remark 4.2(2) | cnelsubc 50712 nelsubc3 50179 |
| [Adamek] p. 48 | Remark 4.2(3) | imasubc 50259 imasubc2 50260 imasubc3 50264 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 18013 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 18014 |
| [Adamek] p. 48 | Definition 4.1(1) | nelsubc3 50179 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 18025 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17987 |
| [Adamek] p. 49 | Remark 4.4 | idsubc 50268 |
| [Adamek] p. 49 | Remark 4.4(1) | idemb 50267 |
| [Adamek] p. 49 | Remark 4.4(2) | idfullsubc 50269 ressffth 18115 |
| [Adamek] p. 58 | Exercise 4A | setc1onsubc 50710 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 18121 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 18142 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 18146 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 18122 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 18148 |
| [Adamek] p. 101 | Definition 7.1 | 0funcg 50193 df-inito 18159 |
| [Adamek] p. 101 | Example 7.2(3) | 0funcg 50193 df-termc 50581 initc 50199 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 21785 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 18160 oppctermo 50344 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 18187 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 18191 |
| [Adamek] p. 103 | Remark 7.8 | oppczeroo 50345 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 18161 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 21786 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 18194 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17922 |
| [Adamek] p. 107 | Example 7.20(7) | thincinv 50577 |
| [Adamek] p. 108 | Example 7.25(4) | thincsect2 50576 |
| [Adamek] p. 110 | Example 7.33(9) | thincmon 50541 |
| [Adamek] p. 110 | Proposition 7.35 | sectmon 17957 |
| [Adamek] p. 112 | Proposition 7.42 | sectepi 17959 |
| [Adamek] p. 185 | Section 10.67 | updjud 10015 |
| [Adamek] p. 193 | Definition 11.1(1) | df-lmd 50753 |
| [Adamek] p. 193 | Definition 11.3(1) | df-lmd 50753 |
| [Adamek] p. 194 | Definition 11.3(2) | df-lmd 50753 |
| [Adamek] p. 202 | Definition 11.27(1) | df-cmd 50754 |
| [Adamek] p. 202 | Definition 11.27(2) | df-cmd 50754 |
| [Adamek] p. 478 | Item Rng | df-ringc 20898 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 49660 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 49682 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14716 df-pfx 14821 df-substr 14789 df-word 14659 lencl 14678 wrd0 14684 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 25027 df-nmoo 31347 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 32755 hmopidmchi 32753 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 32803 pjcmul2i 32804 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 32520 unoplin 32522 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 32521 unopadj2 32540 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 32615 lnopunii 32614 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 32688 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 28313 |
| [Alling] p. 184 | Axiom B | bdayfo 28034 |
| [Alling] p. 184 | Axiom O | ltsso 28033 |
| [Alling] p. 184 | Axiom SD | nodense 28049 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 28141 |
| [Alling] p. 185 | Theorem | conway 28165 |
| [Alling] p. 185 | Axiom FE | noeta 28100 |
| [Alling] p. 186 | Theorem 4 | lesrec 28185 lesrecd 28186 |
| [Alling], p. 2 | Definition | rp-brsslt 44424 |
| [Alling], p. 3 | Note | nla0001 44427 nla0002 44425 nla0003 44426 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11494 addcan2d 11514 addcan2i 11504 addcand 11513 addcani 11503 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11547 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11606 negsubd 11675 negsubi 11636 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11608 negnegd 11660 negnegi 11628 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11749 subdid 11772 subdii 11765 subdir 11750 subdird 11773 subdiri 11766 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11489 mul01d 11509 mul01i 11500 mul02 11488 mul02d 11508 mul02i 11499 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11953 mulcan2d 11950 mulcand 11949 mulcani 11955 |
| [Apostol] p. 18 | Theorem I.8 | receu 11961 xreceu 33488 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11990 divrecd 12096 divreci 12062 divreczi 12055 |
| [Apostol] p. 18 | Theorem I.10 | recrec 12014 recreci 12049 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11956 mul0ord 11964 mul0ori 11963 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11755 mul2negd 11771 mul2negi 11764 mulneg1 11752 mulneg1d 11769 mulneg1i 11762 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 12032 divadddivd 12137 divadddivi 12079 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 12017 divmuldivd 12134 divmuldivi 12077 rdivmuldivd 20643 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 12018 divdivdivd 12140 divdivdivi 12080 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 13144 rpaddcld 13179 rpmulcl 13145 rpmulcld 13180 |
| [Apostol] p. 20 | Axiom 8 | rpneg 13154 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 13157 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11436 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11909 ltadd1dd 11927 ltadd1i 11870 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12167 ltmul1a 12166 ltmul1i 12235 ltmul1ii 12245 ltmul2 12168 ltmul2d 13206 ltmul2dd 13220 ltmul2i 12238 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11836 msqgt0d 11883 msqgt0i 11853 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11838 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11822 lt0neg1d 11885 ltneg 11816 ltnegd 11894 ltnegi 11860 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11801 lt2addd 11939 lt2addi 11878 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 13121 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12163 recgt0d 12251 recgt0i 12222 recgt0ii 12223 |
| [Apostol] p. 22 | Definition of integers | df-z 12694 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12349 |
| [Apostol] p. 22 | Definition of rationals | df-q 13076 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9446 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12602 |
| [Apostol] p. 26 | Theorem I.29 | arch 12603 archd 46177 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12802 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12604 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 13074 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 13073 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13329 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16509 zneo 12782 zneoALTV 48767 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 27058 msqsqrtd 15610 resqrtth 15422 sqrtth 15532 sqrtthi 15538 sqsqrtd 15609 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12338 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 13040 |
| [Apostol] p. 361 | Remark | crreczi 14372 |
| [Apostol] p. 363 | Remark | absgt0i 15567 |
| [Apostol] p. 363 | Example | abssubd 15623 abssubi 15571 |
| [ApostolNT] p. 7 | Remark | fmtno0 48625 fmtno1 48626 fmtno2 48635 fmtno3 48636 fmtno4 48637 fmtno5fac 48667 fmtnofz04prm 48662 |
| [ApostolNT] p. 7 | Definition | df-fmtno 48613 |
| [ApostolNT] p. 8 | Definition | df-ppi 27427 |
| [ApostolNT] p. 14 | Definition | df-dvds 16423 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16439 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16464 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16459 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16452 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16454 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16440 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16441 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16446 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16481 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16483 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16485 |
| [ApostolNT] p. 15 | Definition | df-gcd 16665 dfgcd2 16719 |
| [ApostolNT] p. 16 | Definition | isprm2 16857 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16828 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 17093 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16685 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16720 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16722 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16701 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16692 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16887 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16889 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 17106 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 17100 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16573 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16762 |
| [ApostolNT] p. 24 | Definition | df-mu 27428 |
| [ApostolNT] p. 25 | Definition | df-phi 16943 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 27518 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16968 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16953 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16957 |
| [ApostolNT] p. 32 | Definition | df-vma 27425 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 27520 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 27543 |
| [ApostolNT] p. 38 | Remark | df-sgm 27429 |
| [ApostolNT] p. 38 | Definition | df-sgm 27429 |
| [ApostolNT] p. 75 | Definition | df-chp 27426 df-cht 27424 |
| [ApostolNT] p. 104 | Definition | congr 16839 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16426 |
| [ApostolNT] p. 106 | Definition | moddvds 16433 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16516 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16517 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 14028 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 14068 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14382 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16458 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16842 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 17252 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16844 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16960 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16979 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16961 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 27399 |
| [ApostolNT] p. 179 | Definition | df-lgs 27622 lgsprme0 27666 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 27667 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 27643 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 27658 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 27715 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 27734 2lgsoddprm 27743 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 27701 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 27710 |
| [ApostolNT] p. 188 | Definition | df-lgs 27622 lgs1 27668 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 27659 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 27661 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 27669 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 27670 |
| [Baer] p. 40 | Property (b) | mapdord 42696 |
| [Baer] p. 40 | Property (c) | mapd11 42697 |
| [Baer] p. 40 | Property (e) | mapdin 42720 mapdlsm 42722 |
| [Baer] p. 40 | Property (f) | mapd0 42723 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 42683 mapd1o 42706 |
| [Baer] p. 41 | Property (g) | mapdat 42725 |
| [Baer] p. 44 | Part (1) | mapdpg 42764 |
| [Baer] p. 45 | Part (2) | hdmap1eq 42859 mapdheq 42786 mapdheq2 42787 mapdheq2biN 42788 |
| [Baer] p. 45 | Part (3) | baerlem3 42771 |
| [Baer] p. 46 | Part (4) | mapdheq4 42790 mapdheq4lem 42789 |
| [Baer] p. 46 | Part (5) | baerlem5a 42772 baerlem5abmN 42776 baerlem5amN 42774 baerlem5b 42773 baerlem5bmN 42775 |
| [Baer] p. 47 | Part (6) | hdmap1l6 42879 hdmap1l6a 42867 hdmap1l6e 42872 hdmap1l6f 42873 hdmap1l6g 42874 hdmap1l6lem1 42865 hdmap1l6lem2 42866 mapdh6N 42805 mapdh6aN 42793 mapdh6eN 42798 mapdh6fN 42799 mapdh6gN 42800 mapdh6lem1N 42791 mapdh6lem2N 42792 |
| [Baer] p. 48 | Part 9 | hdmapval 42886 |
| [Baer] p. 48 | Part 10 | hdmap10 42898 |
| [Baer] p. 48 | Part 11 | hdmapadd 42901 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 42875 mapdh6hN 42801 |
| [Baer] p. 48 | Part (7) | mapdh75cN 42811 mapdh75d 42812 mapdh75e 42810 mapdh75fN 42813 mapdh7cN 42807 mapdh7dN 42808 mapdh7eN 42806 mapdh7fN 42809 |
| [Baer] p. 48 | Part (8) | mapdh8 42846 mapdh8a 42833 mapdh8aa 42834 mapdh8ab 42835 mapdh8ac 42836 mapdh8ad 42837 mapdh8b 42838 mapdh8c 42839 mapdh8d 42841 mapdh8d0N 42840 mapdh8e 42842 mapdh8g 42843 mapdh8i 42844 mapdh8j 42845 |
| [Baer] p. 48 | Part (9) | mapdh9a 42847 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 42827 |
| [Baer] p. 49 | Part 12 | hdmap11 42906 hdmapeq0 42902 hdmapf1oN 42923 hdmapneg 42904 hdmaprnN 42922 hdmaprnlem1N 42907 hdmaprnlem3N 42908 hdmaprnlem3uN 42909 hdmaprnlem4N 42911 hdmaprnlem6N 42912 hdmaprnlem7N 42913 hdmaprnlem8N 42914 hdmaprnlem9N 42915 hdmapsub 42905 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 42926 hdmap14lem10 42935 hdmap14lem1a 42924 hdmap14lem2N 42927 hdmap14lem2a 42925 hdmap14lem3 42928 hdmap14lem8 42933 hdmap14lem9 42934 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 42936 hdmap14lem12 42937 hdmap14lem13 42938 hdmap14lem14 42939 hdmap14lem15 42940 hgmapval 42945 |
| [Baer] p. 50 | Part 15 | hgmapadd 42952 hgmapmul 42953 hgmaprnlem2N 42955 hgmapvs 42949 |
| [Baer] p. 50 | Part 16 | hgmaprnN 42959 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 42975 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 42976 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 42977 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 42978 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 42980 hgmapvv 42984 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 42979 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 42981 |
| [Baer] p. 111 | Line 15 | hdmapg 42988 hdmapglem7 42987 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 27059 2irrexpqALT 27128 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 24 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2595 |
| [BellMachover] p. 460 | Notation | df-mo 2565 |
| [BellMachover] p. 460 | Definition | mo3 2590 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2733 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2737 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5239 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5249 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 37979 sepex 5255 |
| [BellMachover] p. 466 | Problem | axpow2 5329 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5330 |
| [BellMachover] p. 466 | Axiom Union | axun2 7753 |
| [BellMachover] p. 468 | Definition | df-ord 6365 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6380 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6387 onelond 36948 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6382 |
| [BellMachover] p. 471 | Definition of N | df-om 7878 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7815 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6367 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9643 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7893 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9768 |
| [BellMachover] p. 478 | Definition | rankval2 9827 rankval2b 9835 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9789 r1ord3g 9786 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9590 |
| [BellMachover] p. 488 | Axiom AC | ac5 10555 dfac4 10201 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10189 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 40377 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 32955 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 32997 chirredi 32996 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 32985 |
| [Beran] p. 3 | Definition of join | sshjval3 31956 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 32218 cmcm2i 32195 cmcm2ii 32200 cmt2N 40308 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 32219 lecmi 32204 lecmii 32205 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 32193 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 32222 cm2ji 32227 cm2mi 32228 |
| [Beran] p. 95 | Definition | df-sh 31809 issh2 31811 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 31688 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 31701 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 31692 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 32430 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 32432 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 32431 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 32433 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 31684 his1i 31702 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 31685 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 31686 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 31687 |
| [Beran] p. 96 | Definition of norm | df-hnorm 31570 dfhnorm2 31724 normval 31726 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 31786 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 31575 |
| [Beran] p. 96 | Definition of complete subspace | isch3 31843 |
| [Beran] p. 96 | Definition of converge | df-hlim 31574 hlimi 31790 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 31735 norm-i 31731 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 31739 norm-ii 31740 normlem0 31711 normlem1 31712 normlem2 31713 normlem3 31714 normlem4 31715 normlem5 31716 normlem6 31717 normlem7 31718 normlem7tALT 31721 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 31741 norm-iii 31742 |
| [Beran] p. 98 | Remark 3.4 | bcs 31783 bcsiALT 31781 bcsiHIL 31782 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 31723 normpar 31757 normpari 31756 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 31748 normpyth 31747 normpythi 31744 |
| [Beran] p. 99 | Remark | lnfn0 32649 lnfn0i 32644 lnop0 32568 lnop0i 32572 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 32628 nmcfnex 32655 nmcfnexi 32653 nmcopex 32631 nmcopexi 32629 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 32656 nmcfnlbi 32654 nmcoplb 32632 nmcoplbi 32630 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 32658 lnfnconi 32657 lnopcon 32637 lnopconi 32636 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 31758 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 31755 norm3adifii 31750 norm3dif 31752 norm3difi 31749 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 31903 pjhth 31995 pjhtheu 31996 pjpjhth 32027 pjpjhthi 32028 pjth 25760 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 32008 ococi 32007 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 32663 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 32664 riesz4 32666 riesz4i 32665 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 32681 cnlnadjeu 32680 cnlnadjeui 32679 cnlnadji 32678 cnlnadjlem1 32669 nmopadjlei 32690 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 32693 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 32692 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 32694 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 32538 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 32704 nmopcoadji 32703 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 32695 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 32705 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 32702 pjadj2coi 32806 pjadjcoi 32763 |
| [Beran] p. 107 | Definition | df-ch 31823 isch2 31825 |
| [Beran] p. 107 | Remark 3.12 | choccl 31908 isch3 31843 occl 31906 ocsh 31885 shoccl 31907 shocsh 31886 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 32010 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 31934 |
| [Beran] p. 109 | Property (i) | pjadj2 32789 pjadj3 32790 pjadji 32287 pjadjii 32276 |
| [Beran] p. 109 | Property (ii) | pjidmco 32783 pjidmcoi 32779 pjidmi 32275 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 32775 |
| [Beran] p. 111 | Remark | ho0val 32352 pjch1 32272 |
| [Beran] p. 111 | Definition | df-hfmul 32336 df-hfsum 32335 df-hodif 32334 df-homul 32333 df-hosum 32332 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 32273 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 32296 pjchi 32034 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 32041 pjoc2i 32040 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 32282 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 32767 pjssmii 32283 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 32766 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 32765 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 32770 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 32768 pjssge0ii 32284 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 32769 pjdifnormii 32285 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1809 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1807 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1810 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1805 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 34924 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 34932 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 34930 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 34934 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 34954 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 34985 df-sitm 34963 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 34985 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 34962 |
| [Bollobas] p. 1 | Section I.1 | df-edg 29626 isuhgrop 29648 isusgrop 29743 isuspgrop 29742 |
| [Bollobas] p. 2 | Section I.1 | df-isubgr 48959 df-subgr 29849 uhgrspan1 29884 uhgrspansubgr 29872 |
| [Bollobas] p. 3 | Definition | df-gric 48979 gricuspgr 49016 isuspgrim 48994 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 30035 df-clnbgr 48917 df-cusgr 29993 df-nbgr 29914 fusgrmaxsize 30045 |
| [Bollobas] p. 4 | Definition | df-upwlks 49232 df-wlks 30180 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 30131 finsumvtxdgeven 30133 fusgr1th 30132 fusgrvtxdgonume 30135 vtxdgoddnumeven 30134 |
| [Bollobas] p. 5 | Notation | df-pths 30299 |
| [Bollobas] p. 5 | Definition | df-crcts 30373 df-cycls 30374 df-trls 30275 df-wlkson 30181 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 29637 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 49297 df-cllaw 49283 df-mgm 18816 df-mgm2 49316 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 49298 df-asslaw 49285 df-sgrp 18908 df-sgrp2 49318 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 49317 df-comlaw 49284 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18924 |
| [BourbakiAlg1] p. 17 | Chapter I. | mndlactf1 33587 mndlactf1o 33591 mndractf1 33589 mndractf1o 33592 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 20461 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 20375 |
| [BourbakiAlg1] p. 298 | Proposition 9 | lvecendof1f1o 34265 |
| [BourbakiAlg2] p. 113 | Chapter 5. | assafld 34269 assarrginv 34268 |
| [BourbakiAlg2] p. 116 | Chapter 5, | fldextrspundgle 34310 fldextrspunfld 34308 fldextrspunlem1 34307 fldextrspunlem2 34309 fldextrspunlsp 34306 fldextrspunlsplem 34305 |
| [BourbakiCAlg2], p. 228 | Proposition 2 | 1arithidom 34069 dfufd2 34082 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7295 fcofo 7296 |
| [BourbakiTop1] p. | Remark | xnegmnf 13340 xnegpnf 13339 |
| [BourbakiTop1] p. | Remark | rexneg 13341 |
| [BourbakiTop1] p. | Remark 3 | ust0 24539 ustfilxp 24532 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 24409 |
| [BourbakiTop1] p. | Criterion | ishmeo 24078 |
| [BourbakiTop1] p. | Example 1 | cstucnd 24602 iducn 24601 snfil 24183 |
| [BourbakiTop1] p. | Example 2 | neifil 24199 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 24386 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 24622 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 34589 |
| [BourbakiTop1] p. | Paragraph 3 | infil 24182 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 24594 df-ust 24520 filintn0 24180 filn0 24181 istgp 24396 ucnprima 24600 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 24605 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 24616 df-usp 24576 df-utop 24550 trust 24548 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 34488 |
| [BourbakiTop1] p. | Property V_i | ssnei2 23434 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 23587 |
| [BourbakiTop1] p. | Condition F_I | ustssel 24525 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 24528 |
| [BourbakiTop1] p. | Property V_ii | innei 23443 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 23451 neissex 23445 |
| [BourbakiTop1] p. | Proposition 1 | neips 23431 neiss 23427 ucncn 24603 ustund 24541 ustuqtop 24565 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 23585 neiptopreu 23451 utop2nei 24569 utop3cls 24570 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 24610 uspreg 24592 utopreg 24571 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 24010 imasncls 24011 imasnopn 24009 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 24319 |
| [BourbakiTop1] p. | Condition F_II | ustincl 24527 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 24529 |
| [BourbakiTop1] p. | Property V_iii | elnei 23429 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 24621 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 24526 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 24530 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 23705 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 24165 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 23212 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 34485 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 47072 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 47074 stoweid 47073 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 47011 stoweidlem10 47020 stoweidlem14 47024 stoweidlem15 47025 stoweidlem35 47045 stoweidlem36 47046 stoweidlem37 47047 stoweidlem38 47048 stoweidlem40 47050 stoweidlem41 47051 stoweidlem43 47053 stoweidlem44 47054 stoweidlem46 47056 stoweidlem5 47015 stoweidlem50 47060 stoweidlem52 47062 stoweidlem53 47063 stoweidlem55 47065 stoweidlem56 47066 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 47033 stoweidlem24 47034 stoweidlem27 47037 stoweidlem28 47038 stoweidlem30 47040 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 47044 stoweidlem59 47069 stoweidlem60 47070 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 47055 stoweidlem49 47059 stoweidlem7 47017 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 47041 stoweidlem39 47049 stoweidlem42 47052 stoweidlem48 47058 stoweidlem51 47061 stoweidlem54 47064 stoweidlem57 47067 stoweidlem58 47068 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 47035 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 47027 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 47021 stoweidlem13 47023 stoweidlem26 47036 stoweidlem61 47071 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 47028 |
| [Bruck] p. 1 | Section I.1 | df-clintop 49297 df-mgm 18816 df-mgm2 49316 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18908 df-sgrp2 49318 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 19249 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5187 |
| [Church] p. 129 | Section II.24 | df-ifp 1079 dfifp2 1080 |
| [Clemente] p. 10 | Definition IT | natded 31004 |
| [Clemente] p. 10 | Definition I` `m,n | natded 31004 |
| [Clemente] p. 11 | Definition E=>m,n | natded 31004 |
| [Clemente] p. 11 | Definition I=>m,n | natded 31004 |
| [Clemente] p. 11 | Definition E` `(1) | natded 31004 |
| [Clemente] p. 11 | Definition E` `(2) | natded 31004 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 31004 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 31004 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 31004 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 31004 |
| [Clemente] p. 14 | Proof 5.11 | natded 31004 |
| [Clemente] p. 14 | Definition E` `n | natded 31004 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 31006 ex-natded5.2 31005 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 31009 ex-natded5.3 31008 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 31011 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 31013 ex-natded5.7 31012 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 31015 ex-natded5.8 31014 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 31017 ex-natded5.13 31016 |
| [Clemente] p. 32 | Definition I` `n | natded 31004 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 31004 |
| [Clemente] p. 32 | Definition E` `n,t | natded 31004 |
| [Clemente] p. 32 | Definition I` `n,t | natded 31004 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 31018 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 31019 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 31021 ex-natded9.26 31020 |
| [Cohen] p. 301 | Remark | relogoprlem 26919 |
| [Cohen] p. 301 | Property 2 | relogmul 26920 relogmuld 26953 |
| [Cohen] p. 301 | Property 3 | relogdiv 26921 relogdivd 26954 |
| [Cohen] p. 301 | Property 4 | relogexp 26924 |
| [Cohen] p. 301 | Property 1a | log1 26913 |
| [Cohen] p. 301 | Property 1b | loge 26914 |
| [Cohen4] p. 348 | Observation | relogbcxpb 27115 |
| [Cohen4] p. 349 | Property | relogbf 27119 |
| [Cohen4] p. 352 | Definition | elogb 27098 |
| [Cohen4] p. 361 | Property 2 | relogbmul 27105 |
| [Cohen4] p. 361 | Property 3 | logbrec 27110 relogbdiv 27107 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 27103 |
| [Cohen4] p. 361 | Property 6 | relogbexp 27108 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 27096 |
| [Cohen4] p. 361 | Property 1(b) | logb1 27097 |
| [Cohen4] p. 367 | Property | logbchbase 27099 |
| [Cohen4] p. 377 | Property 2 | logblt 27112 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 34917 sxbrsigalem4 34919 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18731 acsinfd 18730 acsinfdimd 18732 acsmap2d 18729 acsmapd 18728 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 34922 |
| [Connell] p. 57 | Definition | df-scmat 22806 df-scmatalt 49511 |
| [Conway] p. 4 | Definition | lesrec 28185 lesrecd 28186 |
| [Conway] p. 5 | Definition | addsval 28348 addsval2 28349 df-adds 28346 df-muls 28493 df-negs 28407 |
| [Conway] p. 7 | Theorem | 0lt1s 28198 |
| [Conway] p. 12 | Theorem 12 | pw2cut2 28848 |
| [Conway] p. 16 | Theorem 0(i) | sltsright 28247 |
| [Conway] p. 16 | Theorem 0(ii) | sltsleft 28246 |
| [Conway] p. 16 | Theorem 0(iii) | lesid 28124 |
| [Conway] p. 17 | Theorem 3 | addsass 28391 addsassd 28392 addscom 28352 addscomd 28353 addsrid 28350 addsridd 28351 |
| [Conway] p. 17 | Definition | df-0s 28193 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 28430 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 28427 negsidd 28428 |
| [Conway] p. 18 | Theorem 5 | leadds1 28375 leadds1d 28381 |
| [Conway] p. 18 | Definition | df-1s 28194 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 28422 negscld 28423 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 28366 |
| [Conway] p. 19 | Note | mulsunif2 28556 |
| [Conway] p. 19 | Theorem 7 | addsdi 28541 addsdid 28542 addsdird 28543 mulnegs1d 28546 mulnegs2d 28547 mulsass 28552 mulsassd 28553 mulscom 28525 mulscomd 28526 |
| [Conway] p. 19 | Theorem 8(i) | mulscl 28520 mulscld 28521 |
| [Conway] p. 19 | Theorem 8(iii) | lemulsd 28524 ltmuls 28522 ltmulsd 28523 |
| [Conway] p. 20 | Theorem 9 | mulsgt0 28530 mulsgt0d 28531 |
| [Conway] p. 21 | Theorem 10(iv) | precsex 28604 |
| [Conway] p. 23 | Theorem 11 | eqcuts3 28190 |
| [Conway] p. 24 | Definition | df-reno 28876 |
| [Conway] p. 24 | Theorem 13(ii) | readdscl 28885 remulscl 28888 renegscl 28884 |
| [Conway] p. 27 | Definition | df-ons 28638 elons2 28644 |
| [Conway] p. 27 | Theorem 14 | ltonsex 28648 |
| [Conway] p. 28 | Theorem 15 | oncutlt 28650 onswe 28658 |
| [Conway] p. 29 | Remark | madebday 28286 newbday 28288 oldbday 28287 |
| [Conway] p. 29 | Definition | df-made 28213 df-new 28215 df-old 28214 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 14001 |
| [Crawley] p. 1 | Definition of poset | df-poset 18487 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 40444 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 41248 dalaw 40944 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 43019 |
| [Crawley] p. 111 | Definition of set W | df-watsN 41048 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 41164 df-ldil 41162 isldil 41168 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 41163 df-trnN 41165 isltrn 41177 ltrnu 41179 |
| [Crawley] p. 112 | Lemma A | cdlema1N 40849 cdlema2N 40850 exatleN 40462 |
| [Crawley] p. 112 | Lemma B | 1cvrat 40534 cdlemb 40852 cdlemb2 41099 cdlemb3 41664 idltrn 41208 l1cvat 40113 lhpat 41101 lhpat2 41103 lshpat 40114 ltrnel 41197 ltrnmw 41209 |
| [Crawley] p. 112 | Lemma C | cdlemc1 41249 cdlemc2 41250 ltrnnidn 41232 trlat 41227 trljat1 41224 trljat2 41225 trljat3 41226 trlne 41243 trlnidat 41231 trlnle 41244 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 41049 |
| [Crawley] p. 113 | Lemma C | cdlemc 41255 cdlemc3 41251 cdlemc4 41252 |
| [Crawley] p. 113 | Lemma D | cdlemd 41265 cdlemd1 41256 cdlemd2 41257 cdlemd3 41258 cdlemd4 41259 cdlemd5 41260 cdlemd6 41261 cdlemd7 41262 cdlemd8 41263 cdlemd9 41264 cdleme31sde 41443 cdleme31se 41440 cdleme31se2 41441 cdleme31snd 41444 cdleme32a 41499 cdleme32b 41500 cdleme32c 41501 cdleme32d 41502 cdleme32e 41503 cdleme32f 41504 cdleme32fva 41495 cdleme32fva1 41496 cdleme32fvcl 41498 cdleme32le 41505 cdleme48fv 41557 cdleme4gfv 41565 cdleme50eq 41599 cdleme50f 41600 cdleme50f1 41601 cdleme50f1o 41604 cdleme50laut 41605 cdleme50ldil 41606 cdleme50lebi 41598 cdleme50rn 41603 cdleme50rnlem 41602 cdlemeg49le 41569 cdlemeg49lebilem 41597 |
| [Crawley] p. 113 | Lemma E | cdleme 41618 cdleme00a 41267 cdleme01N 41279 cdleme02N 41280 cdleme0a 41269 cdleme0aa 41268 cdleme0b 41270 cdleme0c 41271 cdleme0cp 41272 cdleme0cq 41273 cdleme0dN 41274 cdleme0e 41275 cdleme0ex1N 41281 cdleme0ex2N 41282 cdleme0fN 41276 cdleme0gN 41277 cdleme0moN 41283 cdleme1 41285 cdleme10 41312 cdleme10tN 41316 cdleme11 41328 cdleme11a 41318 cdleme11c 41319 cdleme11dN 41320 cdleme11e 41321 cdleme11fN 41322 cdleme11g 41323 cdleme11h 41324 cdleme11j 41325 cdleme11k 41326 cdleme11l 41327 cdleme12 41329 cdleme13 41330 cdleme14 41331 cdleme15 41336 cdleme15a 41332 cdleme15b 41333 cdleme15c 41334 cdleme15d 41335 cdleme16 41343 cdleme16aN 41317 cdleme16b 41337 cdleme16c 41338 cdleme16d 41339 cdleme16e 41340 cdleme16f 41341 cdleme16g 41342 cdleme19a 41361 cdleme19b 41362 cdleme19c 41363 cdleme19d 41364 cdleme19e 41365 cdleme19f 41366 cdleme1b 41284 cdleme2 41286 cdleme20aN 41367 cdleme20bN 41368 cdleme20c 41369 cdleme20d 41370 cdleme20e 41371 cdleme20f 41372 cdleme20g 41373 cdleme20h 41374 cdleme20i 41375 cdleme20j 41376 cdleme20k 41377 cdleme20l 41380 cdleme20l1 41378 cdleme20l2 41379 cdleme20m 41381 cdleme20y 41360 cdleme20zN 41359 cdleme21 41395 cdleme21d 41388 cdleme21e 41389 cdleme22a 41398 cdleme22aa 41397 cdleme22b 41399 cdleme22cN 41400 cdleme22d 41401 cdleme22e 41402 cdleme22eALTN 41403 cdleme22f 41404 cdleme22f2 41405 cdleme22g 41406 cdleme23a 41407 cdleme23b 41408 cdleme23c 41409 cdleme26e 41417 cdleme26eALTN 41419 cdleme26ee 41418 cdleme26f 41421 cdleme26f2 41423 cdleme26f2ALTN 41422 cdleme26fALTN 41420 cdleme27N 41427 cdleme27a 41425 cdleme27cl 41424 cdleme28c 41430 cdleme3 41295 cdleme30a 41436 cdleme31fv 41448 cdleme31fv1 41449 cdleme31fv1s 41450 cdleme31fv2 41451 cdleme31id 41452 cdleme31sc 41442 cdleme31sdnN 41445 cdleme31sn 41438 cdleme31sn1 41439 cdleme31sn1c 41446 cdleme31sn2 41447 cdleme31so 41437 cdleme35a 41506 cdleme35b 41508 cdleme35c 41509 cdleme35d 41510 cdleme35e 41511 cdleme35f 41512 cdleme35fnpq 41507 cdleme35g 41513 cdleme35h 41514 cdleme35h2 41515 cdleme35sn2aw 41516 cdleme35sn3a 41517 cdleme36a 41518 cdleme36m 41519 cdleme37m 41520 cdleme38m 41521 cdleme38n 41522 cdleme39a 41523 cdleme39n 41524 cdleme3b 41287 cdleme3c 41288 cdleme3d 41289 cdleme3e 41290 cdleme3fN 41291 cdleme3fa 41294 cdleme3g 41292 cdleme3h 41293 cdleme4 41296 cdleme40m 41525 cdleme40n 41526 cdleme40v 41527 cdleme40w 41528 cdleme41fva11 41535 cdleme41sn3aw 41532 cdleme41sn4aw 41533 cdleme41snaw 41534 cdleme42a 41529 cdleme42b 41536 cdleme42c 41530 cdleme42d 41531 cdleme42e 41537 cdleme42f 41538 cdleme42g 41539 cdleme42h 41540 cdleme42i 41541 cdleme42k 41542 cdleme42ke 41543 cdleme42keg 41544 cdleme42mN 41545 cdleme42mgN 41546 cdleme43aN 41547 cdleme43bN 41548 cdleme43cN 41549 cdleme43dN 41550 cdleme5 41298 cdleme50ex 41617 cdleme50ltrn 41615 cdleme51finvN 41614 cdleme51finvfvN 41613 cdleme51finvtrN 41616 cdleme6 41299 cdleme7 41307 cdleme7a 41301 cdleme7aa 41300 cdleme7b 41302 cdleme7c 41303 cdleme7d 41304 cdleme7e 41305 cdleme7ga 41306 cdleme8 41308 cdleme8tN 41313 cdleme9 41311 cdleme9a 41309 cdleme9b 41310 cdleme9tN 41315 cdleme9taN 41314 cdlemeda 41356 cdlemedb 41355 cdlemednpq 41357 cdlemednuN 41358 cdlemefr27cl 41461 cdlemefr32fva1 41468 cdlemefr32fvaN 41467 cdlemefrs32fva 41458 cdlemefrs32fva1 41459 cdlemefs27cl 41471 cdlemefs32fva1 41481 cdlemefs32fvaN 41480 cdlemesner 41354 cdlemeulpq 41278 |
| [Crawley] p. 114 | Lemma E | 4atex 41134 4atexlem7 41133 cdleme0nex 41348 cdleme17a 41344 cdleme17c 41346 cdleme17d 41556 cdleme17d1 41347 cdleme17d2 41553 cdleme18a 41349 cdleme18b 41350 cdleme18c 41351 cdleme18d 41353 cdleme4a 41297 |
| [Crawley] p. 115 | Lemma E | cdleme21a 41383 cdleme21at 41386 cdleme21b 41384 cdleme21c 41385 cdleme21ct 41387 cdleme21f 41390 cdleme21g 41391 cdleme21h 41392 cdleme21i 41393 cdleme22gb 41352 |
| [Crawley] p. 116 | Lemma F | cdlemf 41621 cdlemf1 41619 cdlemf2 41620 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 41625 cdlemg16 41715 cdlemg28 41762 cdlemg28a 41751 cdlemg28b 41761 cdlemg3a 41655 cdlemg42 41787 cdlemg43 41788 cdlemg44 41791 cdlemg44a 41789 cdlemg46 41793 cdlemg47 41794 cdlemg9 41692 ltrnco 41777 ltrncom 41796 tgrpabl 41809 trlco 41785 |
| [Crawley] p. 116 | Definition of G | df-tgrp 41801 |
| [Crawley] p. 117 | Lemma G | cdlemg17 41735 cdlemg17b 41720 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 41814 df-edring 41815 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 41818 |
| [Crawley] p. 118 | Remark | tendopltp 41838 |
| [Crawley] p. 118 | Lemma H | cdlemh 41875 cdlemh1 41873 cdlemh2 41874 |
| [Crawley] p. 118 | Lemma I | cdlemi 41878 cdlemi1 41876 cdlemi2 41877 |
| [Crawley] p. 118 | Lemma J | cdlemj1 41879 cdlemj2 41880 cdlemj3 41881 tendocan 41882 |
| [Crawley] p. 118 | Lemma K | cdlemk 42032 cdlemk1 41889 cdlemk10 41901 cdlemk11 41907 cdlemk11t 42004 cdlemk11ta 41987 cdlemk11tb 41989 cdlemk11tc 42003 cdlemk11u-2N 41947 cdlemk11u 41929 cdlemk12 41908 cdlemk12u-2N 41948 cdlemk12u 41930 cdlemk13-2N 41934 cdlemk13 41910 cdlemk14-2N 41936 cdlemk14 41912 cdlemk15-2N 41937 cdlemk15 41913 cdlemk16-2N 41938 cdlemk16 41915 cdlemk16a 41914 cdlemk17-2N 41939 cdlemk17 41916 cdlemk18-2N 41944 cdlemk18-3N 41958 cdlemk18 41926 cdlemk19-2N 41945 cdlemk19 41927 cdlemk19u 42028 cdlemk1u 41917 cdlemk2 41890 cdlemk20-2N 41950 cdlemk20 41932 cdlemk21-2N 41949 cdlemk21N 41931 cdlemk22-3 41959 cdlemk22 41951 cdlemk23-3 41960 cdlemk24-3 41961 cdlemk25-3 41962 cdlemk26-3 41964 cdlemk26b-3 41963 cdlemk27-3 41965 cdlemk28-3 41966 cdlemk29-3 41969 cdlemk3 41891 cdlemk30 41952 cdlemk31 41954 cdlemk32 41955 cdlemk33N 41967 cdlemk34 41968 cdlemk35 41970 cdlemk36 41971 cdlemk37 41972 cdlemk38 41973 cdlemk39 41974 cdlemk39u 42026 cdlemk4 41892 cdlemk41 41978 cdlemk42 41999 cdlemk42yN 42002 cdlemk43N 42021 cdlemk45 42005 cdlemk46 42006 cdlemk47 42007 cdlemk48 42008 cdlemk49 42009 cdlemk5 41894 cdlemk50 42010 cdlemk51 42011 cdlemk52 42012 cdlemk53 42015 cdlemk54 42016 cdlemk55 42019 cdlemk55u 42024 cdlemk56 42029 cdlemk5a 41893 cdlemk5auN 41918 cdlemk5u 41919 cdlemk6 41895 cdlemk6u 41920 cdlemk7 41906 cdlemk7u-2N 41946 cdlemk7u 41928 cdlemk8 41896 cdlemk9 41897 cdlemk9bN 41898 cdlemki 41899 cdlemkid 41994 cdlemkj-2N 41940 cdlemkj 41921 cdlemksat 41904 cdlemksel 41903 cdlemksv 41902 cdlemksv2 41905 cdlemkuat 41924 cdlemkuel-2N 41942 cdlemkuel-3 41956 cdlemkuel 41923 cdlemkuv-2N 41941 cdlemkuv2-2 41943 cdlemkuv2-3N 41957 cdlemkuv2 41925 cdlemkuvN 41922 cdlemkvcl 41900 cdlemky 41984 cdlemkyyN 42020 tendoex 42033 |
| [Crawley] p. 120 | Remark | dva1dim 42043 |
| [Crawley] p. 120 | Lemma L | cdleml1N 42034 cdleml2N 42035 cdleml3N 42036 cdleml4N 42037 cdleml5N 42038 cdleml6 42039 cdleml7 42040 cdleml8 42041 cdleml9 42042 dia1dim 42119 |
| [Crawley] p. 120 | Lemma M | dia11N 42106 diaf11N 42107 dialss 42104 diaord 42105 dibf11N 42219 djajN 42195 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 42090 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 42176 dia2dimlem1 42122 dia2dimlem2 42123 dia2dimlem3 42124 dia2dimlem4 42125 dia2dimlem5 42126 diaf1oN 42188 diarnN 42187 dvheveccl 42170 dvhopN 42174 |
| [Crawley] p. 121 | Lemma N | cdlemn 42270 cdlemn10 42264 cdlemn11 42269 cdlemn11a 42265 cdlemn11b 42266 cdlemn11c 42267 cdlemn11pre 42268 cdlemn2 42253 cdlemn2a 42254 cdlemn3 42255 cdlemn4 42256 cdlemn4a 42257 cdlemn5 42259 cdlemn5pre 42258 cdlemn6 42260 cdlemn7 42261 cdlemn8 42262 cdlemn9 42263 diclspsn 42252 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 42231 |
| [Crawley] p. 122 | Lemma N | dih11 42323 dihf11 42325 dihjust 42275 dihjustlem 42274 dihord 42322 dihord1 42276 dihord10 42281 dihord11b 42280 dihord11c 42282 dihord2 42285 dihord2a 42277 dihord2b 42278 dihord2cN 42279 dihord2pre 42283 dihord2pre2 42284 dihordlem6 42271 dihordlem7 42272 dihordlem7b 42273 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 42288 dihfval 42289 dihval 42290 |
| [Diestel] p. 3 | Definition | df-gric 48979 df-grim 48976 isuspgrim 48994 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 29993 df-nbgr 29914 |
| [Diestel] p. 3 | Definition by | df-grisom 48975 |
| [Diestel] p. 4 | Section 1.1 | df-isubgr 48959 df-subgr 29849 uhgrspan1 29884 uhgrspansubgr 29872 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 30135 vtxdgoddnumeven 30134 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 29637 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 34496 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 34508 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 34500 zarcls1 34501 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 34511 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 34514 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 34517 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3902 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9648 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8849 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9656 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 10061 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10639 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5259 |
| [Enderton] p. 19 | Definition | df-tp 4589 |
| [Enderton] p. 26 | Exercise 5 | unissb 4901 |
| [Enderton] p. 26 | Exercise 10 | pwel 5343 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5544 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5039 iinin2 5038 iinun2 5031 iunin1 5030 iunin1f 33152 iunin2 5029 uniin1 5033 uniin2 5034 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5037 iundif2 5032 |
| [Enderton] p. 32 | Exercise 20 | unineq 4234 |
| [Enderton] p. 33 | Exercise 23 | iinuni 5058 |
| [Enderton] p. 33 | Exercise 25 | iununi 5059 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 5066 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 7785 iunpwss 5067 |
| [Enderton] p. 36 | Definition | opthwiener 5487 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5418 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4906 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5439 rnex 7922 rnexg 7914 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5896 rnuni 6140 |
| [Enderton] p. 42 | Definition of a function | dffun7 6567 dffun8 6568 |
| [Enderton] p. 43 | Definition of function value | funfv2 6973 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6609 |
| [Enderton] p. 44 | Definition (d) | dfima2 6058 dfima3 6059 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6982 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10551 ac7g 10552 df-ac 10195 dfac2 10210 dfac2a 10208 dfac2b 10209 dfac3 10200 dfac7 10211 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7250 |
| [Enderton] p. 52 | Definition | df-map 8849 |
| [Enderton] p. 53 | Exercise 21 | coass 6267 |
| [Enderton] p. 53 | Exercise 27 | dmco 6256 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6616 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6055 |
| [Enderton] p. 54 | Remark | ixpf 8948 ixpssmap 8960 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8926 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10561 ac9s 10571 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 39627 erref 8738 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 39630 erthi 8774 |
| [Enderton] p. 57 | Definition | df-ec 8719 |
| [Enderton] p. 58 | Definition | df-qs 8723 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8719 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5892 |
| [Enderton] p. 68 | Definition of successor | df-suc 6368 |
| [Enderton] p. 71 | Definition | df-tr 5213 dftr4 5218 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6444 unisucg 6443 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5228 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5230 trintALT 45863 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8613 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8615 onasuc 8536 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7423 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8614 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8616 onmsuc 8537 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8631 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8618 nnacom 8626 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8632 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8633 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8635 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8619 nnmsucr 8634 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8647 |
| [Enderton] p. 129 | Definition | df-en 8974 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7374 |
| [Enderton] p. 133 | Exercise 1 | xpomen 10094 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16381 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9222 |
| [Enderton] p. 135 | Corollary 6C | php3 9224 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9221 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9253 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9255 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9184 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9188 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9160 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10258 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10259 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10254 dju1en 10250 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9332 unifi 9333 unifi2 9334 |
| [Enderton] p. 144 | Corollary 6K | undif2 4431 unfi 9186 unfi2 9302 |
| [Enderton] p. 145 | Figure 38 | ffoss 7958 |
| [Enderton] p. 145 | Definition | df-dom 8975 |
| [Enderton] p. 146 | Example 1 | domen 8988 domeng 8989 |
| [Enderton] p. 146 | Example 3 | nndomo 9233 nnsdom 9655 nnsdomg 9291 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10262 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9161 xpdom1 9095 xpdom1g 9093 xpdom2g 9092 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9167 |
| [Enderton] p. 151 | Theorem 6M | zorn 10585 zorng 10582 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10570 dfac5 10207 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10660 |
| [Enderton] p. 164 | Example | infdif 10286 |
| [Enderton] p. 168 | Definition | df-po 5559 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6478 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6410 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6477 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6418 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7850 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7795 |
| [Enderton] p. 194 | Remark | onprc 7792 |
| [Enderton] p. 194 | Exercise 16 | suc11 6472 |
| [Enderton] p. 197 | Definition | df-card 10020 |
| [Enderton] p. 197 | Theorem 7P | carden 10635 |
| [Enderton] p. 200 | Exercise 25 | tfis 7866 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9783 |
| [Enderton] p. 202 | Definition | df-r1 9768 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9793 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9884 rankval4b 9880 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9607 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9871 rankprb 9865 rankpw 9856 rankpwi 9832 rankuniss 9883 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9619 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9620 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10189 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10155 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10169 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8349 |
| [Enderton] p. 222 | Definition | df-kard 35818 |
| [Enderton] p. 222 | Definition of kard | karden 9959 kardex 9957 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8606 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8608 |
| [Enderton] p. 240 | Exercise 25 | oarec 8570 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10327 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17816 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17758 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18727 mrieqv2d 17813 mrieqvd 17812 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17817 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17822 mreexexlem2d 17819 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18733 mreexfidimd 17824 |
| [Frege1879] p. 11 | Statement | df3or2 44768 |
| [Frege1879] p. 12 | Statement | df3an2 44769 dfxor4 44766 dfxor5 44767 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 44790 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 44791 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 44795 |
| [Frege1879] p. 31 | Proposition 4 | frege4 44799 |
| [Frege1879] p. 32 | Proposition 5 | frege5 44800 |
| [Frege1879] p. 33 | Proposition 6 | frege6 44806 |
| [Frege1879] p. 34 | Proposition 7 | frege7 44808 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 44809 axfrege8 44807 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 91 wl-luk-pm2.04 38369 |
| [Frege1879] p. 35 | Proposition 9 | frege9 44812 |
| [Frege1879] p. 36 | Proposition 10 | frege10 44820 |
| [Frege1879] p. 36 | Proposition 11 | frege11 44814 |
| [Frege1879] p. 37 | Proposition 12 | frege12 44813 |
| [Frege1879] p. 37 | Proposition 13 | frege13 44822 |
| [Frege1879] p. 37 | Proposition 14 | frege14 44823 |
| [Frege1879] p. 38 | Proposition 15 | frege15 44826 |
| [Frege1879] p. 38 | Proposition 16 | frege16 44816 |
| [Frege1879] p. 39 | Proposition 17 | frege17 44821 |
| [Frege1879] p. 39 | Proposition 18 | frege18 44818 |
| [Frege1879] p. 39 | Proposition 19 | frege19 44824 |
| [Frege1879] p. 40 | Proposition 20 | frege20 44828 |
| [Frege1879] p. 40 | Proposition 21 | frege21 44827 |
| [Frege1879] p. 41 | Proposition 22 | frege22 44819 |
| [Frege1879] p. 42 | Proposition 23 | frege23 44825 |
| [Frege1879] p. 42 | Proposition 24 | frege24 44815 |
| [Frege1879] p. 42 | Proposition 25 | frege25 44817 rp-frege25 44805 |
| [Frege1879] p. 42 | Proposition 26 | frege26 44810 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 44830 |
| [Frege1879] p. 43 | Proposition 27 | frege27 44811 |
| [Frege1879] p. 43 | Proposition 28 | con3 154 |
| [Frege1879] p. 43 | Proposition 29 | frege29 44831 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 44834 axfrege31 44833 |
| [Frege1879] p. 44 | Proposition 30 | frege30 44832 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 131 |
| [Frege1879] p. 44 | Proposition 32 | frege32 44835 |
| [Frege1879] p. 44 | Proposition 33 | frege33 44836 |
| [Frege1879] p. 45 | Proposition 34 | frege34 44837 |
| [Frege1879] p. 45 | Proposition 35 | frege35 44838 |
| [Frege1879] p. 45 | Proposition 36 | frege36 44839 |
| [Frege1879] p. 46 | Proposition 37 | frege37 44840 |
| [Frege1879] p. 46 | Proposition 38 | frege38 44841 |
| [Frege1879] p. 46 | Proposition 39 | frege39 44842 |
| [Frege1879] p. 46 | Proposition 40 | frege40 44843 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 44845 axfrege41 44844 |
| [Frege1879] p. 47 | Proposition 41 | notnot 143 |
| [Frege1879] p. 47 | Proposition 42 | frege42 44846 |
| [Frege1879] p. 47 | Proposition 43 | frege43 44847 |
| [Frege1879] p. 47 | Proposition 44 | frege44 44848 |
| [Frege1879] p. 47 | Proposition 45 | frege45 44849 |
| [Frege1879] p. 48 | Proposition 46 | frege46 44850 |
| [Frege1879] p. 48 | Proposition 47 | frege47 44851 |
| [Frege1879] p. 49 | Proposition 48 | frege48 44852 |
| [Frege1879] p. 49 | Proposition 49 | frege49 44853 |
| [Frege1879] p. 49 | Proposition 50 | frege50 44854 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 44857 ax-frege52c 44888 frege52aid 44858 frege52b 44889 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 44862 ax-frege54c 44892 frege54b 44893 |
| [Frege1879] p. 50 | Proposition 51 | frege51 44855 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3741 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 44860 frege53aid 44859 frege53b 44890 frege53c 44914 |
| [Frege1879] p. 50 | Proposition 54 | biid 264 eqid 2761 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 44868 frege55aid 44865 frege55b 44897 frege55c 44918 frege55cor1a 44869 frege55lem2a 44867 frege55lem2b 44896 frege55lem2c 44917 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 44871 frege56aid 44870 frege56b 44898 frege56c 44919 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 44875 ax-frege58b 44901 frege58bid 44902 frege58c 44921 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 44873 frege57aid 44872 frege57b 44899 frege57c 44920 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3752 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 44877 frege59b 44904 frege59c 44922 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 44878 frege60b 44905 frege60c 44923 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 44879 frege61b 44906 frege61c 44924 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 44880 frege62b 44907 frege62c 44925 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 44881 frege63b 44908 frege63c 44926 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 44882 frege64b 44909 frege64c 44927 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 44883 frege65b 44910 frege65c 44928 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 44884 frege66b 44911 frege66c 44929 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 44885 frege67b 44912 frege67c 44930 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 44886 frege68b 44913 frege68c 44931 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 44932 |
| [Frege1879] p. 58 | Proposition 70 | frege70 44933 |
| [Frege1879] p. 59 | Proposition 71 | frege71 44934 |
| [Frege1879] p. 59 | Proposition 72 | frege72 44935 |
| [Frege1879] p. 59 | Proposition 73 | frege73 44936 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 44939 |
| [Frege1879] p. 60 | Proposition 74 | frege74 44937 |
| [Frege1879] p. 60 | Proposition 75 | frege75 44938 |
| [Frege1879] p. 62 | Proposition 77 | frege77 44940 frege77d 44746 |
| [Frege1879] p. 63 | Proposition 78 | frege78 44941 |
| [Frege1879] p. 63 | Proposition 79 | frege79 44942 |
| [Frege1879] p. 63 | Proposition 80 | frege80 44943 |
| [Frege1879] p. 63 | Proposition 81 | frege81 44944 frege81d 44747 |
| [Frege1879] p. 64 | Proposition 82 | frege82 44945 |
| [Frege1879] p. 65 | Proposition 83 | frege83 44946 frege83d 44748 |
| [Frege1879] p. 65 | Proposition 84 | frege84 44947 |
| [Frege1879] p. 66 | Proposition 85 | frege85 44948 |
| [Frege1879] p. 66 | Proposition 86 | frege86 44949 |
| [Frege1879] p. 66 | Proposition 87 | frege87 44950 frege87d 44750 |
| [Frege1879] p. 67 | Proposition 88 | frege88 44951 |
| [Frege1879] p. 68 | Proposition 89 | frege89 44952 |
| [Frege1879] p. 68 | Proposition 90 | frege90 44953 |
| [Frege1879] p. 68 | Proposition 91 | frege91 44954 frege91d 44751 |
| [Frege1879] p. 69 | Proposition 92 | frege92 44955 |
| [Frege1879] p. 70 | Proposition 93 | frege93 44956 |
| [Frege1879] p. 70 | Proposition 94 | frege94 44957 |
| [Frege1879] p. 70 | Proposition 95 | frege95 44958 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 44962 |
| [Frege1879] p. 71 | Proposition 96 | frege96 44959 frege96d 44749 |
| [Frege1879] p. 71 | Proposition 97 | frege97 44960 frege97d 44752 |
| [Frege1879] p. 71 | Proposition 98 | frege98 44961 frege98d 44753 |
| [Frege1879] p. 72 | Proposition 100 | frege100 44963 |
| [Frege1879] p. 72 | Proposition 101 | frege101 44964 |
| [Frege1879] p. 72 | Proposition 102 | frege102 44965 frege102d 44754 |
| [Frege1879] p. 73 | Proposition 103 | frege103 44966 |
| [Frege1879] p. 73 | Proposition 104 | frege104 44967 |
| [Frege1879] p. 73 | Proposition 105 | frege105 44968 |
| [Frege1879] p. 73 | Proposition 106 | frege106 44969 frege106d 44755 |
| [Frege1879] p. 74 | Proposition 107 | frege107 44970 |
| [Frege1879] p. 74 | Proposition 108 | frege108 44971 frege108d 44756 |
| [Frege1879] p. 74 | Proposition 109 | frege109 44972 frege109d 44757 |
| [Frege1879] p. 75 | Proposition 110 | frege110 44973 |
| [Frege1879] p. 75 | Proposition 111 | frege111 44974 frege111d 44759 |
| [Frege1879] p. 76 | Proposition 112 | frege112 44975 |
| [Frege1879] p. 76 | Proposition 113 | frege113 44976 |
| [Frege1879] p. 76 | Proposition 114 | frege114 44977 frege114d 44758 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 44978 |
| [Frege1879] p. 77 | Proposition 116 | frege116 44979 |
| [Frege1879] p. 78 | Proposition 117 | frege117 44980 |
| [Frege1879] p. 78 | Proposition 118 | frege118 44981 |
| [Frege1879] p. 78 | Proposition 119 | frege119 44982 |
| [Frege1879] p. 78 | Proposition 120 | frege120 44983 |
| [Frege1879] p. 79 | Proposition 121 | frege121 44984 |
| [Frege1879] p. 79 | Proposition 122 | frege122 44985 frege122d 44760 |
| [Frege1879] p. 79 | Proposition 123 | frege123 44986 |
| [Frege1879] p. 80 | Proposition 124 | frege124 44987 frege124d 44761 |
| [Frege1879] p. 81 | Proposition 125 | frege125 44988 |
| [Frege1879] p. 81 | Proposition 126 | frege126 44989 frege126d 44762 |
| [Frege1879] p. 82 | Proposition 127 | frege127 44990 |
| [Frege1879] p. 83 | Proposition 128 | frege128 44991 |
| [Frege1879] p. 83 | Proposition 129 | frege129 44992 frege129d 44763 |
| [Frege1879] p. 84 | Proposition 130 | frege130 44993 |
| [Frege1879] p. 85 | Proposition 131 | frege131 44994 frege131d 44764 |
| [Frege1879] p. 86 | Proposition 132 | frege132 44995 |
| [Frege1879] p. 86 | Proposition 133 | frege133 44996 frege133d 44765 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 47323 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 47646 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 47346 |
| [Fremlin1] p. 14 | Definition 112A | ismea 47461 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 47481 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 47472 meadjunre 47486 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 47473 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 47474 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 47470 meaiunle 47479 meaiunlelem 47478 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 47491 meaiuninc2 47492 meaiuninc3 47495 meaiuninc3v 47494 meaiunincf 47493 meaiuninclem 47490 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 47497 meaiininc2 47498 meaiininclem 47496 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 47516 caragendifcl 47524 caratheodory 47538 omelesplit 47528 |
| [Fremlin1] p. 19 | Definition 113A | isome 47504 isomennd 47541 isomenndlem 47540 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 47526 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 47545 voncmpl 47631 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 47508 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 47533 carageniuncllem1 47531 carageniuncllem2 47532 caragenuncl 47523 caragenuncllem 47522 caragenunicl 47534 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 47542 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 47536 caratheodorylem2 47537 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 47545 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 47604 hoidmv1lelem1 47601 hoidmv1lelem2 47602 hoidmv1lelem3 47603 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 47648 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 47604 hoidmvle 47610 hoidmvlelem1 47605 hoidmvlelem2 47606 hoidmvlelem3 47607 hoidmvlelem4 47608 hoidmvlelem5 47609 hsphoidmvle2 47595 hsphoif 47586 hsphoival 47589 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 47558 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 47566 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 47593 hoidmvn0val 47594 hoidmvval 47587 hoidmvval0 47597 hoidmvval0b 47600 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 47598 hsphoidmvle 47596 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 47547 df-voln 47549 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 47614 ovn0 47576 ovn0lem 47575 ovnf 47573 ovnome 47583 ovnssle 47571 ovnsslelem 47570 ovnsupge0 47567 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 47613 ovnhoilem1 47611 ovnhoilem2 47612 vonhoi 47677 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 47630 hoidifhspf 47628 hoidifhspval 47618 hoidifhspval2 47625 hoidifhspval3 47629 hspmbl 47639 hspmbllem1 47636 hspmbllem2 47637 hspmbllem3 47638 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 47631 vonmea 47584 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 47582 ovnsubadd2 47656 ovnsubadd2lem 47655 ovnsubaddlem1 47580 ovnsubaddlem2 47581 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 47641 hoimbl2 47675 hoimbllem 47640 hspdifhsp 47626 opnvonmbl 47644 opnvonmbllem2 47643 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 47646 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 47689 iccvonmbllem 47688 ioovonmbl 47687 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 47695 vonicclem2 47694 vonioo 47692 vonioolem2 47691 vonn0icc 47698 vonn0icc2 47702 vonn0ioo 47697 vonn0ioo2 47700 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 47699 snvonmbl 47696 vonct 47703 vonsn 47701 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 47369 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 47368 subsaliuncllem 47367 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 47735 salpreimalegt 47719 salpreimaltle 47736 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 47738 issmff 47744 issmflem 47737 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 47755 issmflelem 47754 smfpreimale 47764 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 47766 issmfgtlem 47765 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 47706 issmf 47738 issmff 47744 issmfge 47780 issmfgelem 47779 issmfgt 47766 issmfgtlem 47765 issmfle 47755 issmflelem 47754 issmflem 47737 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 47717 salpreimagtlt 47740 salpreimalelt 47739 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 47780 issmfgelem 47779 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 47763 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 47761 cnfsmf 47750 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 47777 decsmflem 47776 incsmf 47752 incsmflem 47751 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 47711 pimconstlt1 47712 smfconst 47759 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 47775 smfaddlem1 47773 smfaddlem2 47774 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 47806 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 47805 smfmullem1 47801 smfmullem2 47802 smfmullem3 47803 smfmullem4 47804 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 47807 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 47810 smfpimbor1lem2 47809 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 47812 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 47800 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 47799 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 47808 smfresal 47798 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 47787 smflim2 47816 smflimlem1 47781 smflimlem2 47782 smflimlem3 47783 smflimlem4 47784 smflimlem5 47785 smflimlem6 47786 smflimmpt 47820 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 47824 smfsuplem1 47821 smfsuplem2 47822 smfsuplem3 47823 smfsupmpt 47825 smfsupxr 47826 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 47828 smfinflem 47827 smfinfmpt 47829 |
| [Fremlin1] p. 39 | Remark 121G | smflim 47787 smflim2 47816 smflimmpt 47820 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 47818 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 47848 smfdivdmmbl2 47851 smfinfdmmbl 47859 smfinfdmmbllem 47858 smfsupdmmbl 47855 smfsupdmmbllem 47854 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 47838 smflimsuplem2 47831 smflimsuplem6 47835 smflimsuplem7 47836 smflimsuplem8 47837 smflimsupmpt 47839 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 47841 smfliminflem 47840 smfliminfmpt 47842 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 47706 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 47852 fsupdm2 47853 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 47843 adddmmbl2 47844 finfdm 47856 finfdm2 47857 fsupdm 47852 fsupdm2 47853 muldmmbl 47845 muldmmbl2 47846 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 47856 finfdm2 47857 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 25857 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 25900 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 25910 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 38617 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 38620 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9639 inf1 9623 inf2 9624 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10996 enqer 11006 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 11001 df-nq 10997 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10993 df-plq 10999 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7658 df-mpq 10994 df-mq 11000 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 11002 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 11060 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 11061 ltbtwnnq 11063 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 11056 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 11057 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 11064 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 11066 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 11078 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 11080 |
| [Gleason] p. 122 | Definition | df-1p 11067 |
| [Gleason] p. 122 | Remark (1) | prub 11079 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 11118 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 11070 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 11117 psslinpr 11116 supexpr 11139 suplem1pr 11137 suplem2pr 11138 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 11103 addclprlem1 11101 addclprlem2 11102 df-plp 11068 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 11107 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 11106 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 11119 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 11128 ltexprlem1 11121 ltexprlem2 11122 ltexprlem3 11123 ltexprlem4 11124 ltexprlem5 11125 ltexprlem6 11126 ltexprlem7 11127 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 11130 ltaprlem 11129 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 11131 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 11132 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 11069 mulclpr 11105 mulclprlem 11104 reclem2pr 11133 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 11114 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 11109 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 11108 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 11113 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 11136 reclem3pr 11134 reclem4pr 11135 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 11140 enrer 11148 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 11145 df-1r 11146 df-nr 11141 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 11143 df-plr 11142 negexsr 11187 recexsr 11192 recexsrlem 11188 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 11144 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12315 creur 12314 cru 12312 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11273 axcnre 11249 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15282 crimd 15399 crimi 15360 crre 15281 crred 15398 crrei 15359 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15284 remimd 15365 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15451 absval2d 15615 absval2i 15565 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15308 cjaddd 15387 cjaddi 15355 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15309 cjmuld 15388 cjmuli 15356 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15307 cjcjd 15366 cjcji 15338 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15306 cjreb 15290 cjrebd 15369 cjrebi 15341 cjred 15393 rere 15289 rereb 15287 rerebd 15368 rerebi 15340 rered 15391 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15315 addcjd 15379 addcji 15350 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15405 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15446 abscjd 15620 abscji 15569 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15456 abs00d 15616 abs00i 15566 absne0d 15617 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15489 releabsd 15621 releabsi 15570 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15461 absmuld 15624 absmuli 15572 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15449 sqabsaddi 15573 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15498 abstrid 15626 abstrii 15576 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 14205 exp0 14208 expp1 14211 expp1d 14290 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 27007 cxpaddd 27045 expadd 14247 expaddd 14291 expaddz 14249 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 27016 cxpmuld 27065 expmul 14250 expmuld 14292 expmulz 14251 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 27013 mulcxpd 27056 mulexp 14244 mulexpd 14304 mulexpz 14245 |
| [Gleason] p. 140 | Exercise 1 | znnen 16380 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13641 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15799 rlimadd 15810 rlimdiv 15813 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15801 rlimsub 15811 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15800 rlimmul 15812 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15804 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15750 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15771 climcj 15772 climim 15774 climre 15773 rlimabs 15776 rlimcj 15777 rlimim 15779 rlimre 15778 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11348 df-xr 11347 ltxr 13244 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15638 limsupval 15641 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15837 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15846 caucvgb 15847 caucvgbf 46499 caucvgr 15843 climcau 15838 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15983 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 16052 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15503 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13968 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 21672 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 24662 xmet0 24661 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 24678 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 24669 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 24671 mstri 24788 xmettri 24670 xmstri 24787 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 24701 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 23967 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 25631 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 24859 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 25185 addcn2 15761 mulcn 25187 mulcn2 15763 subcn 25186 subcn2 15762 |
| [Gleason] p. 295 | Remark | bcval3 14450 bcval4 14451 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14465 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14448 df-bc 14447 |
| [Gleason] p. 296 | Remark | bcn0 14454 bcnn 14456 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15999 |
| [Gleason] p. 308 | Equation 2 | ef0 16257 |
| [Gleason] p. 308 | Equation 3 | efcj 16258 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 16264 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 16269 |
| [Gleason] p. 310 | Equation 14 | sinadd 16332 |
| [Gleason] p. 310 | Equation 15 | cosadd 16333 |
| [Gleason] p. 311 | Equation 17 | sincossq 16344 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16349 sinbnd 16348 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14360 sqeqori 14358 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 16238 |
| [Godowski] p. 730 | Equation SF | goeqi 32875 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 32270 |
| [Golan] p. 1 | Remark | srgisid 20435 |
| [Golan] p. 1 | Definition | df-srg 20413 |
| [Golan] p. 149 | Definition | df-slmd 33762 |
| [Gonshor] p. 7 | Definition | df-cuts 28146 |
| [Gonshor] p. 9 | Theorem 2.5 | lesrec 28185 lesrecd 28186 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 28306 cofcut1d 28307 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 28308 cofcut2d 28309 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 28310 cofcutr1d 28311 cofcutr2d 28312 |
| [Gonshor] p. 13 | Definition | df-adds 28346 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 28362 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 28388 |
| [Gonshor] p. 17 | Theorem 3.4 | mulsprop 28516 |
| [Gonshor] p. 18 | Theorem 3.5 | mulsunif 28536 |
| [Gonshor] p. 28 | Lemma 4.2 | halfcut 28844 |
| [Gonshor] p. 28 | Theorem 4.2 | pw2cut 28846 |
| [Gonshor] p. 30 | Theorem 4.2 | addhalfcut 28845 |
| [Gonshor] p. 39 | Theorem 4.4(b) | elreno2 28881 |
| [Gonshor] p. 95 | Theorem 6.1 | addbday 28404 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 36924 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17756 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17758 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 49285 df-cllaw 49283 df-comlaw 49284 |
| [Hall] p. 2 | Section 1.2 | df-clintop 49297 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 49318 |
| [Halmos] p. 28 | Partition ` ` | df-parts 39801 dfmembpart2 39806 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 32667 riesz2 32668 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 32543 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 32775 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 32787 elpjidm 32786 pjnmopi 32750 |
| [Halmos] p. 44 | Remark | pjinormi 32289 pjinormii 32278 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 32791 pjrn 32309 pjrni 32304 pjvec 32298 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 32329 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 32756 hmopidmpji 32754 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 32793 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 32782 pjocvec 32299 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 32771 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 32774 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 32777 pjssdif2i 32776 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 32457 |
| [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 1828 |
| [Hatcher] p. 25 | Definition | df-phtpc 25313 df-phtpy 25292 |
| [Hatcher] p. 26 | Definition | df-pco 25326 df-pi1 25329 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 25316 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 25371 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 22805 df-dmatalt 49510 |
| [Helfgott] p. 2 | Theorem | tgoldbach 48915 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 48900 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 48912 bgoldbtbnd 48907 bgoldbtbnd 48907 tgblthelfgott 48913 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 35271 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 35272 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 35286 hgt750lemb 35285 hgt750leme 35287 hgt750lemf 35282 hgt750lemg 35283 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 48909 tgoldbachgt 35292 tgoldbachgtALTV 48910 tgoldbachgtd 35291 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 35273 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 31095 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 19155 grpoideu 31111 mndideu 18934 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 19185 grpoinveu 31121 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 19216 grpo2inv 31133 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 19228 grpoinvop 31135 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 19250 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1801 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1802 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1804 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 33022 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 33035 cdj3i 33043 cdj3lem1 33036 cdjreui 33034 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 33033 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 43019 |
| [Holland95] p. 14 | Line 15 | hgmapvs 42949 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 42971 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 42972 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 42969 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 42975 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 42894 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 42989 |
| [Holland95] p. 204 | Definition of involution | df-srng 21097 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 40561 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 42586 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 42539 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 40991 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 42435 poml4N 41011 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 42526 pexmidALTN 41036 pexmidN 41027 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 42591 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 40182 ldualset 40183 |
| [Holland95] p. 222 | Item 1 | df-lines 40559 df-pointsN 40560 |
| [Holland95] p. 222 | Item 2 | df-polarityN 40961 |
| [Holland95] p. 223 | Remark | ispsubcl2N 41005 omllaw4 40304 pol1N 40968 polcon3N 40975 |
| [Holland95] p. 223 | Definition | df-psubclN 40993 |
| [Holland95] p. 223 | Equation for polarity | polval2N 40964 |
| [Holmes] p. 40 | Definition | df-xrn 39313 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 31686 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 32784 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 32565 eigre 32437 eigrei 32436 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 32566 eigorth 32440 eigorthi 32439 |
| [Hughes] p. 137 | Remark (ii) | eigposi 32438 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 30910 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 30906 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 30907 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 30908 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 30926 frgrregorufr0 30925 frgrregorufrg 30927 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 30933 frrusgrord 30942 frrusgrord0 30941 |
| [Huneke] p. 2 | Statement | df-clwwlknon 30679 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 30916 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 30919 frgrwopreg2 30920 frgrwopregasn 30917 frgrwopregbsn 30918 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 30922 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 30936 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 30939 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 30677 numclwlk1 30972 numclwlk1lem1 30970 numclwlk1lem2 30971 numclwwlk1 30962 numclwwlk8 30993 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 30913 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 30358 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 30948 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 30974 numclwwlkovh0 30973 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 30982 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 30569 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 30986 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 30989 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 30992 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 31004 natded 31004 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 31004 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 31004 natded 31004 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 31004 |
| [Jech] p. 4 | Definition of class | cv 1569 cvjust 2755 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10664 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10662 alephmul 10663 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10661 infmap2 10295 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9822 |
| [Jech] p. 72 | Equation 9.3 | df-scott 9929 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9884 rankval4b 9880 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9954 |
| [Jech] p. 78 | Note | opthprc 5715 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 43922 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 44010 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 44011 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 43934 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 43938 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 43939 rmyp1 43940 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 43941 rmym1 43942 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 43932 rmx1 43933 rmxluc 43943 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 43936 rmy1 43937 rmyluc 43944 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 43946 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 43947 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 43967 jm2.17b 43968 jm2.17c 43969 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 44000 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 44004 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 43995 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 43970 jm2.24nn 43966 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 44009 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 44015 rmygeid 43971 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 44027 |
| [Juillerat] p. 11 | Section *5 | etransc 47293 etransclem47 47291 etransclem48 47292 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 47288 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 47290 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 47276 |
| [Juillerat] p. 13 | Proof | etransclem35 47279 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 47282 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 47268 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 47285 |
| [Juillerat] p. 14 | Proof | etransclem23 47267 |
| [KalishMontague] p. 81 | Note 1 | ax-6 2000 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2045 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2050 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2040 cbvaliw 2039 wl-cbvmotv 38446 wl-motae 38448 wl-moteq 38447 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 2019 spimw 2003 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2066 spw 2067 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 32118 chabs1i 32120 chabs2 32119 chabs2i 32121 chjass 32135 chjassi 32088 latabs1 18649 latabs2 18650 |
| [Kalmbach] p. 15 | Definition of atom | df-at 32940 ela 32941 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 32885 cvrval2 40332 |
| [Kalmbach] p. 16 | Definition | df-ol 40236 df-oml 40237 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 32186 cmbri 32192 cmtvalN 40269 df-cm 32185 df-cmtN 40235 |
| [Kalmbach] p. 22 | Remark | omllaw5N 40305 pjoml5 32215 pjoml5i 32190 |
| [Kalmbach] p. 22 | Definition | pjoml2 32213 pjoml2i 32187 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 32216 cmcmi 32194 cmcmii 32199 cmtcomN 40307 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 40303 omlsi 32006 pjoml 32038 pjomli 32037 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 40302 |
| [Kalmbach] p. 23 | Remark | cmbr2i 32198 cmcm3 32217 cmcm3i 32196 cmcm3ii 32201 cmcm4i 32197 cmt3N 40309 cmt4N 40310 cmtbr2N 40311 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 32210 cmbr3i 32202 cmtbr3N 40312 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 32220 fh1i 32223 fh2 32221 fh2i 32224 omlfh1N 40316 |
| [Kalmbach] p. 65 | Remark | chjatom 32959 chslej 32100 chsleji 32060 shslej 31982 shsleji 31972 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 32097 chocini 32056 chsupcl 31942 chsupval2 32012 h0elch 31857 helch 31845 hsupval2 32011 ocin 31898 ococss 31895 shococss 31896 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 31914 |
| [Kalmbach] p. 66 | Remark | df-pjh 31997 pjssmi 32767 pjssmii 32283 |
| [Kalmbach] p. 67 | Lemma 3 | osum 32247 osumi 32244 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 32802 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 33002 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 32912 |
| [Kalmbach] p. 140 | Remark | hatomic 32962 hatomici 32961 hatomistici 32964 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 40377 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 32983 lsatexch 40101 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 32957 cvlcvr1 40397 cvr1 40468 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 32976 cvexchi 32971 cvrexch 40478 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 32966 hlrelat 40460 hlrelat5N 40459 lrelat 40072 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 21419 lsmsatcv 40068 spansncv 32255 spansncvi 32254 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 40087 spansncv2 32895 |
| [Kalmbach] p. 266 | Definition | df-st 32813 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 32451 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10731 fpwwe2 10728 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10732 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10739 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10734 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10736 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10749 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10753 gchxpidm 10754 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10765 gchhar 10764 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10293 unxpwdom 9583 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10755 |
| [Kreyszig] p. 3 | Property M1 | metcl 24651 xmetcl 24650 |
| [Kreyszig] p. 4 | Property M2 | meteq0 24658 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 24891 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 12034 muleqadd 11960 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 24757 |
| [Kreyszig] p. 19 | Remark | mopntopon 24758 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 24817 mopnm 24763 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 24815 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 24820 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 24861 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 23576 lmmbr 25579 lmmbr2 25580 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 23698 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 25634 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 25597 iscmet2 25615 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 25637 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 23780 metelcls 25626 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 25627 metcld2 25628 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 25420 lmodvneg1 21180 nvinv 31241 vcm 31178 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 25416 lmod0vs 21170 slmd0vs 33785 vc0 31176 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 21171 slmdvs0 33786 vcz 31177 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 31293 ngpmet 24922 nrmmetd 24893 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 31288 imsdval2 31289 ncvspds 25482 ngpds 24923 |
| [Kreyszig] p. 63 | Problem 1 | nmval 24908 nvnd 31290 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 24937 nmge0 24936 nvge0 31275 nvz 31271 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 24943 nvabs 31274 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 31403 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 31347 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 31409 blocni 31407 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 31408 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 25525 ipeq0 21944 ipz 31321 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 25537 pythi 31452 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 31456 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 25559 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 16025 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 25757 minveco 31486 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 31352 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 25650 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 31475 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 32725 leopg 32724 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 32743 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 31520 |
| [Kulpa] p. 547 | Theorem | poimir 38572 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 38571 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 38570 |
| [Kulpa] p. 548 | Theorem | broucube 38573 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 38565 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 38566 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2413 axnul 5259 |
| [Kunen] p. 11 | Axiom 3 | axnul 5259 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 5242 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8858 mapvalg 8856 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10600 |
| [Kunen] p. 31 | Definition 10.24 | mapex 7952 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9768 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9814 r1elssi 9813 |
| [Kunen] p. 107 | Exercise 4 | rankop 9872 rankopb 9866 rankuni 9879 rankxplim 9896 rankxpsuc 9899 |
| [Kunen2] p. 47 | Lemma I.9.9 | relpfr 45944 |
| [Kunen2] p. 53 | Lemma I.9.21 | trfr 45952 |
| [Kunen2] p. 53 | Lemma I.9.24(2) | wffr 45951 |
| [Kunen2] p. 53 | Definition I.9.20 | tcfr 45953 |
| [Kunen2] p. 95 | Lemma I.16.2 | ralabso 45958 rexabso 45959 |
| [Kunen2] p. 96 | Example I.16.3 | disjabso 45965 n0abso 45966 ssabso 45964 |
| [Kunen2] p. 111 | Lemma II.2.4(1) | traxext 45967 |
| [Kunen2] p. 111 | Lemma II.2.4(2) | sswfaxreg 45977 |
| [Kunen2] p. 111 | Lemma II.2.4(3) | ssclaxsep 45972 |
| [Kunen2] p. 111 | Lemma II.2.4(4) | prclaxpr 45975 |
| [Kunen2] p. 111 | Lemma II.2.4(5) | uniclaxun 45976 |
| [Kunen2] p. 111 | Lemma II.2.4(6) | modelaxrep 45971 |
| [Kunen2] p. 112 | Corollary II.2.5 | wfaxext 45983 wfaxpr 45988 wfaxreg 45990 wfaxrep 45984 wfaxsep 45985 wfaxun 45989 |
| [Kunen2] p. 113 | Lemma II.2.8 | pwclaxpow 45974 |
| [Kunen2] p. 113 | Corollary II.2.9 | wfaxpow 45987 |
| [Kunen2] p. 114 | Theorem II.2.13 | wfaxext 45983 |
| [Kunen2] p. 114 | Lemma II.2.11(7) | modelac8prim 45982 omelaxinf2 45979 |
| [Kunen2] p. 114 | Corollary II.2.12 | wfac8prim 45992 wfaxinf2 45991 |
| [Kunen2] p. 148 | Exercise II.9.2 | nregmodelf1o 46005 permaxext 45995 permaxinf2 46003 permaxnul 45998 permaxpow 45999 permaxpr 46000 permaxrep 45996 permaxsep 45997 permaxun 46001 |
| [Kunen2] p. 148 | Definition II.9.1 | brpermmodel 45993 |
| [Kunen2] p. 149 | Exercise II.9.3 | permac8prim 46004 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4964 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 34297 |
| [Lang] p. | Definition | df-rn 5662 |
| [Lang] p. 3 | Statement | lidrideqd 18850 mndbn0 18940 |
| [Lang] p. 3 | Definition | df-mnd 18924 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18876 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 19037 |
| [Lang] p. 5 | Equation | gsumreidx 20131 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 49279 |
| [Lang] p. 6 | Example | nn0mnd 49276 |
| [Lang] p. 6 | Equation | gsumxp2 20194 |
| [Lang] p. 6 | Statement | cycsubm 19417 |
| [Lang] p. 6 | Definition | mulgnn0gsum 19290 |
| [Lang] p. 6 | Observation | mndlsmidm 19884 |
| [Lang] p. 7 | Definition | dfgrp2e 19174 |
| [Lang] p. 30 | Definition | df-tocyc 33668 |
| [Lang] p. 32 | Property (a) | cyc3genpm 33713 |
| [Lang] p. 32 | Property (b) | cyc3conja 33718 cycpmconjv 33703 |
| [Lang] p. 53 | Definition | df-cat 17842 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 18272 cat1lem 18271 |
| [Lang] p. 54 | Definition | df-iso 17924 |
| [Lang] p. 57 | Definition | df-inito 18159 df-termo 18160 |
| [Lang] p. 58 | Example | irinitoringc 21785 |
| [Lang] p. 58 | Statement | initoeu1 18186 termoeu1 18193 |
| [Lang] p. 62 | Definition | df-func 18033 |
| [Lang] p. 65 | Definition | df-nat 18121 |
| [Lang] p. 83 | Definition of "ring with unit" | dfring2 20517 |
| [Lang] p. 91 | Note | df-ringc 20898 |
| [Lang] p. 92 | Statement | mxidlprm 33995 |
| [Lang] p. 92 | Definition | isprmidlc 21628 |
| [Lang] p. 128 | Remark | dsmmlmod 22051 |
| [Lang] p. 129 | Proof | lincscm 49542 lincscmcl 49544 lincsum 49541 lincsumcl 49543 |
| [Lang] p. 129 | Statement | lincolss 49546 |
| [Lang] p. 129 | Observation | dsmmfi 22044 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 34259 qusdimsum 34260 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 34240 |
| [Lang] p. 147 | Definition | snlindsntor 49583 |
| [Lang] p. 504 | Statement | mat1 22762 matring 22758 |
| [Lang] p. 504 | Definition | df-mamu 22706 |
| [Lang] p. 505 | Statement | mamuass 22717 mamutpos 22773 matassa 22759 mattposvs 22770 tposmap 22772 |
| [Lang] p. 513 | Definition | mdet1 22916 mdetf 22910 |
| [Lang] p. 513 | Theorem 4.4 | cramer 23009 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 22902 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 22926 |
| [Lang] p. 515 | Definition | df-minmar1 22950 smadiadetr 22990 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 22925 mdetralt 22923 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 22938 |
| [Lang] p. 518 | Definition | df-madu 22949 |
| [Lang] p. 518 | Proposition 4.16 | madulid 22960 madurid 22959 matinv 22992 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 23208 |
| [Lang], p. 190 | Chapter 6 | vieta 34212 |
| [Lang], p. 224 | Proposition 1.1 | extdgfialg 34326 finextalg 34330 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 34295 fedgmul 34263 |
| [Lang], p. 225 | Proposition 1.4 | algextdeg 34357 |
| [Lang], p. 561 | Remark | chpmatply1 23150 |
| [Lang], p. 561 | Definition | df-chpmat 23145 |
| [Lang2] p. 3 | Notations | df-ind 12321 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 45318 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 45313 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 45319 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5259 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2740 wl-df.clab 38431 |
| [Levy] p. 59 | Definition | df-ttrcl 9709 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9755 |
| [Levy] p. 338 | Axiom | df-clel 2836 df-cleq 2753 wl-df.cleq 38432 |
| [Levy] p. 338 | Axiom. See also comments under ~ df-clab , ~ df-cleq , and ~ eqabb . Alternate characterizations | wl-df.clel 38435 |
| [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 38435 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2836 df-cleq 2753 wl-df.cleq 38432 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2740 wl-df.clab 38431 |
| [Levy] p. 358 | Axiom | df-clab 2740 wl-df.clab 38431 |
| [Levy58] p. 2 | Definition I | isfin1-3 10464 |
| [Levy58] p. 2 | Definition II | df-fin2 10364 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10363 |
| [Levy58] p. 2 | Definition III | df-fin3 10366 |
| [Levy58] p. 3 | Definition V | df-fin5 10367 |
| [Levy58] p. 3 | Definition IV | df-fin4 10365 |
| [Levy58] p. 4 | Definition VI | df-fin6 10368 |
| [Levy58] p. 4 | Definition VII | df-fin7 10369 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10493 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 28043 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 28054 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 28086 nosupbnd1 28071 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 28088 nosupbnd2 28073 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 28092 noetasuplem4 28093 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 28089 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1801 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1802 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1804 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 33010 |
| [Maeda] p. 168 | Lemma 5 | mdsym 33014 mdsymi 33013 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 33008 mdsymlem6 33010 mdsymlem7 33011 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 33012 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 32915 ssdmd2 32916 ssmd1 32913 ssmd2 32914 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 32911 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 32883 df-md 32882 mdbr 32896 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 32933 mdslj1i 32921 mdslj2i 32922 mdslle1i 32919 mdslle2i 32920 mdslmd1i 32931 mdslmd2i 32932 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 32923 mdsl2bi 32925 mdsl2i 32924 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 32937 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 32934 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 32935 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 32912 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 32917 mdsl3 32918 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 32936 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 33031 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 40379 hlrelat1 40458 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 40097 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 32938 cvmdi 32926 cvnbtwn4 32891 cvrnbtwn4 40337 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 32939 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 40398 cvp 32977 cvrp 40474 lcvp 40098 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 33001 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 33000 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 40391 hlexch4N 40450 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 33003 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 40501 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 40807 atpsubN 40811 df-pointsN 40560 pointpsubN 40809 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 40562 pmap11 40820 pmaple 40819 pmapsub 40826 pmapval 40815 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 40823 pmap1N 40825 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 40828 pmapglb2N 40829 pmapglb2xN 40830 pmapglbx 40827 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 40910 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 40535 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 40854 paddclN 40900 paddidm 40899 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 40536 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 40896 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 40535 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 40536 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19889 lsmmod2 19890 lssats 40070 shatomici 32960 shatomistici 32963 shmodi 31992 shmodsi 31991 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 32902 mdsymlem7 33011 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 32191 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 32095 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 33017 |
| [Margaris] p. 40 | Rule C | exlimiv 1963 |
| [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 402 df-ex 1813 df-or 862 dfbi2 480 |
| [Margaris] p. 51 | Theorem 1 | idALT 24 |
| [Margaris] p. 56 | Theorem 3 | conventions 31001 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 45897 |
| [Margaris] p. 60 | Theorem 8 | jcn 163 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 45898 |
| [Margaris] p. 79 | Rule C | exinst01 45608 exinst11 45609 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 2009 19.2g 2225 r19.2z 4455 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2239 rr19.3v 3621 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2196 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1859 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1814 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2218 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2242 19.9h 2320 exlimd 2255 exlimdh 2324 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2199 excomim 2200 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2358 |
| [Margaris] p. 90 | Section 19 | conventions-labels 31002 conventions-labels 31002 conventions-labels 31002 conventions-labels 31002 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1860 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 45362 albi 1851 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2262 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2263 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 45364 exbi 1880 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2266 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 45361 2alimdv 1951 alimd 2249 alimdh 1850 alimdv 1949 ax-4 1842 ralimdaa 3264 ralimdv 3177 ralimdva 3175 ralimdvva 3210 sbcimdv 3807 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2244 19.21h 2321 19.21t 2243 19.21vv 45360 alrimd 2252 alrimdd 2251 alrimdh 1896 alrimdv 1962 alrimi 2250 alrimih 1857 alrimiv 1960 alrimivv 1961 bj-alrimdh 37494 hbralrimi 3153 r19.21be 3256 r19.21bi 3255 ralrimd 3268 ralrimdv 3161 ralrimdva 3163 ralrimdvv 3207 ralrimdvva 3218 ralrimi 3261 ralrimia 3262 ralrimiv 3154 ralrimiva 3155 ralrimivv 3204 ralrimivva 3206 ralrimivvva 3209 ralrimivw 3159 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 45363 2eximdv 1952 bj-exim 37509 exim 1867 eximd 2253 eximdh 1897 eximdv 1950 rexim 3104 reximd2a 3273 reximdai 3265 reximdd 46163 reximddv 3179 reximddv2 3222 reximddv3 3180 reximdv 3178 reximdv2 3173 reximdva 3176 reximdvai 3174 reximdvva 3211 reximi2 3096 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2248 19.23bi 2228 19.23h 2322 19.23t 2247 exlimdv 1966 exlimdvv 1967 exlimexi 45507 exlimiv 1963 exlimivv 1965 rexlimd3 46159 rexlimdv 3162 rexlimdv3a 3168 rexlimdva 3164 rexlimdva2 3166 rexlimdvaa 3165 rexlimdvv 3219 rexlimdvva 3220 rexlimdvvva 3221 rexlimdvw 3169 rexlimiv 3157 rexlimiva 3156 rexlimivv 3205 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 2024 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1913 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1903 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2264 r19.27z 4466 r19.27zv 4467 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2265 19.28vv 45370 r19.28z 4458 r19.28zf 46174 r19.28zv 4462 rr19.28v 3622 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1906 r19.29d2r 3150 r19.29imd 3128 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1914 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2271 19.31vv 45368 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2270 r19.32 48168 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 45366 19.33 1917 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 2025 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1910 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2267 19.36vv 45367 r19.36zv 4468 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2269 19.37vv 45369 r19.37zv 4463 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1872 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 2023 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1920 19.40 1919 r19.40 3129 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2272 19.41rg 45533 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2273 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1915 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2274 r19.44zv 4465 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2275 r19.45zv 4464 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2636 |
| [Mayet] p. 370 | Remark | jpi 32872 largei 32869 stri 32859 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 32814 ishst 32816 |
| [Mayet3] p. 10 | Theorem | hstrbi 32868 hstri 32867 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 32330 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 32331 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 32880 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 31934 chsupcl 31942 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 32962 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 32956 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 32983 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 41041 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18661 latj32 18659 latjass 18657 |
| [Megill] p. 444 | Axiom C5 | ax-5 1943 ax5ALT 39965 |
| [Megill] p. 444 | Section 7 | conventions 31001 |
| [Megill] p. 445 | Lemma L12 | aecom-o 39959 ax-c11n 39946 axc11n 2456 |
| [Megill] p. 446 | Lemma L17 | equtrr 2055 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 39954 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 39986 hbnae 2462 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2511 sbid 2291 sbidd-misc 50812 sbidd 50811 |
| [Megill] p. 448 | Remark 9.6 | axc14 2493 |
| [Megill] p. 448 | Scheme C4' | ax-c4 39942 |
| [Megill] p. 448 | Scheme C5' | ax-c5 39941 sp 2220 |
| [Megill] p. 448 | Scheme C6' | ax-11 2194 |
| [Megill] p. 448 | Scheme C7' | ax-c7 39943 |
| [Megill] p. 448 | Scheme C8' | ax-7 2041 |
| [Megill] p. 448 | Scheme C9' | ax-c9 39948 |
| [Megill] p. 448 | Scheme C10' | ax-6 2000 ax-c10 39944 |
| [Megill] p. 448 | Scheme C11' | ax-c11 39945 |
| [Megill] p. 448 | Scheme C12' | ax-8 2147 |
| [Megill] p. 448 | Scheme C13' | ax-9 2155 |
| [Megill] p. 448 | Scheme C14' | ax-c14 39949 |
| [Megill] p. 448 | Scheme C15' | ax-c15 39947 |
| [Megill] p. 448 | Scheme C16' | ax-c16 39950 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 39962 dral1 2469 dral2-o 39988 dral2 2468 drex1 2471 drex2 2472 drsb1 2525 drsb2 2301 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2209 sbequ 2120 sbid2v 2539 |
| [Megill] p. 450 | Example in Appendix | hba1-o 39955 hba1 2327 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 47962 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 24 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3826 rspsbca 3827 stdpc4 2105 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 39942 ra4 3833 stdpc5 2245 |
| [Mendelson] p. 81 | Rule C | exlimiv 1963 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2061 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2286 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3738 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5487 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4348 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4349 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4223 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4280 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4224 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4088 |
| [Mendelson] p. 231 | Definition of union | dfun3 4222 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5419 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4864 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5542 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4575 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5543 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4891 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5804 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6271 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7789 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6368 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8604 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9159 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 9080 xpsneng 9081 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9087 xpcomeng 9088 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9090 |
| [Mendelson] p. 255 | Definition | brsdom 9001 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9083 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8851 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 9065 mapsnend 9064 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9165 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9164 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8910 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 9068 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9084 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10257 djucomen 10256 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10261 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10255 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8539 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8566 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10643 |
| [Mendelson] p. 281 | Definition | df-r1 9768 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9821 |
| [Mendelson] p. 287 | Axiom system MK | ru 3738 |
| [MertziosUnger] p. 152 | Definition | df-frgr 30860 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 30895 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 30897 vdgn1frgrv3 30898 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 30899 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 30892 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 30885 2pthfrgrrn 30883 2pthfrgrrn2 30884 |
| [Mittelstaedt] p. 9 | Definition | df-oc 31854 |
| [Monk1] p. 22 | Remark | conventions 31001 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 31001 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4184 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5759 ssrelf 33209 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5760 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5168 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6264 coi2 6265 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5902 rn0 5908 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5863 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5669 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5911 rnxp 6162 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5750 xp0 5751 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6075 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6072 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7926 imaexg 7925 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6197 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7075 funfvop 7049 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6939 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6950 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6586 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7258 dff13f 7259 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7225 funrnex 7966 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7251 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6228 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4924 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 8018 df-1st 8001 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 8019 df-2nd 8002 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9868 ranksnb 9837 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9869 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9870 rankunb 9864 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9850 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9768 r1val2 9849 |
| [Monk1] p. 117 | Lemma | zorn2 10584 zorn2g 10581 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 10067 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10645 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 10062 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1842 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2041 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2213 ax-c15 39947 ax12v2 2215 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 39942 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2194 |
| [Monk2] p. 109 | Lemma 15 | equvini 2485 equvinv 2062 eqvinop 5456 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1943 ax5ALT 39965 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2178 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2194 |
| [Monk2] p. 114 | Lemma 21 | sp 2220 |
| [Monk2] p. 114 | Lemma 22 | axc4 2352 hba1-o 39955 hba1 2327 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2190 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2210 nfra2 3362 nfra2w 3299 |
| [Moore] p. 53 | Part I | df-mre 17756 |
| [Munkres] p. 77 | Example 2 | distop 23313 indistop 23320 indistopon 23319 |
| [Munkres] p. 77 | Example 3 | fctop 23322 fctop2 23323 |
| [Munkres] p. 77 | Example 4 | cctop 23324 |
| [Munkres] p. 78 | Definition of basis | df-bases 23264 isbasis3g 23267 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17614 tgval2 23274 |
| [Munkres] p. 79 | Remark | tgcl 23287 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 23281 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 23305 tgss3 23304 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 23306 basgen2 23307 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 38273 topdifinfeq 38274 topdifinffin 38272 topdifinfindis 38270 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 23478 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 23356 topcld 23353 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 23357 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 23359 |
| [Munkres] p. 94 | Definition of closure | clsval 23355 |
| [Munkres] p. 94 | Definition of interior | ntrval 23354 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 23393 elcls 23391 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 23401 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 23466 neindisj 23435 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 23468 |
| [Munkres] p. 97 | Definition of limit point | islp2 23463 lpval 23457 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 23633 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 23545 iscn 23553 iscn2 23556 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 23598 cncnp2 23599 cncnpi 23596 df-cnp 23546 iscnp 23555 iscnp2 23557 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 24862 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 25632 |
| [Nathanson] p. 123 | Remark | reprgt 35250 reprinfz1 35251 reprlt 35248 |
| [Nathanson] p. 123 | Definition | df-repr 35238 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 35270 |
| [Nathanson] p. 123 | Proposition | breprexp 35262 breprexpnat 35263 itgexpif 35235 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 32706 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 48908 |
| [Pfenning] p. 17 | Definition XM | natded 31004 |
| [Pfenning] p. 17 | Definition NNC | natded 31004 notnotrd 134 |
| [Pfenning] p. 17 | Definition ` `C | natded 31004 |
| [Pfenning] p. 18 | Rule" | natded 31004 |
| [Pfenning] p. 18 | Definition /\I | natded 31004 |
| [Pfenning] p. 18 | Definition ` `E | natded 31004 natded 31004 natded 31004 natded 31004 natded 31004 |
| [Pfenning] p. 18 | Definition ` `I | natded 31004 natded 31004 natded 31004 natded 31004 natded 31004 |
| [Pfenning] p. 18 | Definition ` `EL | natded 31004 |
| [Pfenning] p. 18 | Definition ` `ER | natded 31004 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 31004 |
| [Pfenning] p. 18 | Definition ` `IR | natded 31004 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 31004 |
| [Pfenning] p. 127 | Definition =E | natded 31004 |
| [Pfenning] p. 127 | Definition =I | natded 31004 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 25523 df-dip 31303 dip0l 31320 ip0l 21942 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 25564 ipval 31305 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 31316 ipcj 21940 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 25526 dipdir 31444 ipdir 21945 ipdiri 31432 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 31312 nmsq 25515 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 31427 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 31429 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 31430 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 25532 dipass 31447 ipass 21951 ipassi 31443 |
| [Prugovecki] p. 186 | Definition of bra | braval 32546 df-bra 32452 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 32453 kbval 32556 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 32984 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 40946 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 32998 atcvat4i 32999 cvrat3 40500 cvrat4 40501 lsatcvat3 40110 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 32884 cvrval 40327 df-cv 32881 df-lcv 40077 lspsncv0 21424 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 40958 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 40959 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2740 rabid 3433 rabidd 46170 wl-df.clab 38431 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2313 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2753 wl-df.cleq 38432 |
| [Quine] p. 19 | Definition 2.9 | conventions 31001 df-v 3453 |
| [Quine] p. 34 | Theorem 5.1 | eqabb 2900 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2897 abid2f 2953 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2310 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2122 sbalex 2279 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2836 wl-df.clel 38435 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2761 eqid1 31068 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2768 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3740 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3741 dfsbcq2 3742 |
| [Quine] p. 43 | Theorem 6.8 | vex 3455 |
| [Quine] p. 43 | Theorem 6.9 | isset 3465 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3546 spcgv 3551 spcimgf 3514 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3752 spsbcd 3753 |
| [Quine] p. 44 | Theorem 6.12 | elex 3472 |
| [Quine] p. 44 | Theorem 6.13 | elab 3633 elabg 3630 elabgf 3628 |
| [Quine] p. 44 | Theorem 6.14 | noel 4284 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4678 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4587 df-sn 4585 |
| [Quine] p. 49 | Theorem 7.4 | snss 4745 snssg 4744 |
| [Quine] p. 49 | Theorem 7.5 | prss 4781 prssg 4780 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4723 prid1g 4721 prid2 4724 prid2g 4722 snid 4623 snidg 4621 |
| [Quine] p. 51 | Theorem 7.12 | snex 5397 |
| [Quine] p. 51 | Theorem 7.13 | prex 5396 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4886 unisnALT 45908 unisng 4885 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4890 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4899 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4896 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6508 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 48156 dfiota2 6495 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 48165 iotaval 6512 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6518 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6514 |
| [Quine] p. 58 | Definition 9.1 | df-op 4591 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5499 opabidw 5498 opelopab 5517 opelopaba 5510 opelopabaf 5519 opelopabf 5520 opelopabg 5513 opelopabga 5507 opelopabgf 5515 oprabid 7452 oprabidw 7451 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5657 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5659 |
| [Quine] p. 64 | Definition 9.15 | df-id 5546 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6605 |
| [Quine] p. 65 | Theorem 10.4 | funi 6572 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6593 funsng 6591 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6540 |
| [Quine] p. 65 | Definition 10.2 | args 6090 dffv4 6882 |
| [Quine] p. 68 | Definition 10.11 | conventions 31001 df-fv 6546 fv2 6880 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14416 nn0opth2i 14415 nn0opthi 14414 omopthi 8670 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8418 |
| [Quine] p. 232 | Equation i | carddom 10638 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6627 funimaexg 6626 |
| [Quine] p. 331 | Axiom system NF | ru 3738 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 31686 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 31303 polid 31761 polid2i 31759 polidi 31760 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 31415 |
| [ReedSimon] p. 195 | Remark | lnophm 32621 lnophmi 32620 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 32734 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 32736 leopmuli 32735 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 32739 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 32454 leoppos 32728 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 32738 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 32727 |
| [Ribenboim] p. 181 | Remark | nprmdvdsfacm1 48709 |
| [Ribenboim], p. 181 | Statement | ppivalnn 48717 |
| [Roman] p. 4 | Definition | df-dmat 22805 df-dmatalt 49510 |
| [Roman] p. 18 | Part Preliminaries | df-rng 20375 |
| [Roman] p. 19 | Part Preliminaries | df-ring 20461 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 49597 |
| [Roman] p. 112 | Note | isldepslvec2 49597 ldepsnlinc 49620 zlmodzxznm 49609 |
| [Roman] p. 112 | Example | zlmodzxzequa 49608 zlmodzxzequap 49611 zlmodzxzldep 49616 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 23208 |
| [Rosenlicht] p. 80 | Theorem | heicant 38574 |
| [Rosser] p. 281 | Definition | df-op 4591 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 35274 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 35275 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 49478 pmtr3ncom 19689 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19685 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19628 cayleyth 19629 |
| [Rudin] p. 164 | Equation 27 | efcan 16262 |
| [Rudin] p. 164 | Equation 30 | efzval 16270 |
| [Rudin] p. 167 | Equation 48 | absefi 16364 |
| [Russell1905] p. 482 | Example of "the father | dfalseu2 50932 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 200 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1804 |
| [Sanford] p. 39 | Rule 4 | mptxor 1802 |
| [Sanford] p. 40 | Rule 1 | mptnan 1801 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6109 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6112 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6108 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6106 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17756 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17757 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17757 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17759 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10215 |
| [Schechter] p. 141 | Definition (MC) | dfac11 44064 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10524 axdc3 10532 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 20463 isrngo 38832 |
| [Schechter] p. 276 | Remark 11.6.e | span0 32144 |
| [Schechter] p. 276 | Definition of span | df-span 31911 spanval 31935 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 23311 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6387 onelond 36948 onelord 44253 ordelon 6386 ordelord 6384 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 44254 sucidg 6446 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6418 onsuc 7824 ord0 6417 ordsuci 7822 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 44255 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5216 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 44035 elon2 6373 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6368 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5554 epelg 5552 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9594 epirron 44256 ordirr 6380 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 44258 oneptr 44257 ontr1 6410 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 6406 oneptri 44259 ordtri3or 6395 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8509 ord0eln0 6419 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6432 onsucss 44268 trsucss 6453 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7829 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6459 ordnbtwn 6458 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 44270 ordnexbtwnsuc 44269 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10479 onsucf1lem 44271 onsucf1o 44274 onsucf1olem 44272 onsucrn 44273 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 44275 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7856 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 44264 ordne0gt0 44263 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 44266 limnsuc 44267 onsucelab 44265 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9644 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7871 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9647 ordom 7887 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9648 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8649 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7794 ssorduni 7793 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8539 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9651 limom 7893 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8476 df1o2 8483 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8524 oa0suclim 44277 oalim 8540 oasuc 8532 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8525 om0suclim 44278 omlim 8541 omsuc 8534 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8530 oe0m1 8529 oe0suclim 44279 oelim 8542 oesuc 8535 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 44231 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 44281 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 44282 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 44283 limexissupab 44285 limiun 44284 limuni 6425 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8546 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8550 om1om1r 44286 om1r 8551 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8543 oaomoecl 44280 oecl 8545 omcl 8544 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 44233 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8552 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8553 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 44287 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 44288 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8620 nnamecl 44289 nnecl 8622 nnmcl 8621 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 44290 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8560 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8561 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8568 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 44292 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 44293 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 44295 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8567 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 44299 omword1 8581 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 44298 oaordnrex 44297 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 44294 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 44300 omword2 8582 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 44301 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 44302 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 44303 omordi 8574 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8576 omord2com 44304 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 44305 df-2o 8477 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 44308 oewordi 8600 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 44309 oeworde 8602 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 44310 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 44311 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 44307 omnord1ex 44306 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 44312 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 44314 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 44318 oenord1ex 44317 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 44319 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8569 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 44313 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8587 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8588 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 44321 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8606 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 44322 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 44323 cantnfub2 44324 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 44327 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 29492 axtgcgrrflx 28924 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 29493 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 29494 axtgcgrid 28925 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 28910 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 29505 axtgsegcon 28926 df-trkgcb 28912 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 29516 axtg5seg 28927 df-trkgcb 28912 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 29517 axtgbtwnid 28928 df-trkgb 28911 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 29519 axtgpasch 28929 df-trkgb 28911 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 29538 df-trkg2d 35294 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 28932 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 28933 df-trkg2d 35294 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 29541 axtgeucl 28934 df-trkge 28913 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 29554 axtgcont 28931 axtgcont1 28930 df-trkgb 28911 |
| [Schwabhauser] p. 24 | Theorem A10 | prlngmo 29432 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 36752 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 36754 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 36757 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 36761 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 36762 tgcgrcomimp 28939 tgcgrcoml 28941 tgcgrcomr 28940 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 36767 tgcgrtriv 28946 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 36771 tg5segofs 35305 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 35302 df-ofs 36748 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 36773 tgcgrextend 28947 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 36775 tgsegconeq 28948 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 36787 btwntriv2 36777 tgbtwntriv2 28950 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 36778 tgbtwncom 28951 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 36781 tgbtwntriv1 28954 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 36782 tgbtwnswapid 28955 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 36788 btwnintr 36784 tgbtwnexch2 28959 tgbtwnintr 28956 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 36790 btwnexch3 36785 tgbtwnexch 28961 tgbtwnexch3 28957 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 36789 tgbtwnouttr 28960 tgbtwnouttr2 28958 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 29537 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 36792 tgbtwndiff 28969 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 28962 trisegint 36793 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 36809 tgifscgr 28971 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 29021 colrot1 29022 colrot2 29023 lncom 29090 lnrot1 29091 lnrot2 29092 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 36805 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 36810 tgcgrsub 28972 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 36820 tgcgrxfr 28981 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 28980 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 36806 df-cgrg 28974 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 28974 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 36821 tgbtwnxfr 28993 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 36827 colinearperm2 36829 colinearperm3 36828 colinearperm4 36830 colinearperm5 36831 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 28996 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 36804 tgellng 29016 tglng 29009 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 36832 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 36840 lnxfr 29029 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 36841 lnext 29030 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 36845 tgfscgr 29031 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 36846 lncgr 29032 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 36807 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 36848 lnid 29033 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 36849 tgidinside 29034 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 36866 tgbtwnconn1 29038 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 36867 tgbtwnconn2 29039 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 36868 tgbtwnconn3 29040 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 36874 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 36872 legov 29048 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 29049 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 29062 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 36875 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 36877 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 36879 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 36880 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 36881 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 36878 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 36883 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 29050 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 29052 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 29053 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 29054 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 29055 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 36890 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 36891 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 36886 df-outsideof 36885 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 36887 ishlg 29068 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 29073 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 29075 outsideofrflx 36892 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 29069 hlcomd 29070 outsideofcom 36893 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 29076 outsideoftr 36894 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreq 29085 hlcgreu 29084 outsideofeu 36896 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 36903 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 36904 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 36897 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 36912 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 36913 tglineelsb2 29100 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 36915 linerflx1 36914 linerflx2 36916 tglinecom 29103 tglinerflx1 29101 tglinerflx2 29102 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 36918 tglinethru 29104 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 36902 tglng 29009 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 29057 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 36921 tglinethrueu 29107 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 36922 tglineineq 29111 tglineinsn 29112 tglineinteq 29114 tglineintmo 29110 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 29118 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 29119 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 29120 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 29138 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 29134 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 29126 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 29125 ismir 29131 mirbtwn 29130 mircgr 29129 mirfv 29128 mirval 29127 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 29136 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 29137 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 29138 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 29141 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 29142 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 29147 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 29144 mirbtwni 29143 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 29145 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 29157 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 29161 symquadmid 29304 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 29158 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 29159 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 29160 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 29163 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 29164 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 29173 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 29169 israg 29172 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 29174 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 29175 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 29177 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 29178 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 29179 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 29180 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 29181 ragncol 29184 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 29182 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 29188 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 29192 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 29189 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 29171 isperp 29187 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 29190 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 29197 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 29206 colperpexlem2 29207 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 29209 colperpexlem3 29208 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 29214 midex 29213 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 29211 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 29220 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 29215 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 29224 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 29227 opphllem6 29228 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 29230 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 28929 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 29233 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 29241 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 29236 hpgbr 29238 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 29243 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 29242 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 29244 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 29245 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 29246 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 29247 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 29248 |
| [Schwabhauser] p. 74 | Lemma 9.22 | lnincplng 29262 |
| [Schwabhauser] p. 74 | Theorem 9.21 | plngcp 29264 |
| [Schwabhauser] p. 74 | Theorem 9.24 | plngrot 29268 |
| [Schwabhauser] p. 74 | Definition 9.20 | df-plng 29252 elplng 29258 |
| [Schwabhauser] p. 75 | Theorem 9.25 | lnssplng 29270 lnssplng1 29271 |
| [Schwabhauser] p. 76 | Theorem 9.26 | plng3p 29275 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 29289 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 29279 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 29293 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 29294 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 29295 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 29296 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 29297 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 29300 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 29302 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 29280 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 29303 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 29307 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 29308 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 29309 lnperpexs 29310 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 29311 trgcopyeu 29313 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 29338 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 29316 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 29325 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 29323 cgrahl2 29324 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 29326 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 29327 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 29329 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 29330 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 29334 cgrahl 29335 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 29339 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 29340 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 29341 acopyeu 29342 |
| [Schwabhauser] p. 98 | Theorem 11.16 | ragcgra 29343 |
| [Schwabhauser] p. 98 | Theorem 11.17 | cgrarag 29344 |
| [Schwabhauser] p. 98 | Theorem 11.18 | ragsupplcgra 29345 |
| [Schwabhauser] p. 99 | Theorem 11.19 | ragraghl 29346 |
| [Schwabhauser] p. 99 | Theorem 11.20 | perpeq 29348 |
| [Schwabhauser] p. 99 | Theorem 11.22 | tgaaddcpbl 29352 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 29360 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 29364 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 29357 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 29372 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 29365 isleag 29366 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 29400 tgsas1 29399 tgsas2 29401 tgsas3 29402 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 29404 tgasa1 29403 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 29405 tgsss2 29406 tgsss3 29407 |
| [Schwabhauser] p. 121 | Definition 12.2 | df-prlng 29415 |
| [Schwabhauser] p. 122 | Theorem 12.4 | prlngref 29418 |
| [Schwabhauser] p. 122 | Theorem 12.5 | prlngsym 29419 |
| [Schwabhauser] p. 122 | Theorem 12.6 | prlnghpg 29424 |
| [Schwabhauser] p. 122 | Theorem 12.7 | dfprlng2 29425 dfprlng3 29426 |
| [Schwabhauser] p. 122 | Theorem 12.9 | perpprlng 29428 |
| [Schwabhauser] p. 122 | Theorem 12.10 | prlngex 29429 |
| [Schwabhauser] p. 123 | Theorem 12.11 | prlngmo 29432 prlngmo2 29434 |
| [Schwabhauser] p. 124 | Theorem 12.13 | prlngeu 29433 |
| [Schwabhauser] p. 124 | Theorem 12.14 | prlngpln4 29436 |
| [Schwabhauser] p. 124 | Theorem 12.15 | prlngplngtr 29437 |
| [Schwabhauser] p. 125 | Theorem 12.16 | prlnginn0 29438 |
| [Schwabhauser] p. 125 | Theorem 12.17 | prlngmid2 29439 |
| [Schwabhauser] p. 126 | Theorem 12.18 | symquadprlng 29440 |
| [Schwabhauser] p. 126 | Theorem 12.19 | prlngsymquad 29442 prlngsymquadopp 29443 |
| [Schwabhauser] p. 126 | Theorem 12.20 | quadcgrprlng 29444 |
| [Schwabhauser] p. 126 | Theorem 12.21 | tgaltai 29445 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 27598 dchrsum 27596 dchrsum2 27595 sumdchr 27599 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 27600 sum2dchr 27601 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 20282 ablfacrp2 20283 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 27543 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 27544 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 27551 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 27809 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 27812 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 27866 vmalogdivsum2 27865 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 27856 dirith2 27855 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 27854 rpvmasum 27853 rpvmasum2 27839 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 27814 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 27852 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 27819 dchrisumlem1 27816 dchrisumlem2 27817 dchrisumlem3 27818 dchrisumlema 27815 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 27822 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 27851 dchrmusumlem 27849 dchrvmasumlem 27850 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 27821 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 27823 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 27847 dchrisum0re 27840 dchrisumn0 27848 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 27833 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 27837 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 27838 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 27893 pntrsumbnd2 27894 pntrsumo1 27892 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 27857 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 27859 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 27861 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 27864 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 27869 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 27870 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 27875 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 27877 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 27878 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 27886 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 27887 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 27884 selberg3lem2 27885 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 27888 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 27882 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 27895 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 27896 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 27897 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 27911 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 27923 pntlemb 27924 pntlemc 27922 pntlemd 27921 pntlemg 27925 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 27923 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 27915 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 27920 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 27923 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 27936 pntleml 27938 |
| [Stewart] p. 91 | Lemma 7.3 | constrss 34375 |
| [Stewart] p. 92 | Definition 7.4. | df-constr 34362 |
| [Stewart] p. 96 | Theorem 7.10 | constraddcl 34394 constrinvcl 34405 constrmulcl 34403 constrnegcl 34395 constrsqrtcl 34411 |
| [Stewart] p. 97 | Theorem 7.11 | constrextdg2 34381 |
| [Stewart] p. 98 | Theorem 7.12 | constrext2chn 34391 |
| [Stewart] p. 99 | Theorem 7.13 | 2sqr3nconstr 34413 |
| [Stewart] p. 99 | Theorem 7.14 | cos9thpinconstr 34423 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4252 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4356 dif0 4327 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4447 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4429 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4243 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4244 |
| [Stoll] p. 20 | Remark | invdif 4225 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4593 |
| [Stoll] p. 43 | Definition | uniiun 5017 |
| [Stoll] p. 44 | Definition | intiin 5018 |
| [Stoll] p. 45 | Definition | df-iin 4954 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4953 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 407 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4252 |
| [Strang] p. 242 | Section 6.3 | expgrowth 45319 |
| [Suppes] p. 22 | Theorem 2 | eq0 4297 eq0f 4294 |
| [Suppes] p. 22 | Theorem 4 | eqss 3946 eqssd 3948 eqssi 3947 |
| [Suppes] p. 23 | Theorem 5 | ss0 4352 ss0b 4351 |
| [Suppes] p. 23 | Theorem 6 | sstr 3939 sstrALT2 45817 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4051 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4053 |
| [Suppes] p. 23 | Theorem 9 | psstr 4056 |
| [Suppes] p. 23 | Theorem 10 | pssss 4046 |
| [Suppes] p. 25 | Theorem 12 | elin 3915 elun 4100 |
| [Suppes] p. 26 | Theorem 15 | inidm 4172 |
| [Suppes] p. 26 | Theorem 16 | in0 4345 |
| [Suppes] p. 27 | Theorem 23 | unidm 4104 |
| [Suppes] p. 27 | Theorem 24 | un0 4344 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4124 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4132 |
| [Suppes] p. 27 | Theorem 27 | unss 4136 |
| [Suppes] p. 27 | Theorem 28 | indir 4232 |
| [Suppes] p. 27 | Theorem 29 | undir 4233 |
| [Suppes] p. 28 | Theorem 32 | difid 4325 |
| [Suppes] p. 29 | Theorem 33 | difin 4218 |
| [Suppes] p. 29 | Theorem 34 | indif 4226 |
| [Suppes] p. 29 | Theorem 35 | undif1 4430 |
| [Suppes] p. 29 | Theorem 36 | difun2 4437 |
| [Suppes] p. 29 | Theorem 37 | difin0 4428 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4426 |
| [Suppes] p. 29 | Theorem 39 | difundi 4236 |
| [Suppes] p. 29 | Theorem 40 | difindi 4238 |
| [Suppes] p. 30 | Theorem 41 | nalset 5268 |
| [Suppes] p. 39 | Theorem 61 | uniss 4875 |
| [Suppes] p. 39 | Theorem 65 | uniop 5488 |
| [Suppes] p. 41 | Theorem 70 | intsn 4944 |
| [Suppes] p. 42 | Theorem 71 | intpr 4942 intprg 4941 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5440 |
| [Suppes] p. 42 | Theorem 78 | intun 4940 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4990 dfiun2g 4988 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4991 |
| [Suppes] p. 47 | Theorem 86 | elpw 4561 elpw2 5296 elpw2g 5295 elpwg 4560 elpwgdedVD 45899 |
| [Suppes] p. 47 | Theorem 87 | pwid 4580 |
| [Suppes] p. 47 | Theorem 89 | pw0 4773 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4774 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5666 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5810 xpindir 5811 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5720 xpundir 5721 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9591 |
| [Suppes] p. 58 | Theorem 2 | relss 5758 |
| [Suppes] p. 59 | Theorem 4 | eldm 5882 eldm2 5883 eldm2g 5881 eldmg 5880 |
| [Suppes] p. 59 | Definition 3 | df-dm 5661 |
| [Suppes] p. 60 | Theorem 6 | dmin 5893 |
| [Suppes] p. 60 | Theorem 8 | rnun 6136 |
| [Suppes] p. 60 | Theorem 9 | rnin 6137 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5870 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5860 brcnvg 5857 |
| [Suppes] p. 62 | Equation 5 | elcnv 5854 elcnv2 5855 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6100 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6135 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6133 |
| [Suppes] p. 63 | Definition | dftrrels2 39592 |
| [Suppes] p. 63 | Theorem 20 | co02 6262 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5957 |
| [Suppes] p. 63 | Definition 7 | df-co 5660 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5867 |
| [Suppes] p. 64 | Theorem 27 | coass 6267 |
| [Suppes] p. 65 | Theorem 31 | resundi 5984 |
| [Suppes] p. 65 | Theorem 34 | elima 6061 elima2 6062 elima3 6063 elimag 6060 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6141 |
| [Suppes] p. 66 | Theorem 40 | dminss 6143 |
| [Suppes] p. 66 | Theorem 41 | imainss 6144 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6147 |
| [Suppes] p. 81 | Definition 34 | dfec2 8720 |
| [Suppes] p. 82 | Theorem 72 | elec 8764 elecALTV 39204 elecg 8762 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 39628 erth 8772 erth2 8773 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 39631 erdisj 8775 |
| [Suppes] p. 83 | Definition 35, | df-parts 39801 dfmembpart2 39806 |
| [Suppes] p. 89 | Theorem 96 | map0b 8911 |
| [Suppes] p. 89 | Theorem 97 | map0 8915 map0g 8912 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8916 mapsnd 8914 |
| [Suppes] p. 89 | Theorem 99 | mapss 8917 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10147 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10146 |
| [Suppes] p. 92 | Theorem 1 | enref 9012 enrefg 9011 |
| [Suppes] p. 92 | Theorem 2 | ensym 9030 ensymb 9029 ensymi 9031 |
| [Suppes] p. 92 | Theorem 3 | entr 9033 |
| [Suppes] p. 92 | Theorem 4 | unen 9073 |
| [Suppes] p. 94 | Theorem 15 | endom 9006 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 9027 |
| [Suppes] p. 94 | Theorem 17 | domtr 9034 |
| [Suppes] p. 95 | Theorem 18 | sbth 9116 |
| [Suppes] p. 97 | Theorem 23 | canth2 9149 canth2g 9150 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9120 df-sdom 8976 dfsdom2 9119 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9133 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9122 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9121 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9131 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 9009 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9134 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9129 |
| [Suppes] p. 98 | Exercise 4 | fundmen 9059 fundmeng 9060 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9094 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9130 |
| [Suppes] p. 104 | Theorem 37 | fofi 9305 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9310 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9310 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10635 |
| [Suppes] p. 130 | Definition 3 | df-tr 5213 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7794 |
| [Suppes] p. 134 | Definition 6 | df-suc 6368 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7912 finds 7908 finds1 7911 finds2 7910 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9653 isfinite2 9290 isfiniteg 9292 unbnn 9288 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 11003 df-ltpq 10995 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7874 tfinds 7871 tfinds2 7875 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8559 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8561 |
| [Suppes] p. 211 | Theorem 25 | oaass 8569 |
| [Suppes] p. 225 | Definition 8 | iscard2 10057 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10647 |
| [Suppes] p. 228 | Theorem 59 | harcard 10059 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10145 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6415 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7807 onminsb 7808 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10657 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10149 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10156 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10150 |
| [Suppes] p. 229 | Definition 12 | df-aleph 10021 |
| [Suppes] p. 242 | Theorem 6 | weth 10573 |
| [Suppes] p. 242 | Theorem 8 | entric 10641 |
| [Suppes] p. 242 | Theorem 9 | carden 10635 |
| [Szendrei] p. 11 | Line 6 | df-cloneop 36461 |
| [Szendrei] p. 11 | Paragraph 3 | df-suppos 36465 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2733 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2753 wl-df.cleq 38432 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2836 wl-df.clel 38435 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2755 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2781 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7424 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3738 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5383 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4609 elpr2 4611 elpr2g 4610 elprg 4607 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4599 elsn2 4626 elsn2g 4625 elsng 4598 velsn 4600 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5436 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4594 sneqr 4800 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4605 dfsn2 4597 dfsn2ALT 4606 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7758 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5445 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5432 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5416 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7761 unexg 7760 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4652 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4868 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3906 df-un 3904 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4884 uniprg 4883 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5339 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4650 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6435 elsucg 6433 sstr2 3938 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4105 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4155 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4118 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4173 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4230 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4231 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3919 df-ss 3916 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4559 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4133 |
| [TakeutiZaring] p. 18 | Exercise 9 | dfss2 3917 sseqin2 4169 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3953 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4182 inss2 4183 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 3995 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4878 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5417 sspwimp 45900 sspwimpALT 45907 sspwimpALT2 45910 sspwimpcf 45902 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5424 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5232 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3414 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5261 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3902 |
| [TakeutiZaring] p. 20 | Definition 5.14 | bj-dfnul2 37440 dfnul2 4282 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4325 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4300 n0f 4296 neq0 4299 neq0f 4295 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9590 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9733 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9748 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3453 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5274 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4350 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5282 ssexg 5281 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5277 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9602 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9594 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4314 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4082 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4246 undif3VD 45864 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4083 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4090 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3078 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3088 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7767 xpexg 7764 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5658 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6611 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6789 fun11 6614 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6551 svrelfun 6612 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5869 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5871 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5663 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5664 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5660 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6186 dfrel2 6181 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5667 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5789 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5796 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5809 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5996 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5976 opelresi 5978 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 6003 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5992 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5997 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6582 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6104 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6580 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6791 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2635 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 31001 df-fv 6546 fv3 6903 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7937 cnvexg 7936 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7921 dmexg 7913 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7922 rnexg 7914 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 45436 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7932 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6898 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 48244 tz6.12-1-afv2 48311 tz6.12-1 6908 tz6.12-afv 48243 tz6.12-afv2 48310 tz6.12 6909 tz6.12c-afv2 48312 tz6.12c 6907 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 48307 tz6.12-2 6872 tz6.12i-afv2 48313 tz6.12i 6911 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6541 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6542 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6544 wfo 6536 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6543 wf1 6535 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6545 wf1o 6537 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 7029 eqfnfv2 7030 eqfnfv2f 7033 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6983 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7223 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7221 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6627 funimaexg 6626 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5104 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5560 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5612 dffr3 6097 eliniseg 6092 iniseg 6095 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5551 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5628 fr3nr 7786 frirr 5627 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5604 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7788 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5615 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5637 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6350 tz6.26i 6351 wefrc 5645 wereu2 5648 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6352 wfii 6353 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6547 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7337 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7338 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7344 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7345 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7346 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7350 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7357 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7359 |
| [TakeutiZaring] p. 35 | Notation | wtr 5212 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 45437 tz7.2 5634 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5217 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6375 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6383 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6384 ordelordALT 45520 ordelordALTVD 45849 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6390 ordelssne 6389 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6388 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6393 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7796 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7797 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6366 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6395 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 45532 ordon 7791 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7792 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7864 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6411 ontr2d 36949 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5214 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7806 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7842 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6469 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6468 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7793 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4899 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6368 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6445 sucidg 6446 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7824 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6459 ordnbtwn 6458 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7839 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6367 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7892 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7897 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7852 ordelsuc 7831 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7833 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7862 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7879 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7900 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7901 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7902 |
| [TakeutiZaring] p. 43 | Remark | omon 7889 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9636 omex 9644 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7887 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7907 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7904 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7905 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7882 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4922 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5231 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4923 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5305 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7809 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6414 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4908 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9661 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7804 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8383 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8405 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8406 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8407 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8414 tz7.44-2 8415 tz7.44-3 8416 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8375 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8370 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8354 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8455 tz7.49c 8456 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8453 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8452 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8454 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2681 |
| [TakeutiZaring] p. 54 | Definition 7.55 | df-lexo 35872 |
| [TakeutiZaring] p. 54 | Definition 7.57 | df-r0 35873 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 10090 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 10091 |
| [TakeutiZaring] p. 55 | Definition 7.59 | df-j0 35874 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8540 oasuc 8532 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7872 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8543 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8524 oa0r 8546 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8544 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8556 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8628 nnaordi 8627 oaord 8555 oaordi 8554 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5008 uniss2 4902 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8558 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8563 oawordex 8565 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8620 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8657 |
| [TakeutiZaring] p. 60 | Remark | oancom 9652 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8568 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8625 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8560 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8527 omlim 8541 omsuc 8534 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8525 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8622 nnmcl 8621 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8641 nnmordi 8640 omord 8576 omordi 8574 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8577 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8645 omwordri 8580 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8547 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8550 om1r 8551 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8583 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8585 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8586 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8587 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8588 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8617 oe0 8530 oelim 8542 oesuc 8535 onesuc 8538 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8528 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8595 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8596 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8529 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8553 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8597 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8603 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8601 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8602 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8606 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8608 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9729 tz9.1 9730 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9768 r10 9775 r1lim 9779 r1limg 9778 r1suc 9777 r1sucg 9776 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9787 r1ord2 9788 r1ordg 9785 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9797 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9824 tz9.13 9798 tz9.13g 9799 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9769 rankval 9825 rankvalb 9805 rankvalg 9826 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9851 rankelb 9833 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9867 rankval3 9853 rankval3b 9836 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9839 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9803 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9846 rankr1c 9830 rankr1g 9844 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9847 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9863 rankssb 9862 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9855 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9854 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10553 dfac3 10200 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 10109 numth 10550 numth2 10549 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10630 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10631 cardid2 10034 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 10041 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10635 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 10040 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 10025 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 10046 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 10038 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9169 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 9045 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9174 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9098 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 10044 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10177 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9221 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9229 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10178 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9226 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10167 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10145 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 10053 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10294 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9314 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8977 isfi 9002 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9230 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10613 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9091 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10605 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10264 unxpdom 9250 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 10055 cardsdomelir 10054 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9252 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 10093 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8849 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10646 infxpidm2 10096 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10285 infxp 10292 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9103 pw2f1o 9101 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9162 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10565 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10560 ac6s5 10569 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10627 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10628 uniimadomf 10629 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10352 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10347 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10331 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10328 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10335 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10342 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10351 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10667 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10329 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10354 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10176 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10175 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10187 alephfp2 10188 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10784 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10191 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10654 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10668 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10669 |
| [TakeutiZaring] p. 143 | Definition 14.1(1) | df-cnv2 35852 |
| [TakeutiZaring] p. 143 | Definition 14.1(2) | df-cnv3 35853 |
| [TakeutiZaring] p. 144 | Definition 14.2 | df-gdlop1 35854 df-gdlop2 35855 df-gdlop3 35856 df-gdlop4 35857 df-gdlop5 35858 df-gdlop6 35859 df-gdlop7 35860 df-gdlop8 35861 df-gdlopc 35862 |
| [TakeutiZaring] p. 155 | Definition 15.2 | df-j 35875 |
| [TakeutiZaring] p. 156 | Definition 15.7 | df-k1 35876 df-k2 35877 df-k3 35878 |
| [TakeutiZaring] p. 158 | Definition 15.13 | df-fnl 35879 |
| [TakeutiZaring] p. 158 | Definition 15.15 | df-l 35880 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 39941 |
| [Tarski] p. 67 | Scheme B5 | sp 2220 |
| [Tarski] p. 68 | Lemma 6 | avril1 31064 equid 2045 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2050 |
| [Tarski] p. 70 | Lemma 14 | spim 2417 spime 2419 spimew 2004 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2213 ax-c15 39947 ax12i 1999 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2122 |
| [Tarski] p. 75 | Axiom B7 | ax6v 2001 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1943 ax5ALT 39965 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2041 ax-8 2147 ax-9 2155 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 28926 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 28927 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 28929 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 28929 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 28930 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16411 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 38578 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 38580 |
| [Weierstrass] p. 272 | Definition | df-mdet 22900 mdetuni 22937 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 917 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 882 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 883 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 933 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 983 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 190 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 136 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 91 wl-luk-pm2.04 38369 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 44800 imim2 59 wl-luk-imim2 38364 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 48089 imim1 84 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 910 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2688 syl 18 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 916 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 23 wl-luk-id 38367 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 908 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 143 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 911 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 131 notnotrALT2 45909 wl-luk-notnotr 38368 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 147 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 44830 axfrege28 44829 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 881 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 938 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 124 wl-luk-pm2.21 38361 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 125 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 903 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 954 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 31002 pm2.27 43 wl-luk-pm2.27 38359 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 936 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 39304 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 937 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 985 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 986 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 984 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1104 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 920 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 921 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 957 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 57 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 895 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 896 |
| [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 | pm2.47 897 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 899 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 174 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 865 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 866 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 902 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 904 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 194 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 913 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 955 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 956 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 195 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 905 pm2.67 906 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 177 pm2.521g 175 pm2.521g2 176 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 912 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 988 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 914 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 206 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 989 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 990 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 947 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 945 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 987 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 991 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 85 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 946 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 110 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 1007 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 475 pm3.2im 161 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 1008 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 1009 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 1010 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 1011 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 477 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 465 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 408 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 815 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 454 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 455 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 488 simplim 168 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 490 simprim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 777 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 778 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 820 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 634 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 822 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 498 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 499 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 975 pm3.44 974 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 821 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 479 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 978 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 319 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 264 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 322 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 356 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 819 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 846 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 225 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 818 bitr 817 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 574 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 918 pm4.25 919 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 466 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1025 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 884 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 474 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 935 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 645 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 931 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 649 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 992 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1105 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1023 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1069 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1040 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 1012 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 1014 pm4.45 1013 pm4.45im 841 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 998 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 867 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 555 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 997 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 1000 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 1001 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 1002 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 1003 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 999 pm4.56 1004 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 1005 pm4.57 1006 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 410 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 870 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 403 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 863 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 411 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 864 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 404 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 567 pm4.71d 571 pm4.71i 569 pm4.71r 568 pm4.71rd 572 pm4.71ri 570 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 964 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 537 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 950 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 527 pm4.76 528 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 976 pm4.77 977 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 948 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1021 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 398 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 399 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1041 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1042 |
| [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 | bi2.04 392 impexp 456 pm4.87 857 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 836 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 959 pm5.11g 958 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 960 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 962 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 961 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1030 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1031 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1029 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 386 pm5.18 384 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 391 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 837 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1032 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1065 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1066 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 915 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 583 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 393 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 364 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 968 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 844 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 584 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 849 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 838 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 847 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 394 pm5.41 395 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 553 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 552 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1022 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1035 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 963 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1036 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1037 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1045 |
| [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 1046 |
| [WhiteheadRussell] p. 145 | Theorem *10.3 | bj-alsyl 37491 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 45342 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 45343 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1903 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 45344 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 45345 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 45346 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1926 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 45347 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 45348 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 45349 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 45350 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 45351 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 45353 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 45354 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 45355 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 45352 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2127 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 45358 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 45359 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2107 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2197 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1862 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1863 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 45360 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 45361 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 45362 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 45363 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 45365 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 45364 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1920 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 45367 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 45368 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 45366 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1861 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 45369 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 45370 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1879 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 45371 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2376 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1893 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 45376 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 45372 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 45373 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 45374 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 45375 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 45380 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 45377 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 45378 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 45379 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 45381 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2595 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 45391 pm13.13b 45392 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 45393 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3037 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3038 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3620 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 45399 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 45400 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 45394 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 45535 pm13.193 45395 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 45396 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 45397 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 45398 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 45405 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 45404 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 45403 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3801 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 45406 pm14.122b 45407 pm14.122c 45408 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 45409 pm14.123b 45410 pm14.123c 45411 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 45413 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 45412 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 45414 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6519 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 45415 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6520 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 45416 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 45418 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2659 eupickbi 2662 sbaniota 45419 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 45417 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2610 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 45420 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 31001 df-fv 6546 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 10082 pm54.43lem 10081 |
| [Young] p. 141 | Definition of operator ordering | leop2 32726 |
| [Young] p. 142 | Example 12.2(i) | 0leop 32732 idleop 32733 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 43835 |
| [vandenDries] p. 43 | Theorem 62 | pellex 43842 pellexlem1 43836 |