Bibliographic Cross-References
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Metamath Proof Explorer Bibliographic Cross-References |
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| Bibliographic Reference | Description | Metamath Proof Explorer Page(s) |
|---|---|---|
| [Adamek] p. 21 | Definition 3.1 | df-cat 17548 |
| [Adamek] p. 21 | Condition 3.1(b) | df-cat 17548 |
| [Adamek] p. 22 | Example 3.3(1) | df-setc 17962 |
| [Adamek] p. 24 | Example 3.3(4.c) | 0cat 17569 |
| [Adamek] p. 24 | Example 3.3(4.d) | df-prstc 47073 prsthinc 47064 |
| [Adamek] p. 24 | Example 3.3(4.e) | df-mndtc 47094 df-mndtc 47094 |
| [Adamek] p. 25 | Definition 3.5 | df-oppc 17592 |
| [Adamek] p. 28 | Remark 3.9 | oppciso 17664 |
| [Adamek] p. 28 | Remark 3.12 | invf1o 17652 invisoinvl 17673 |
| [Adamek] p. 28 | Example 3.13 | idinv 17672 idiso 17671 |
| [Adamek] p. 28 | Corollary 3.11 | inveq 17657 |
| [Adamek] p. 28 | Definition 3.8 | df-inv 17631 df-iso 17632 dfiso2 17655 |
| [Adamek] p. 28 | Proposition 3.10 | sectcan 17638 |
| [Adamek] p. 29 | Remark 3.16 | cicer 17689 |
| [Adamek] p. 29 | Definition 3.15 | cic 17682 df-cic 17679 |
| [Adamek] p. 29 | Definition 3.17 | df-func 17744 |
| [Adamek] p. 29 | Proposition 3.14(1) | invinv 17653 |
| [Adamek] p. 29 | Proposition 3.14(2) | invco 17654 isoco 17660 |
| [Adamek] p. 30 | Remark 3.19 | df-func 17744 |
| [Adamek] p. 30 | Example 3.20(1) | idfucl 17767 |
| [Adamek] p. 32 | Proposition 3.21 | funciso 17760 |
| [Adamek] p. 33 | Example 3.26(2) | df-thinc 47030 prsthinc 47064 thincciso 47059 |
| [Adamek] p. 33 | Example 3.26(3) | df-mndtc 47094 |
| [Adamek] p. 33 | Proposition 3.23 | cofucl 17774 |
| [Adamek] p. 34 | Remark 3.28(2) | catciso 17997 |
| [Adamek] p. 34 | Remark 3.28 (1) | embedsetcestrc 18055 |
| [Adamek] p. 34 | Definition 3.27(2) | df-fth 17792 |
| [Adamek] p. 34 | Definition 3.27(3) | df-full 17791 |
| [Adamek] p. 34 | Definition 3.27 (1) | embedsetcestrc 18055 |
| [Adamek] p. 35 | Corollary 3.32 | ffthiso 17816 |
| [Adamek] p. 35 | Proposition 3.30(c) | cofth 17822 |
| [Adamek] p. 35 | Proposition 3.30(d) | cofull 17821 |
| [Adamek] p. 36 | Definition 3.33 (1) | equivestrcsetc 18040 |
| [Adamek] p. 36 | Definition 3.33 (2) | equivestrcsetc 18040 |
| [Adamek] p. 39 | Definition 3.41 | funcoppc 17761 |
| [Adamek] p. 39 | Definition 3.44. | df-catc 17985 |
| [Adamek] p. 39 | Proposition 3.43(c) | fthoppc 17810 |
| [Adamek] p. 39 | Proposition 3.43(d) | fulloppc 17809 |
| [Adamek] p. 40 | Remark 3.48 | catccat 17994 |
| [Adamek] p. 40 | Definition 3.47 | df-catc 17985 |
| [Adamek] p. 48 | Example 4.3(1.a) | 0subcat 17724 |
| [Adamek] p. 48 | Example 4.3(1.b) | catsubcat 17725 |
| [Adamek] p. 48 | Definition 4.1(2) | fullsubc 17736 |
| [Adamek] p. 48 | Definition 4.1(a) | df-subc 17695 |
| [Adamek] p. 49 | Remark 4.4(2) | ressffth 17825 |
| [Adamek] p. 83 | Definition 6.1 | df-nat 17830 |
| [Adamek] p. 87 | Remark 6.14(a) | fuccocl 17853 |
| [Adamek] p. 87 | Remark 6.14(b) | fucass 17857 |
| [Adamek] p. 87 | Definition 6.15 | df-fuc 17831 |
| [Adamek] p. 88 | Remark 6.16 | fuccat 17859 |
| [Adamek] p. 101 | Definition 7.1 | df-inito 17870 |
| [Adamek] p. 101 | Example 7.2 (6) | irinitoringc 46357 |
| [Adamek] p. 102 | Definition 7.4 | df-termo 17871 |
| [Adamek] p. 102 | Proposition 7.3 (1) | initoeu1w 17898 |
| [Adamek] p. 102 | Proposition 7.3 (2) | initoeu2 17902 |
| [Adamek] p. 103 | Definition 7.7 | df-zeroo 17872 |
| [Adamek] p. 103 | Example 7.9 (3) | nzerooringczr 46360 |
| [Adamek] p. 103 | Proposition 7.6 | termoeu1w 17905 |
| [Adamek] p. 106 | Definition 7.19 | df-sect 17630 |
| [Adamek] p. 185 | Section 10.67 | updjud 9870 |
| [Adamek] p. 478 | Item Rng | df-ringc 46293 |
| [AhoHopUll] p. 2 | Section 1.1 | df-bigo 46624 |
| [AhoHopUll] p. 12 | Section 1.3 | df-blen 46646 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 14459 df-pfx 14559 df-substr 14529 df-word 14403 lencl 14421 wrd0 14427 |
| [AkhiezerGlazman] p. 39 | Linear operator norm | df-nmo 24072 df-nmoo 29687 |
| [AkhiezerGlazman] p. 64 | Theorem | hmopidmch 31095 hmopidmchi 31093 |
| [AkhiezerGlazman] p. 65 | Theorem 1 | pjcmul1i 31143 pjcmul2i 31144 |
| [AkhiezerGlazman] p. 72 | Theorem | cnvunop 30860 unoplin 30862 |
| [AkhiezerGlazman] p. 72 | Equation 2 | unopadj 30861 unopadj2 30880 |
| [AkhiezerGlazman] p. 73 | Theorem | elunop2 30955 lnopunii 30954 |
| [AkhiezerGlazman] p. 80 | Proposition 1 | adjlnop 31028 |
| [Alling] p. 125 | Theorem 4.02(12) | cofcutrtime 27246 |
| [Alling] p. 184 | Axiom B | bdayfo 27025 |
| [Alling] p. 184 | Axiom O | sltso 27024 |
| [Alling] p. 184 | Axiom SD | nodense 27040 |
| [Alling] p. 185 | Lemma 0 | nocvxmin 27118 |
| [Alling] p. 185 | Theorem | conway 27138 |
| [Alling] p. 185 | Axiom FE | noeta 27091 |
| [Alling] p. 186 | Theorem 4 | slerec 27158 |
| [Alling], p. 2 | Definition | rp-brsslt 41685 |
| [Alling], p. 3 | Note | nla0001 41688 nla0002 41686 nla0003 41687 |
| [Apostol] p. 18 | Theorem I.1 | addcan 11339 addcan2d 11359 addcan2i 11349 addcand 11358 addcani 11348 |
| [Apostol] p. 18 | Theorem I.2 | negeu 11391 |
| [Apostol] p. 18 | Theorem I.3 | negsub 11449 negsubd 11518 negsubi 11479 |
| [Apostol] p. 18 | Theorem I.4 | negneg 11451 negnegd 11503 negnegi 11471 |
| [Apostol] p. 18 | Theorem I.5 | subdi 11588 subdid 11611 subdii 11604 subdir 11589 subdird 11612 subdiri 11605 |
| [Apostol] p. 18 | Theorem I.6 | mul01 11334 mul01d 11354 mul01i 11345 mul02 11333 mul02d 11353 mul02i 11344 |
| [Apostol] p. 18 | Theorem I.7 | mulcan 11792 mulcan2d 11789 mulcand 11788 mulcani 11794 |
| [Apostol] p. 18 | Theorem I.8 | receu 11800 xreceu 31778 |
| [Apostol] p. 18 | Theorem I.9 | divrec 11829 divrecd 11934 divreci 11900 divreczi 11893 |
| [Apostol] p. 18 | Theorem I.10 | recrec 11852 recreci 11887 |
| [Apostol] p. 18 | Theorem I.11 | mul0or 11795 mul0ord 11805 mul0ori 11803 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 11594 mul2negd 11610 mul2negi 11603 mulneg1 11591 mulneg1d 11608 mulneg1i 11601 |
| [Apostol] p. 18 | Theorem I.13 | divadddiv 11870 divadddivd 11975 divadddivi 11917 |
| [Apostol] p. 18 | Theorem I.14 | divmuldiv 11855 divmuldivd 11972 divmuldivi 11915 rdivmuldivd 32071 |
| [Apostol] p. 18 | Theorem I.15 | divdivdiv 11856 divdivdivd 11978 divdivdivi 11918 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 12937 rpaddcld 12972 rpmulcl 12938 rpmulcld 12973 |
| [Apostol] p. 20 | Axiom 8 | rpneg 12947 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 12950 |
| [Apostol] p. 20 | Theorem I.17 | lttri 11281 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 11748 ltadd1dd 11766 ltadd1i 11709 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 12005 ltmul1a 12004 ltmul1i 12073 ltmul1ii 12083 ltmul2 12006 ltmul2d 12999 ltmul2dd 13013 ltmul2i 12076 |
| [Apostol] p. 20 | Theorem I.20 | msqgt0 11675 msqgt0d 11722 msqgt0i 11692 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 11677 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 11661 lt0neg1d 11724 ltneg 11655 ltnegd 11733 ltnegi 11699 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 11640 lt2addd 11778 lt2addi 11717 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 12916 |
| [Apostol] p. 21 | Exercise 4 | recgt0 12001 recgt0d 12089 recgt0i 12060 recgt0ii 12061 |
| [Apostol] p. 22 | Definition of integers | df-z 12500 |
| [Apostol] p. 22 | Definition of positive integers | dfnn3 12167 |
| [Apostol] p. 22 | Definition of rationals | df-q 12874 |
| [Apostol] p. 24 | Theorem I.26 | supeu 9390 |
| [Apostol] p. 26 | Theorem I.28 | nnunb 12409 |
| [Apostol] p. 26 | Theorem I.29 | arch 12410 archd 43367 |
| [Apostol] p. 28 | Exercise 2 | btwnz 12606 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 12411 |
| [Apostol] p. 28 | Exercise 4 | rebtwnz 12872 |
| [Apostol] p. 28 | Exercise 5 | zbtwnre 12871 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 13118 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 16221 zneo 12586 zneoALTV 45851 |
| [Apostol] p. 29 | Theorem I.35 | cxpsqrtth 26084 msqsqrtd 15325 resqrtth 15140 sqrtth 15249 sqrtthi 15255 sqsqrtd 15324 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 12156 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwo 12838 |
| [Apostol] p. 361 | Remark | crreczi 14131 |
| [Apostol] p. 363 | Remark | absgt0i 15284 |
| [Apostol] p. 363 | Example | abssubd 15338 abssubi 15288 |
| [ApostolNT] p. 7 | Remark | fmtno0 45722 fmtno1 45723 fmtno2 45732 fmtno3 45733 fmtno4 45734 fmtno5fac 45764 fmtnofz04prm 45759 |
| [ApostolNT] p. 7 | Definition | df-fmtno 45710 |
| [ApostolNT] p. 8 | Definition | df-ppi 26449 |
| [ApostolNT] p. 14 | Definition | df-dvds 16137 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 16152 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 16176 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 16171 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 16165 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 16167 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 16153 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 16154 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 16159 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 16193 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 16195 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 16197 |
| [ApostolNT] p. 15 | Definition | df-gcd 16375 dfgcd2 16427 |
| [ApostolNT] p. 16 | Definition | isprm2 16558 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 16529 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 16787 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 16393 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 16428 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 16430 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 16408 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 16400 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 16587 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 16589 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 16800 |
| [ApostolNT] p. 18 | Theorem 1.13 | prmrec 16794 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 16285 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 16463 |
| [ApostolNT] p. 24 | Definition | df-mu 26450 |
| [ApostolNT] p. 25 | Definition | df-phi 16638 |
| [ApostolNT] p. 25 | Theorem 2.1 | musum 26540 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 16662 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 16648 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 16652 |
| [ApostolNT] p. 32 | Definition | df-vma 26447 |
| [ApostolNT] p. 32 | Theorem 2.9 | muinv 26542 |
| [ApostolNT] p. 32 | Theorem 2.10 | vmasum 26564 |
| [ApostolNT] p. 38 | Remark | df-sgm 26451 |
| [ApostolNT] p. 38 | Definition | df-sgm 26451 |
| [ApostolNT] p. 75 | Definition | df-chp 26448 df-cht 26446 |
| [ApostolNT] p. 104 | Definition | congr 16540 |
| [ApostolNT] p. 106 | Remark | dvdsval3 16140 |
| [ApostolNT] p. 106 | Definition | moddvds 16147 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 16228 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 16229 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 13793 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modmul12d 13830 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modexp 14141 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 16170 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 16543 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 16946 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 16545 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 16655 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 16673 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 16656 |
| [ApostolNT] p. 116 | Theorem 5.24 | wilthimp 26421 |
| [ApostolNT] p. 179 | Definition | df-lgs 26643 lgsprme0 26687 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 26688 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 26664 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 26679 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 26736 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 26755 2lgsoddprm 26764 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 26722 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 26731 |
| [ApostolNT] p. 188 | Definition | df-lgs 26643 lgs1 26689 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 26680 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 26682 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 26690 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 26691 |
| [Baer] p. 40 | Property (b) | mapdord 40101 |
| [Baer] p. 40 | Property (c) | mapd11 40102 |
| [Baer] p. 40 | Property (e) | mapdin 40125 mapdlsm 40127 |
| [Baer] p. 40 | Property (f) | mapd0 40128 |
| [Baer] p. 40 | Definition of projectivity | df-mapd 40088 mapd1o 40111 |
| [Baer] p. 41 | Property (g) | mapdat 40130 |
| [Baer] p. 44 | Part (1) | mapdpg 40169 |
| [Baer] p. 45 | Part (2) | hdmap1eq 40264 mapdheq 40191 mapdheq2 40192 mapdheq2biN 40193 |
| [Baer] p. 45 | Part (3) | baerlem3 40176 |
| [Baer] p. 46 | Part (4) | mapdheq4 40195 mapdheq4lem 40194 |
| [Baer] p. 46 | Part (5) | baerlem5a 40177 baerlem5abmN 40181 baerlem5amN 40179 baerlem5b 40178 baerlem5bmN 40180 |
| [Baer] p. 47 | Part (6) | hdmap1l6 40284 hdmap1l6a 40272 hdmap1l6e 40277 hdmap1l6f 40278 hdmap1l6g 40279 hdmap1l6lem1 40270 hdmap1l6lem2 40271 mapdh6N 40210 mapdh6aN 40198 mapdh6eN 40203 mapdh6fN 40204 mapdh6gN 40205 mapdh6lem1N 40196 mapdh6lem2N 40197 |
| [Baer] p. 48 | Part 9 | hdmapval 40291 |
| [Baer] p. 48 | Part 10 | hdmap10 40303 |
| [Baer] p. 48 | Part 11 | hdmapadd 40306 |
| [Baer] p. 48 | Part (6) | hdmap1l6h 40280 mapdh6hN 40206 |
| [Baer] p. 48 | Part (7) | mapdh75cN 40216 mapdh75d 40217 mapdh75e 40215 mapdh75fN 40218 mapdh7cN 40212 mapdh7dN 40213 mapdh7eN 40211 mapdh7fN 40214 |
| [Baer] p. 48 | Part (8) | mapdh8 40251 mapdh8a 40238 mapdh8aa 40239 mapdh8ab 40240 mapdh8ac 40241 mapdh8ad 40242 mapdh8b 40243 mapdh8c 40244 mapdh8d 40246 mapdh8d0N 40245 mapdh8e 40247 mapdh8g 40248 mapdh8i 40249 mapdh8j 40250 |
| [Baer] p. 48 | Part (9) | mapdh9a 40252 |
| [Baer] p. 48 | Equation 10 | mapdhvmap 40232 |
| [Baer] p. 49 | Part 12 | hdmap11 40311 hdmapeq0 40307 hdmapf1oN 40328 hdmapneg 40309 hdmaprnN 40327 hdmaprnlem1N 40312 hdmaprnlem3N 40313 hdmaprnlem3uN 40314 hdmaprnlem4N 40316 hdmaprnlem6N 40317 hdmaprnlem7N 40318 hdmaprnlem8N 40319 hdmaprnlem9N 40320 hdmapsub 40310 |
| [Baer] p. 49 | Part 14 | hdmap14lem1 40331 hdmap14lem10 40340 hdmap14lem1a 40329 hdmap14lem2N 40332 hdmap14lem2a 40330 hdmap14lem3 40333 hdmap14lem8 40338 hdmap14lem9 40339 |
| [Baer] p. 50 | Part 14 | hdmap14lem11 40341 hdmap14lem12 40342 hdmap14lem13 40343 hdmap14lem14 40344 hdmap14lem15 40345 hgmapval 40350 |
| [Baer] p. 50 | Part 15 | hgmapadd 40357 hgmapmul 40358 hgmaprnlem2N 40360 hgmapvs 40354 |
| [Baer] p. 50 | Part 16 | hgmaprnN 40364 |
| [Baer] p. 110 | Lemma 1 | hdmapip0com 40380 |
| [Baer] p. 110 | Line 27 | hdmapinvlem1 40381 |
| [Baer] p. 110 | Line 28 | hdmapinvlem2 40382 |
| [Baer] p. 110 | Line 30 | hdmapinvlem3 40383 |
| [Baer] p. 110 | Part 1.2 | hdmapglem5 40385 hgmapvv 40389 |
| [Baer] p. 110 | Proposition 1 | hdmapinvlem4 40384 |
| [Baer] p. 111 | Line 10 | hgmapvvlem1 40386 |
| [Baer] p. 111 | Line 15 | hdmapg 40393 hdmapglem7 40392 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 26085 2irrexpqALT 26150 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 23 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2567 |
| [BellMachover] p. 460 | Notation | df-mo 2538 |
| [BellMachover] p. 460 | Definition | mo3 2562 |
| [BellMachover] p. 461 | Axiom Ext | ax-ext 2707 |
| [BellMachover] p. 462 | Theorem 1.1 | axextmo 2711 |
| [BellMachover] p. 463 | Axiom Rep | axrep5 5248 |
| [BellMachover] p. 463 | Scheme Sep | ax-sep 5256 |
| [BellMachover] p. 463 | Theorem 1.3(ii) | bj-bm1.3ii 35535 bm1.3ii 5259 |
| [BellMachover] p. 466 | Problem | axpow2 5322 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 5323 |
| [BellMachover] p. 466 | Axiom Union | axun2 7674 |
| [BellMachover] p. 468 | Definition | df-ord 6320 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 6335 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 6342 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 6337 |
| [BellMachover] p. 471 | Definition of N | df-om 7803 |
| [BellMachover] p. 471 | Problem 2.5(ii) | uniordint 7736 |
| [BellMachover] p. 471 | Definition of Lim | df-lim 6322 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 9578 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 7818 |
| [BellMachover] p. 477 | Equation 3.1 | df-r1 9700 |
| [BellMachover] p. 478 | Definition | rankval2 9754 |
| [BellMachover] p. 478 | Theorem 3.3(i) | r1ord3 9718 r1ord3g 9715 |
| [BellMachover] p. 480 | Axiom Reg | zfreg 9531 |
| [BellMachover] p. 488 | Axiom AC | ac5 10413 dfac4 10058 |
| [BellMachover] p. 490 | Definition of aleph | alephval3 10046 |
| [BeltramettiCassinelli] p. 98 | Remark | atlatmstc 37781 |
| [BeltramettiCassinelli] p. 107 | Remark 10.3.5 | atom1d 31295 |
| [BeltramettiCassinelli] p. 166 | Theorem 14.8.4 | chirred 31337 chirredi 31336 |
| [BeltramettiCassinelli1] p. 400 | Proposition P8(ii) | atoml2i 31325 |
| [Beran] p. 3 | Definition of join | sshjval3 30296 |
| [Beran] p. 39 | Theorem 2.3(i) | cmcm2 30558 cmcm2i 30535 cmcm2ii 30540 cmt2N 37712 |
| [Beran] p. 40 | Theorem 2.3(iii) | lecm 30559 lecmi 30544 lecmii 30545 |
| [Beran] p. 45 | Theorem 3.4 | cmcmlem 30533 |
| [Beran] p. 49 | Theorem 4.2 | cm2j 30562 cm2ji 30567 cm2mi 30568 |
| [Beran] p. 95 | Definition | df-sh 30149 issh2 30151 |
| [Beran] p. 95 | Lemma 3.1(S5) | his5 30028 |
| [Beran] p. 95 | Lemma 3.1(S6) | his6 30041 |
| [Beran] p. 95 | Lemma 3.1(S7) | his7 30032 |
| [Beran] p. 95 | Lemma 3.2(S8) | ho01i 30770 |
| [Beran] p. 95 | Lemma 3.2(S9) | hoeq1 30772 |
| [Beran] p. 95 | Lemma 3.2(S10) | ho02i 30771 |
| [Beran] p. 95 | Lemma 3.2(S11) | hoeq2 30773 |
| [Beran] p. 95 | Postulate (S1) | ax-his1 30024 his1i 30042 |
| [Beran] p. 95 | Postulate (S2) | ax-his2 30025 |
| [Beran] p. 95 | Postulate (S3) | ax-his3 30026 |
| [Beran] p. 95 | Postulate (S4) | ax-his4 30027 |
| [Beran] p. 96 | Definition of norm | df-hnorm 29910 dfhnorm2 30064 normval 30066 |
| [Beran] p. 96 | Definition for Cauchy sequence | hcau 30126 |
| [Beran] p. 96 | Definition of Cauchy sequence | df-hcau 29915 |
| [Beran] p. 96 | Definition of complete subspace | isch3 30183 |
| [Beran] p. 96 | Definition of converge | df-hlim 29914 hlimi 30130 |
| [Beran] p. 97 | Theorem 3.3(i) | norm-i-i 30075 norm-i 30071 |
| [Beran] p. 97 | Theorem 3.3(ii) | norm-ii-i 30079 norm-ii 30080 normlem0 30051 normlem1 30052 normlem2 30053 normlem3 30054 normlem4 30055 normlem5 30056 normlem6 30057 normlem7 30058 normlem7tALT 30061 |
| [Beran] p. 97 | Theorem 3.3(iii) | norm-iii-i 30081 norm-iii 30082 |
| [Beran] p. 98 | Remark 3.4 | bcs 30123 bcsiALT 30121 bcsiHIL 30122 |
| [Beran] p. 98 | Remark 3.4(B) | normlem9at 30063 normpar 30097 normpari 30096 |
| [Beran] p. 98 | Remark 3.4(C) | normpyc 30088 normpyth 30087 normpythi 30084 |
| [Beran] p. 99 | Remark | lnfn0 30989 lnfn0i 30984 lnop0 30908 lnop0i 30912 |
| [Beran] p. 99 | Theorem 3.5(i) | nmcexi 30968 nmcfnex 30995 nmcfnexi 30993 nmcopex 30971 nmcopexi 30969 |
| [Beran] p. 99 | Theorem 3.5(ii) | nmcfnlb 30996 nmcfnlbi 30994 nmcoplb 30972 nmcoplbi 30970 |
| [Beran] p. 99 | Theorem 3.5(iii) | lnfncon 30998 lnfnconi 30997 lnopcon 30977 lnopconi 30976 |
| [Beran] p. 100 | Lemma 3.6 | normpar2i 30098 |
| [Beran] p. 101 | Lemma 3.6 | norm3adifi 30095 norm3adifii 30090 norm3dif 30092 norm3difi 30089 |
| [Beran] p. 102 | Theorem 3.7(i) | chocunii 30243 pjhth 30335 pjhtheu 30336 pjpjhth 30367 pjpjhthi 30368 pjth 24803 |
| [Beran] p. 102 | Theorem 3.7(ii) | ococ 30348 ococi 30347 |
| [Beran] p. 103 | Remark 3.8 | nlelchi 31003 |
| [Beran] p. 104 | Theorem 3.9 | riesz3i 31004 riesz4 31006 riesz4i 31005 |
| [Beran] p. 104 | Theorem 3.10 | cnlnadj 31021 cnlnadjeu 31020 cnlnadjeui 31019 cnlnadji 31018 cnlnadjlem1 31009 nmopadjlei 31030 |
| [Beran] p. 106 | Theorem 3.11(i) | adjeq0 31033 |
| [Beran] p. 106 | Theorem 3.11(v) | nmopadji 31032 |
| [Beran] p. 106 | Theorem 3.11(ii) | adjmul 31034 |
| [Beran] p. 106 | Theorem 3.11(iv) | adjadj 30878 |
| [Beran] p. 106 | Theorem 3.11(vi) | nmopcoadj2i 31044 nmopcoadji 31043 |
| [Beran] p. 106 | Theorem 3.11(iii) | adjadd 31035 |
| [Beran] p. 106 | Theorem 3.11(vii) | nmopcoadj0i 31045 |
| [Beran] p. 106 | Theorem 3.11(viii) | adjcoi 31042 pjadj2coi 31146 pjadjcoi 31103 |
| [Beran] p. 107 | Definition | df-ch 30163 isch2 30165 |
| [Beran] p. 107 | Remark 3.12 | choccl 30248 isch3 30183 occl 30246 ocsh 30225 shoccl 30247 shocsh 30226 |
| [Beran] p. 107 | Remark 3.12(B) | ococin 30350 |
| [Beran] p. 108 | Theorem 3.13 | chintcl 30274 |
| [Beran] p. 109 | Property (i) | pjadj2 31129 pjadj3 31130 pjadji 30627 pjadjii 30616 |
| [Beran] p. 109 | Property (ii) | pjidmco 31123 pjidmcoi 31119 pjidmi 30615 |
| [Beran] p. 110 | Definition of projector ordering | pjordi 31115 |
| [Beran] p. 111 | Remark | ho0val 30692 pjch1 30612 |
| [Beran] p. 111 | Definition | df-hfmul 30676 df-hfsum 30675 df-hodif 30674 df-homul 30673 df-hosum 30672 |
| [Beran] p. 111 | Lemma 4.4(i) | pjo 30613 |
| [Beran] p. 111 | Lemma 4.4(ii) | pjch 30636 pjchi 30374 |
| [Beran] p. 111 | Lemma 4.4(iii) | pjoc2 30381 pjoc2i 30380 |
| [Beran] p. 112 | Theorem 4.5(i)->(ii) | pjss2i 30622 |
| [Beran] p. 112 | Theorem 4.5(i)->(iv) | pjssmi 31107 pjssmii 30623 |
| [Beran] p. 112 | Theorem 4.5(i)<->(ii) | pjss2coi 31106 |
| [Beran] p. 112 | Theorem 4.5(i)<->(iii) | pjss1coi 31105 |
| [Beran] p. 112 | Theorem 4.5(i)<->(vi) | pjnormssi 31110 |
| [Beran] p. 112 | Theorem 4.5(iv)->(v) | pjssge0i 31108 pjssge0ii 30624 |
| [Beran] p. 112 | Theorem 4.5(v)<->(vi) | pjdifnormi 31109 pjdifnormii 30625 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1778 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1776 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1779 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1774 |
| [Bogachev] p. 16 | Definition 1.5 | df-oms 32892 |
| [Bogachev] p. 17 | Lemma 1.5.4 | omssubadd 32900 |
| [Bogachev] p. 17 | Example 1.5.2 | omsmon 32898 |
| [Bogachev] p. 41 | Definition 1.11.2 | df-carsg 32902 |
| [Bogachev] p. 42 | Theorem 1.11.4 | carsgsiga 32922 |
| [Bogachev] p. 116 | Definition 2.3.1 | df-itgm 32953 df-sitm 32931 |
| [Bogachev] p. 118 | Chapter 2.4.4 | df-itgm 32953 |
| [Bogachev] p. 118 | Definition 2.4.1 | df-sitg 32930 |
| [Bollobas] p. 1 | Section I.1 | df-edg 27999 isuhgrop 28021 isusgrop 28113 isuspgrop 28112 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 28216 uhgrspan1 28251 uhgrspansubgr 28239 |
| [Bollobas] p. 3 | Definition | isomuspgr 46016 |
| [Bollobas] p. 3 | Section I.1 | cusgrsize 28402 df-cusgr 28360 df-nbgr 28281 fusgrmaxsize 28412 |
| [Bollobas] p. 4 | Definition | df-upwlks 46026 df-wlks 28547 |
| [Bollobas] p. 4 | Section I.1 | finsumvtxdg2size 28498 finsumvtxdgeven 28500 fusgr1th 28499 fusgrvtxdgonume 28502 vtxdgoddnumeven 28501 |
| [Bollobas] p. 5 | Notation | df-pths 28664 |
| [Bollobas] p. 5 | Definition | df-crcts 28734 df-cycls 28735 df-trls 28640 df-wlkson 28548 |
| [Bollobas] p. 7 | Section I.1 | df-ushgr 28010 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-clintop 46124 df-cllaw 46110 df-mgm 18497 df-mgm2 46143 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-assintop 46125 df-asslaw 46112 df-sgrp 18546 df-sgrp2 46145 |
| [BourbakiAlg1] p. 7 | Definition 8 | df-cmgm2 46144 df-comlaw 46111 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 18557 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 19966 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 46163 |
| [BourbakiEns] p. | Proposition 8 | fcof1 7233 fcofo 7234 |
| [BourbakiTop1] p. | Remark | xnegmnf 13129 xnegpnf 13128 |
| [BourbakiTop1] p. | Remark | rexneg 13130 |
| [BourbakiTop1] p. | Remark 3 | ust0 23571 ustfilxp 23564 |
| [BourbakiTop1] p. | Axiom GT' | tgpsubcn 23441 |
| [BourbakiTop1] p. | Criterion | ishmeo 23110 |
| [BourbakiTop1] p. | Example 1 | cstucnd 23636 iducn 23635 snfil 23215 |
| [BourbakiTop1] p. | Example 2 | neifil 23231 |
| [BourbakiTop1] p. | Theorem 1 | cnextcn 23418 |
| [BourbakiTop1] p. | Theorem 2 | ucnextcn 23656 |
| [BourbakiTop1] p. | Theorem 3 | df-hcmp 32538 |
| [BourbakiTop1] p. | Paragraph 3 | infil 23214 |
| [BourbakiTop1] p. | Definition 1 | df-ucn 23628 df-ust 23552 filintn0 23212 filn0 23213 istgp 23428 ucnprima 23634 |
| [BourbakiTop1] p. | Definition 2 | df-cfilu 23639 |
| [BourbakiTop1] p. | Definition 3 | df-cusp 23650 df-usp 23609 df-utop 23583 trust 23581 |
| [BourbakiTop1] p. | Definition 6 | df-pcmp 32437 |
| [BourbakiTop1] p. | Property V_i | ssnei2 22467 |
| [BourbakiTop1] p. | Theorem 1(d) | iscncl 22620 |
| [BourbakiTop1] p. | Condition F_I | ustssel 23557 |
| [BourbakiTop1] p. | Condition U_I | ustdiag 23560 |
| [BourbakiTop1] p. | Property V_ii | innei 22476 |
| [BourbakiTop1] p. | Property V_iv | neiptopreu 22484 neissex 22478 |
| [BourbakiTop1] p. | Proposition 1 | neips 22464 neiss 22460 ucncn 23637 ustund 23573 ustuqtop 23598 |
| [BourbakiTop1] p. | Proposition 2 | cnpco 22618 neiptopreu 22484 utop2nei 23602 utop3cls 23603 |
| [BourbakiTop1] p. | Proposition 3 | fmucnd 23644 uspreg 23626 utopreg 23604 |
| [BourbakiTop1] p. | Proposition 4 | imasncld 23042 imasncls 23043 imasnopn 23041 |
| [BourbakiTop1] p. | Proposition 9 | cnpflf2 23351 |
| [BourbakiTop1] p. | Condition F_II | ustincl 23559 |
| [BourbakiTop1] p. | Condition U_II | ustinvel 23561 |
| [BourbakiTop1] p. | Property V_iii | elnei 22462 |
| [BourbakiTop1] p. | Proposition 11 | cnextucn 23655 |
| [BourbakiTop1] p. | Condition F_IIb | ustbasel 23558 |
| [BourbakiTop1] p. | Condition U_III | ustexhalf 23562 |
| [BourbakiTop1] p. | Definition C''' | df-cmp 22738 |
| [BourbakiTop1] p. | Axioms FI, FIIa, FIIb, FIII) | df-fil 23197 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 22243 |
| [BourbakiTop2] p. 195 | Definition 1 | df-ldlf 32434 |
| [BrosowskiDeutsh] p. 89 | Proof follows | stoweidlem62 44293 |
| [BrosowskiDeutsh] p. 89 | Lemmas are written following | stowei 44295 stoweid 44294 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem1 44232 stoweidlem10 44241 stoweidlem14 44245 stoweidlem15 44246 stoweidlem35 44266 stoweidlem36 44267 stoweidlem37 44268 stoweidlem38 44269 stoweidlem40 44271 stoweidlem41 44272 stoweidlem43 44274 stoweidlem44 44275 stoweidlem46 44277 stoweidlem5 44236 stoweidlem50 44281 stoweidlem52 44283 stoweidlem53 44284 stoweidlem55 44286 stoweidlem56 44287 |
| [BrosowskiDeutsh] p. 90 | Lemma 1 | stoweidlem23 44254 stoweidlem24 44255 stoweidlem27 44258 stoweidlem28 44259 stoweidlem30 44261 |
| [BrosowskiDeutsh] p. 91 | Proof | stoweidlem34 44265 stoweidlem59 44290 stoweidlem60 44291 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem45 44276 stoweidlem49 44280 stoweidlem7 44238 |
| [BrosowskiDeutsh] p. 91 | Lemma 2 | stoweidlem31 44262 stoweidlem39 44270 stoweidlem42 44273 stoweidlem48 44279 stoweidlem51 44282 stoweidlem54 44285 stoweidlem57 44288 stoweidlem58 44289 |
| [BrosowskiDeutsh] p. 91 | Lemma 1 | stoweidlem25 44256 |
| [BrosowskiDeutsh] p. 91 | Lemma proves that the function ` ` (as defined | stoweidlem17 44248 |
| [BrosowskiDeutsh] p. 92 | Proof | stoweidlem11 44242 stoweidlem13 44244 stoweidlem26 44257 stoweidlem61 44292 |
| [BrosowskiDeutsh] p. 92 | Lemma 2 | stoweidlem18 44249 |
| [Bruck] p. 1 | Section I.1 | df-clintop 46124 df-mgm 18497 df-mgm2 46143 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 18546 df-sgrp2 46145 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3 18846 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 5189 |
| [Church] p. 129 | Section II.24 | df-ifp 1062 dfifp2 1063 |
| [Clemente] p. 10 | Definition IT | natded 29347 |
| [Clemente] p. 10 | Definition I` `m,n | natded 29347 |
| [Clemente] p. 11 | Definition E=>m,n | natded 29347 |
| [Clemente] p. 11 | Definition I=>m,n | natded 29347 |
| [Clemente] p. 11 | Definition E` `(1) | natded 29347 |
| [Clemente] p. 11 | Definition E` `(2) | natded 29347 |
| [Clemente] p. 12 | Definition E` `m,n,p | natded 29347 |
| [Clemente] p. 12 | Definition I` `n(1) | natded 29347 |
| [Clemente] p. 12 | Definition I` `n(2) | natded 29347 |
| [Clemente] p. 13 | Definition I` `m,n,p | natded 29347 |
| [Clemente] p. 14 | Proof 5.11 | natded 29347 |
| [Clemente] p. 14 | Definition E` `n | natded 29347 |
| [Clemente] p. 15 | Theorem 5.2 | ex-natded5.2-2 29349 ex-natded5.2 29348 |
| [Clemente] p. 16 | Theorem 5.3 | ex-natded5.3-2 29352 ex-natded5.3 29351 |
| [Clemente] p. 18 | Theorem 5.5 | ex-natded5.5 29354 |
| [Clemente] p. 19 | Theorem 5.7 | ex-natded5.7-2 29356 ex-natded5.7 29355 |
| [Clemente] p. 20 | Theorem 5.8 | ex-natded5.8-2 29358 ex-natded5.8 29357 |
| [Clemente] p. 20 | Theorem 5.13 | ex-natded5.13-2 29360 ex-natded5.13 29359 |
| [Clemente] p. 32 | Definition I` `n | natded 29347 |
| [Clemente] p. 32 | Definition E` `m,n,p,a | natded 29347 |
| [Clemente] p. 32 | Definition E` `n,t | natded 29347 |
| [Clemente] p. 32 | Definition I` `n,t | natded 29347 |
| [Clemente] p. 43 | Theorem 9.20 | ex-natded9.20 29361 |
| [Clemente] p. 45 | Theorem 9.20 | ex-natded9.20-2 29362 |
| [Clemente] p. 45 | Theorem 9.26 | ex-natded9.26-2 29364 ex-natded9.26 29363 |
| [Cohen] p. 301 | Remark | relogoprlem 25946 |
| [Cohen] p. 301 | Property 2 | relogmul 25947 relogmuld 25980 |
| [Cohen] p. 301 | Property 3 | relogdiv 25948 relogdivd 25981 |
| [Cohen] p. 301 | Property 4 | relogexp 25951 |
| [Cohen] p. 301 | Property 1a | log1 25941 |
| [Cohen] p. 301 | Property 1b | loge 25942 |
| [Cohen4] p. 348 | Observation | relogbcxpb 26137 |
| [Cohen4] p. 349 | Property | relogbf 26141 |
| [Cohen4] p. 352 | Definition | elogb 26120 |
| [Cohen4] p. 361 | Property 2 | relogbmul 26127 |
| [Cohen4] p. 361 | Property 3 | logbrec 26132 relogbdiv 26129 |
| [Cohen4] p. 361 | Property 4 | relogbreexp 26125 |
| [Cohen4] p. 361 | Property 6 | relogbexp 26130 |
| [Cohen4] p. 361 | Property 1(a) | logbid1 26118 |
| [Cohen4] p. 361 | Property 1(b) | logb1 26119 |
| [Cohen4] p. 367 | Property | logbchbase 26121 |
| [Cohen4] p. 377 | Property 2 | logblt 26134 |
| [Cohn] p. 4 | Proposition 1.1.5 | sxbrsigalem1 32885 sxbrsigalem4 32887 |
| [Cohn] p. 81 | Section II.5 | acsdomd 18446 acsinfd 18445 acsinfdimd 18447 acsmap2d 18444 acsmapd 18443 |
| [Cohn] p. 143 | Example 5.1.1 | sxbrsiga 32890 |
| [Connell] p. 57 | Definition | df-scmat 21840 df-scmatalt 46470 |
| [Conway] p. 4 | Definition | slerec 27158 |
| [Conway] p. 5 | Definition | addsval 27274 addsval2 27275 df-adds 27272 df-muls 34406 df-negs 27320 |
| [Conway] p. 7 | Theorem | 0slt1s 27168 |
| [Conway] p. 16 | Theorem 0(i) | ssltright 27201 |
| [Conway] p. 16 | Theorem 0(ii) | ssltleft 27200 |
| [Conway] p. 16 | Theorem 0(iii) | slerflex 27111 |
| [Conway] p. 17 | Theorem 3 | addsass 27313 addsassd 27314 addscom 27278 addscomd 27279 addsid1 27276 addsid1d 27277 |
| [Conway] p. 17 | Definition | df-0s 27163 |
| [Conway] p. 17 | Theorem 4(ii) | negnegs 27342 |
| [Conway] p. 17 | Theorem 4(iii) | negsid 27339 negsidd 27340 |
| [Conway] p. 18 | Theorem 5 | sleadd1 27298 sleadd1d 27304 |
| [Conway] p. 18 | Definition | df-1s 27164 |
| [Conway] p. 18 | Theorem 6(ii) | negscl 27334 negscld 27335 |
| [Conway] p. 18 | Theorem 6(iii) | addscld 27290 |
| [Conway] p. 29 | Remark | madebday 27229 newbday 27231 oldbday 27230 |
| [Conway] p. 29 | Definition | df-made 27177 df-new 27179 df-old 27178 |
| [CormenLeisersonRivest] p. 33 | Equation 2.4 | fldiv2 13766 |
| [Crawley] p. 1 | Definition of poset | df-poset 18202 |
| [Crawley] p. 107 | Theorem 13.2 | hlsupr 37849 |
| [Crawley] p. 110 | Theorem 13.3 | arglem1N 38653 dalaw 38349 |
| [Crawley] p. 111 | Theorem 13.4 | hlathil 40428 |
| [Crawley] p. 111 | Definition of set W | df-watsN 38453 |
| [Crawley] p. 111 | Definition of dilation | df-dilN 38569 df-ldil 38567 isldil 38573 |
| [Crawley] p. 111 | Definition of translation | df-ltrn 38568 df-trnN 38570 isltrn 38582 ltrnu 38584 |
| [Crawley] p. 112 | Lemma A | cdlema1N 38254 cdlema2N 38255 exatleN 37867 |
| [Crawley] p. 112 | Lemma B | 1cvrat 37939 cdlemb 38257 cdlemb2 38504 cdlemb3 39069 idltrn 38613 l1cvat 37517 lhpat 38506 lhpat2 38508 lshpat 37518 ltrnel 38602 ltrnmw 38614 |
| [Crawley] p. 112 | Lemma C | cdlemc1 38654 cdlemc2 38655 ltrnnidn 38637 trlat 38632 trljat1 38629 trljat2 38630 trljat3 38631 trlne 38648 trlnidat 38636 trlnle 38649 |
| [Crawley] p. 112 | Definition of automorphism | df-pautN 38454 |
| [Crawley] p. 113 | Lemma C | cdlemc 38660 cdlemc3 38656 cdlemc4 38657 |
| [Crawley] p. 113 | Lemma D | cdlemd 38670 cdlemd1 38661 cdlemd2 38662 cdlemd3 38663 cdlemd4 38664 cdlemd5 38665 cdlemd6 38666 cdlemd7 38667 cdlemd8 38668 cdlemd9 38669 cdleme31sde 38848 cdleme31se 38845 cdleme31se2 38846 cdleme31snd 38849 cdleme32a 38904 cdleme32b 38905 cdleme32c 38906 cdleme32d 38907 cdleme32e 38908 cdleme32f 38909 cdleme32fva 38900 cdleme32fva1 38901 cdleme32fvcl 38903 cdleme32le 38910 cdleme48fv 38962 cdleme4gfv 38970 cdleme50eq 39004 cdleme50f 39005 cdleme50f1 39006 cdleme50f1o 39009 cdleme50laut 39010 cdleme50ldil 39011 cdleme50lebi 39003 cdleme50rn 39008 cdleme50rnlem 39007 cdlemeg49le 38974 cdlemeg49lebilem 39002 |
| [Crawley] p. 113 | Lemma E | cdleme 39023 cdleme00a 38672 cdleme01N 38684 cdleme02N 38685 cdleme0a 38674 cdleme0aa 38673 cdleme0b 38675 cdleme0c 38676 cdleme0cp 38677 cdleme0cq 38678 cdleme0dN 38679 cdleme0e 38680 cdleme0ex1N 38686 cdleme0ex2N 38687 cdleme0fN 38681 cdleme0gN 38682 cdleme0moN 38688 cdleme1 38690 cdleme10 38717 cdleme10tN 38721 cdleme11 38733 cdleme11a 38723 cdleme11c 38724 cdleme11dN 38725 cdleme11e 38726 cdleme11fN 38727 cdleme11g 38728 cdleme11h 38729 cdleme11j 38730 cdleme11k 38731 cdleme11l 38732 cdleme12 38734 cdleme13 38735 cdleme14 38736 cdleme15 38741 cdleme15a 38737 cdleme15b 38738 cdleme15c 38739 cdleme15d 38740 cdleme16 38748 cdleme16aN 38722 cdleme16b 38742 cdleme16c 38743 cdleme16d 38744 cdleme16e 38745 cdleme16f 38746 cdleme16g 38747 cdleme19a 38766 cdleme19b 38767 cdleme19c 38768 cdleme19d 38769 cdleme19e 38770 cdleme19f 38771 cdleme1b 38689 cdleme2 38691 cdleme20aN 38772 cdleme20bN 38773 cdleme20c 38774 cdleme20d 38775 cdleme20e 38776 cdleme20f 38777 cdleme20g 38778 cdleme20h 38779 cdleme20i 38780 cdleme20j 38781 cdleme20k 38782 cdleme20l 38785 cdleme20l1 38783 cdleme20l2 38784 cdleme20m 38786 cdleme20y 38765 cdleme20zN 38764 cdleme21 38800 cdleme21d 38793 cdleme21e 38794 cdleme22a 38803 cdleme22aa 38802 cdleme22b 38804 cdleme22cN 38805 cdleme22d 38806 cdleme22e 38807 cdleme22eALTN 38808 cdleme22f 38809 cdleme22f2 38810 cdleme22g 38811 cdleme23a 38812 cdleme23b 38813 cdleme23c 38814 cdleme26e 38822 cdleme26eALTN 38824 cdleme26ee 38823 cdleme26f 38826 cdleme26f2 38828 cdleme26f2ALTN 38827 cdleme26fALTN 38825 cdleme27N 38832 cdleme27a 38830 cdleme27cl 38829 cdleme28c 38835 cdleme3 38700 cdleme30a 38841 cdleme31fv 38853 cdleme31fv1 38854 cdleme31fv1s 38855 cdleme31fv2 38856 cdleme31id 38857 cdleme31sc 38847 cdleme31sdnN 38850 cdleme31sn 38843 cdleme31sn1 38844 cdleme31sn1c 38851 cdleme31sn2 38852 cdleme31so 38842 cdleme35a 38911 cdleme35b 38913 cdleme35c 38914 cdleme35d 38915 cdleme35e 38916 cdleme35f 38917 cdleme35fnpq 38912 cdleme35g 38918 cdleme35h 38919 cdleme35h2 38920 cdleme35sn2aw 38921 cdleme35sn3a 38922 cdleme36a 38923 cdleme36m 38924 cdleme37m 38925 cdleme38m 38926 cdleme38n 38927 cdleme39a 38928 cdleme39n 38929 cdleme3b 38692 cdleme3c 38693 cdleme3d 38694 cdleme3e 38695 cdleme3fN 38696 cdleme3fa 38699 cdleme3g 38697 cdleme3h 38698 cdleme4 38701 cdleme40m 38930 cdleme40n 38931 cdleme40v 38932 cdleme40w 38933 cdleme41fva11 38940 cdleme41sn3aw 38937 cdleme41sn4aw 38938 cdleme41snaw 38939 cdleme42a 38934 cdleme42b 38941 cdleme42c 38935 cdleme42d 38936 cdleme42e 38942 cdleme42f 38943 cdleme42g 38944 cdleme42h 38945 cdleme42i 38946 cdleme42k 38947 cdleme42ke 38948 cdleme42keg 38949 cdleme42mN 38950 cdleme42mgN 38951 cdleme43aN 38952 cdleme43bN 38953 cdleme43cN 38954 cdleme43dN 38955 cdleme5 38703 cdleme50ex 39022 cdleme50ltrn 39020 cdleme51finvN 39019 cdleme51finvfvN 39018 cdleme51finvtrN 39021 cdleme6 38704 cdleme7 38712 cdleme7a 38706 cdleme7aa 38705 cdleme7b 38707 cdleme7c 38708 cdleme7d 38709 cdleme7e 38710 cdleme7ga 38711 cdleme8 38713 cdleme8tN 38718 cdleme9 38716 cdleme9a 38714 cdleme9b 38715 cdleme9tN 38720 cdleme9taN 38719 cdlemeda 38761 cdlemedb 38760 cdlemednpq 38762 cdlemednuN 38763 cdlemefr27cl 38866 cdlemefr32fva1 38873 cdlemefr32fvaN 38872 cdlemefrs32fva 38863 cdlemefrs32fva1 38864 cdlemefs27cl 38876 cdlemefs32fva1 38886 cdlemefs32fvaN 38885 cdlemesner 38759 cdlemeulpq 38683 |
| [Crawley] p. 114 | Lemma E | 4atex 38539 4atexlem7 38538 cdleme0nex 38753 cdleme17a 38749 cdleme17c 38751 cdleme17d 38961 cdleme17d1 38752 cdleme17d2 38958 cdleme18a 38754 cdleme18b 38755 cdleme18c 38756 cdleme18d 38758 cdleme4a 38702 |
| [Crawley] p. 115 | Lemma E | cdleme21a 38788 cdleme21at 38791 cdleme21b 38789 cdleme21c 38790 cdleme21ct 38792 cdleme21f 38795 cdleme21g 38796 cdleme21h 38797 cdleme21i 38798 cdleme22gb 38757 |
| [Crawley] p. 116 | Lemma F | cdlemf 39026 cdlemf1 39024 cdlemf2 39025 |
| [Crawley] p. 116 | Lemma G | cdlemftr1 39030 cdlemg16 39120 cdlemg28 39167 cdlemg28a 39156 cdlemg28b 39166 cdlemg3a 39060 cdlemg42 39192 cdlemg43 39193 cdlemg44 39196 cdlemg44a 39194 cdlemg46 39198 cdlemg47 39199 cdlemg9 39097 ltrnco 39182 ltrncom 39201 tgrpabl 39214 trlco 39190 |
| [Crawley] p. 116 | Definition of G | df-tgrp 39206 |
| [Crawley] p. 117 | Lemma G | cdlemg17 39140 cdlemg17b 39125 |
| [Crawley] p. 117 | Definition of E | df-edring-rN 39219 df-edring 39220 |
| [Crawley] p. 117 | Definition of trace-preserving endomorphism | istendo 39223 |
| [Crawley] p. 118 | Remark | tendopltp 39243 |
| [Crawley] p. 118 | Lemma H | cdlemh 39280 cdlemh1 39278 cdlemh2 39279 |
| [Crawley] p. 118 | Lemma I | cdlemi 39283 cdlemi1 39281 cdlemi2 39282 |
| [Crawley] p. 118 | Lemma J | cdlemj1 39284 cdlemj2 39285 cdlemj3 39286 tendocan 39287 |
| [Crawley] p. 118 | Lemma K | cdlemk 39437 cdlemk1 39294 cdlemk10 39306 cdlemk11 39312 cdlemk11t 39409 cdlemk11ta 39392 cdlemk11tb 39394 cdlemk11tc 39408 cdlemk11u-2N 39352 cdlemk11u 39334 cdlemk12 39313 cdlemk12u-2N 39353 cdlemk12u 39335 cdlemk13-2N 39339 cdlemk13 39315 cdlemk14-2N 39341 cdlemk14 39317 cdlemk15-2N 39342 cdlemk15 39318 cdlemk16-2N 39343 cdlemk16 39320 cdlemk16a 39319 cdlemk17-2N 39344 cdlemk17 39321 cdlemk18-2N 39349 cdlemk18-3N 39363 cdlemk18 39331 cdlemk19-2N 39350 cdlemk19 39332 cdlemk19u 39433 cdlemk1u 39322 cdlemk2 39295 cdlemk20-2N 39355 cdlemk20 39337 cdlemk21-2N 39354 cdlemk21N 39336 cdlemk22-3 39364 cdlemk22 39356 cdlemk23-3 39365 cdlemk24-3 39366 cdlemk25-3 39367 cdlemk26-3 39369 cdlemk26b-3 39368 cdlemk27-3 39370 cdlemk28-3 39371 cdlemk29-3 39374 cdlemk3 39296 cdlemk30 39357 cdlemk31 39359 cdlemk32 39360 cdlemk33N 39372 cdlemk34 39373 cdlemk35 39375 cdlemk36 39376 cdlemk37 39377 cdlemk38 39378 cdlemk39 39379 cdlemk39u 39431 cdlemk4 39297 cdlemk41 39383 cdlemk42 39404 cdlemk42yN 39407 cdlemk43N 39426 cdlemk45 39410 cdlemk46 39411 cdlemk47 39412 cdlemk48 39413 cdlemk49 39414 cdlemk5 39299 cdlemk50 39415 cdlemk51 39416 cdlemk52 39417 cdlemk53 39420 cdlemk54 39421 cdlemk55 39424 cdlemk55u 39429 cdlemk56 39434 cdlemk5a 39298 cdlemk5auN 39323 cdlemk5u 39324 cdlemk6 39300 cdlemk6u 39325 cdlemk7 39311 cdlemk7u-2N 39351 cdlemk7u 39333 cdlemk8 39301 cdlemk9 39302 cdlemk9bN 39303 cdlemki 39304 cdlemkid 39399 cdlemkj-2N 39345 cdlemkj 39326 cdlemksat 39309 cdlemksel 39308 cdlemksv 39307 cdlemksv2 39310 cdlemkuat 39329 cdlemkuel-2N 39347 cdlemkuel-3 39361 cdlemkuel 39328 cdlemkuv-2N 39346 cdlemkuv2-2 39348 cdlemkuv2-3N 39362 cdlemkuv2 39330 cdlemkuvN 39327 cdlemkvcl 39305 cdlemky 39389 cdlemkyyN 39425 tendoex 39438 |
| [Crawley] p. 120 | Remark | dva1dim 39448 |
| [Crawley] p. 120 | Lemma L | cdleml1N 39439 cdleml2N 39440 cdleml3N 39441 cdleml4N 39442 cdleml5N 39443 cdleml6 39444 cdleml7 39445 cdleml8 39446 cdleml9 39447 dia1dim 39524 |
| [Crawley] p. 120 | Lemma M | dia11N 39511 diaf11N 39512 dialss 39509 diaord 39510 dibf11N 39624 djajN 39600 |
| [Crawley] p. 120 | Definition of isomorphism map | diaval 39495 |
| [Crawley] p. 121 | Lemma M | cdlemm10N 39581 dia2dimlem1 39527 dia2dimlem2 39528 dia2dimlem3 39529 dia2dimlem4 39530 dia2dimlem5 39531 diaf1oN 39593 diarnN 39592 dvheveccl 39575 dvhopN 39579 |
| [Crawley] p. 121 | Lemma N | cdlemn 39675 cdlemn10 39669 cdlemn11 39674 cdlemn11a 39670 cdlemn11b 39671 cdlemn11c 39672 cdlemn11pre 39673 cdlemn2 39658 cdlemn2a 39659 cdlemn3 39660 cdlemn4 39661 cdlemn4a 39662 cdlemn5 39664 cdlemn5pre 39663 cdlemn6 39665 cdlemn7 39666 cdlemn8 39667 cdlemn9 39668 diclspsn 39657 |
| [Crawley] p. 121 | Definition of phi(q) | df-dic 39636 |
| [Crawley] p. 122 | Lemma N | dih11 39728 dihf11 39730 dihjust 39680 dihjustlem 39679 dihord 39727 dihord1 39681 dihord10 39686 dihord11b 39685 dihord11c 39687 dihord2 39690 dihord2a 39682 dihord2b 39683 dihord2cN 39684 dihord2pre 39688 dihord2pre2 39689 dihordlem6 39676 dihordlem7 39677 dihordlem7b 39678 |
| [Crawley] p. 122 | Definition of isomorphism map | dihffval 39693 dihfval 39694 dihval 39695 |
| [Diestel] p. 3 | Section 1.1 | df-cusgr 28360 df-nbgr 28281 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 28216 uhgrspan1 28251 uhgrspansubgr 28239 |
| [Diestel] p. 5 | Proposition 1.2.1 | fusgrvtxdgonume 28502 vtxdgoddnumeven 28501 |
| [Diestel] p. 27 | Section 1.10 | df-ushgr 28010 |
| [EGA] p. 80 | Notation 1.1.1 | rspecval 32445 |
| [EGA] p. 80 | Proposition 1.1.2 | zartop 32457 |
| [EGA] p. 80 | Proposition 1.1.2(i) | zarcls0 32449 zarcls1 32450 |
| [EGA] p. 81 | Corollary 1.1.8 | zart0 32460 |
| [EGA], p. 82 | Proposition 1.1.10(ii) | zarcmp 32463 |
| [EGA], p. 83 | Corollary 1.2.3 | rhmpreimacn 32466 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3913 |
| [Eisenberg] p. 82 | Definition 6.3 | dfom3 9583 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 8767 |
| [Eisenberg] p. 216 | Example 13.2(4) | omenps 9591 |
| [Eisenberg] p. 310 | Theorem 19.8 | cardprc 9916 |
| [Eisenberg] p. 310 | Corollary 19.7(2) | cardsdom 10491 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 5262 |
| [Enderton] p. 19 | Definition | df-tp 4591 |
| [Enderton] p. 26 | Exercise 5 | unissb 4900 |
| [Enderton] p. 26 | Exercise 10 | pwel 5336 |
| [Enderton] p. 28 | Exercise 7(b) | pwun 5529 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1 5039 iinin2 5038 iinun2 5033 iunin1 5032 iunin1f 31476 iunin2 5031 uniin1 31470 uniin2 31471 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2 5037 iundif2 5034 |
| [Enderton] p. 32 | Exercise 20 | unineq 4237 |
| [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 7705 iunpwss 5067 |
| [Enderton] p. 36 | Definition | opthwiener 5471 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 5407 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4906 |
| [Enderton] p. 41 | Lemma 3D | opeluu 5427 rnex 7849 rnexg 7841 |
| [Enderton] p. 41 | Exercise 8 | dmuni 5870 rnuni 6101 |
| [Enderton] p. 42 | Definition of a function | dffun7 6528 dffun8 6529 |
| [Enderton] p. 43 | Definition of function value | funfv2 6929 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 6570 |
| [Enderton] p. 44 | Definition (d) | dfima2 6015 dfima3 6016 |
| [Enderton] p. 47 | Theorem 3H | fvco2 6938 |
| [Enderton] p. 49 | Axiom of Choice (first form) | ac7 10409 ac7g 10410 df-ac 10052 dfac2 10067 dfac2a 10065 dfac2b 10066 dfac3 10057 dfac7 10068 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 7193 |
| [Enderton] p. 52 | Definition | df-map 8767 |
| [Enderton] p. 53 | Exercise 21 | coass 6217 |
| [Enderton] p. 53 | Exercise 27 | dmco 6206 |
| [Enderton] p. 53 | Exercise 14(a) | funin 6577 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 6054 |
| [Enderton] p. 54 | Remark | ixpf 8858 ixpssmap 8870 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 8836 |
| [Enderton] p. 55 | Axiom of Choice (second form) | ac9 10419 ac9s 10429 |
| [Enderton] p. 56 | Theorem 3M | eqvrelref 37072 erref 8668 |
| [Enderton] p. 57 | Lemma 3N | eqvrelthi 37075 erthi 8699 |
| [Enderton] p. 57 | Definition | df-ec 8650 |
| [Enderton] p. 58 | Definition | df-qs 8654 |
| [Enderton] p. 61 | Exercise 35 | df-ec 8650 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 5866 |
| [Enderton] p. 68 | Definition of successor | df-suc 6323 |
| [Enderton] p. 71 | Definition | df-tr 5223 dftr4 5229 |
| [Enderton] p. 72 | Theorem 4E | unisuc 6396 unisucg 6395 |
| [Enderton] p. 73 | Exercise 6 | unisuc 6396 unisucg 6395 |
| [Enderton] p. 73 | Exercise 5(a) | truni 5238 |
| [Enderton] p. 73 | Exercise 5(b) | trint 5240 trintALT 43153 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 8551 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 8553 onasuc 8474 |
| [Enderton] p. 79 | Definition of operation value | df-ov 7360 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 8552 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 8554 onmsuc 8475 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 8569 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 8556 nnacom 8564 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 8570 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 8571 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 8573 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 8557 nnmsucr 8572 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 8585 |
| [Enderton] p. 129 | Definition | df-en 8884 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 7310 |
| [Enderton] p. 133 | Exercise 1 | xpomen 9951 |
| [Enderton] p. 133 | Exercise 2 | qnnen 16095 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | php 9154 |
| [Enderton] p. 135 | Corollary 6C | php3 9156 |
| [Enderton] p. 136 | Corollary 6E | nneneq 9153 |
| [Enderton] p. 136 | Corollary 6D(a) | pssinf 9200 |
| [Enderton] p. 136 | Corollary 6D(b) | ominf 9202 |
| [Enderton] p. 137 | Lemma 6F | pssnn 9112 |
| [Enderton] p. 138 | Corollary 6G | ssfi 9117 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 9085 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 10115 |
| [Enderton] p. 142 | Theorem 6I(4) | mapdjuen 10116 |
| [Enderton] p. 143 | Theorem 6J | dju0en 10111 dju1en 10107 |
| [Enderton] p. 144 | Exercise 13 | iunfi 9284 unifi 9285 unifi2 9286 |
| [Enderton] p. 144 | Corollary 6K | undif2 4436 unfi 9116 unfi2 9259 |
| [Enderton] p. 145 | Figure 38 | ffoss 7878 |
| [Enderton] p. 145 | Definition | df-dom 8885 |
| [Enderton] p. 146 | Example 1 | domen 8901 domeng 8902 |
| [Enderton] p. 146 | Example 3 | nndomo 9177 nnsdom 9590 nnsdomg 9246 |
| [Enderton] p. 149 | Theorem 6L(a) | djudom2 10119 |
| [Enderton] p. 149 | Theorem 6L(c) | mapdom1 9086 xpdom1 9015 xpdom1g 9013 xpdom2g 9012 |
| [Enderton] p. 149 | Theorem 6L(d) | mapdom2 9092 |
| [Enderton] p. 151 | Theorem 6M | zorn 10443 zorng 10440 |
| [Enderton] p. 151 | Theorem 6M(4) | ac8 10428 dfac5 10064 |
| [Enderton] p. 159 | Theorem 6Q | unictb 10511 |
| [Enderton] p. 164 | Example | infdif 10145 |
| [Enderton] p. 168 | Definition | df-po 5545 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 6431 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 6363 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 6430 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 6371 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 7774 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 7715 |
| [Enderton] p. 194 | Remark | onprc 7712 |
| [Enderton] p. 194 | Exercise 16 | suc11 6424 |
| [Enderton] p. 197 | Definition | df-card 9875 |
| [Enderton] p. 197 | Theorem 7P | carden 10487 |
| [Enderton] p. 200 | Exercise 25 | tfis 7791 |
| [Enderton] p. 202 | Lemma 7T | r1tr 9712 |
| [Enderton] p. 202 | Definition | df-r1 9700 |
| [Enderton] p. 202 | Theorem 7Q | r1val1 9722 |
| [Enderton] p. 204 | Theorem 7V(b) | rankval4 9803 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 9542 |
| [Enderton] p. 207 | Exercise 30 | rankpr 9793 rankprb 9787 rankpw 9779 rankpwi 9759 rankuniss 9802 |
| [Enderton] p. 207 | Exercise 34 | opthreg 9554 |
| [Enderton] p. 208 | Exercise 35 | suc11reg 9555 |
| [Enderton] p. 212 | Definition of aleph | alephval3 10046 |
| [Enderton] p. 213 | Theorem 8A(a) | alephord2 10012 |
| [Enderton] p. 213 | Theorem 8A(b) | cardalephex 10026 |
| [Enderton] p. 218 | Theorem Schema 8E | onfununi 8287 |
| [Enderton] p. 222 | Definition of kard | karden 9831 kardex 9830 |
| [Enderton] p. 238 | Theorem 8R | oeoa 8544 |
| [Enderton] p. 238 | Theorem 8S | oeoe 8546 |
| [Enderton] p. 240 | Exercise 25 | oarec 8509 |
| [Enderton] p. 257 | Definition of cofinality | cflm 10186 |
| [FaureFrolicher] p. 57 | Definition 3.1.9 | mreexd 17522 |
| [FaureFrolicher] p. 83 | Definition 4.1.1 | df-mri 17468 |
| [FaureFrolicher] p. 83 | Proposition 4.1.3 | acsfiindd 18442 mrieqv2d 17519 mrieqvd 17518 |
| [FaureFrolicher] p. 84 | Lemma 4.1.5 | mreexmrid 17523 |
| [FaureFrolicher] p. 86 | Proposition 4.2.1 | mreexexd 17528 mreexexlem2d 17525 |
| [FaureFrolicher] p. 87 | Theorem 4.2.2 | acsexdimd 18448 mreexfidimd 17530 |
| [Frege1879] p. 11 | Statement | df3or2 42030 |
| [Frege1879] p. 12 | Statement | df3an2 42031 dfxor4 42028 dfxor5 42029 |
| [Frege1879] p. 26 | Axiom 1 | ax-frege1 42052 |
| [Frege1879] p. 26 | Axiom 2 | ax-frege2 42053 |
| [Frege1879] p. 26 | Proposition 1 | ax-1 6 |
| [Frege1879] p. 26 | Proposition 2 | ax-2 7 |
| [Frege1879] p. 29 | Proposition 3 | frege3 42057 |
| [Frege1879] p. 31 | Proposition 4 | frege4 42061 |
| [Frege1879] p. 32 | Proposition 5 | frege5 42062 |
| [Frege1879] p. 33 | Proposition 6 | frege6 42068 |
| [Frege1879] p. 34 | Proposition 7 | frege7 42070 |
| [Frege1879] p. 35 | Axiom 8 | ax-frege8 42071 axfrege8 42069 |
| [Frege1879] p. 35 | Proposition 8 | pm2.04 90 wl-luk-pm2.04 35916 |
| [Frege1879] p. 35 | Proposition 9 | frege9 42074 |
| [Frege1879] p. 36 | Proposition 10 | frege10 42082 |
| [Frege1879] p. 36 | Proposition 11 | frege11 42076 |
| [Frege1879] p. 37 | Proposition 12 | frege12 42075 |
| [Frege1879] p. 37 | Proposition 13 | frege13 42084 |
| [Frege1879] p. 37 | Proposition 14 | frege14 42085 |
| [Frege1879] p. 38 | Proposition 15 | frege15 42088 |
| [Frege1879] p. 38 | Proposition 16 | frege16 42078 |
| [Frege1879] p. 39 | Proposition 17 | frege17 42083 |
| [Frege1879] p. 39 | Proposition 18 | frege18 42080 |
| [Frege1879] p. 39 | Proposition 19 | frege19 42086 |
| [Frege1879] p. 40 | Proposition 20 | frege20 42090 |
| [Frege1879] p. 40 | Proposition 21 | frege21 42089 |
| [Frege1879] p. 41 | Proposition 22 | frege22 42081 |
| [Frege1879] p. 42 | Proposition 23 | frege23 42087 |
| [Frege1879] p. 42 | Proposition 24 | frege24 42077 |
| [Frege1879] p. 42 | Proposition 25 | frege25 42079 rp-frege25 42067 |
| [Frege1879] p. 42 | Proposition 26 | frege26 42072 |
| [Frege1879] p. 43 | Axiom 28 | ax-frege28 42092 |
| [Frege1879] p. 43 | Proposition 27 | frege27 42073 |
| [Frege1879] p. 43 | Proposition 28 | con3 153 |
| [Frege1879] p. 43 | Proposition 29 | frege29 42093 |
| [Frege1879] p. 44 | Axiom 31 | ax-frege31 42096 axfrege31 42095 |
| [Frege1879] p. 44 | Proposition 30 | frege30 42094 |
| [Frege1879] p. 44 | Proposition 31 | notnotr 130 |
| [Frege1879] p. 44 | Proposition 32 | frege32 42097 |
| [Frege1879] p. 44 | Proposition 33 | frege33 42098 |
| [Frege1879] p. 45 | Proposition 34 | frege34 42099 |
| [Frege1879] p. 45 | Proposition 35 | frege35 42100 |
| [Frege1879] p. 45 | Proposition 36 | frege36 42101 |
| [Frege1879] p. 46 | Proposition 37 | frege37 42102 |
| [Frege1879] p. 46 | Proposition 38 | frege38 42103 |
| [Frege1879] p. 46 | Proposition 39 | frege39 42104 |
| [Frege1879] p. 46 | Proposition 40 | frege40 42105 |
| [Frege1879] p. 47 | Axiom 41 | ax-frege41 42107 axfrege41 42106 |
| [Frege1879] p. 47 | Proposition 41 | notnot 142 |
| [Frege1879] p. 47 | Proposition 42 | frege42 42108 |
| [Frege1879] p. 47 | Proposition 43 | frege43 42109 |
| [Frege1879] p. 47 | Proposition 44 | frege44 42110 |
| [Frege1879] p. 47 | Proposition 45 | frege45 42111 |
| [Frege1879] p. 48 | Proposition 46 | frege46 42112 |
| [Frege1879] p. 48 | Proposition 47 | frege47 42113 |
| [Frege1879] p. 49 | Proposition 48 | frege48 42114 |
| [Frege1879] p. 49 | Proposition 49 | frege49 42115 |
| [Frege1879] p. 49 | Proposition 50 | frege50 42116 |
| [Frege1879] p. 50 | Axiom 52 | ax-frege52a 42119 ax-frege52c 42150 frege52aid 42120 frege52b 42151 |
| [Frege1879] p. 50 | Axiom 54 | ax-frege54a 42124 ax-frege54c 42154 frege54b 42155 |
| [Frege1879] p. 50 | Proposition 51 | frege51 42117 |
| [Frege1879] p. 50 | Proposition 52 | dfsbcq 3741 |
| [Frege1879] p. 50 | Proposition 53 | frege53a 42122 frege53aid 42121 frege53b 42152 frege53c 42176 |
| [Frege1879] p. 50 | Proposition 54 | biid 260 eqid 2736 |
| [Frege1879] p. 50 | Proposition 55 | frege55a 42130 frege55aid 42127 frege55b 42159 frege55c 42180 frege55cor1a 42131 frege55lem2a 42129 frege55lem2b 42158 frege55lem2c 42179 |
| [Frege1879] p. 50 | Proposition 56 | frege56a 42133 frege56aid 42132 frege56b 42160 frege56c 42181 |
| [Frege1879] p. 51 | Axiom 58 | ax-frege58a 42137 ax-frege58b 42163 frege58bid 42164 frege58c 42183 |
| [Frege1879] p. 51 | Proposition 57 | frege57a 42135 frege57aid 42134 frege57b 42161 frege57c 42182 |
| [Frege1879] p. 51 | Proposition 58 | spsbc 3752 |
| [Frege1879] p. 51 | Proposition 59 | frege59a 42139 frege59b 42166 frege59c 42184 |
| [Frege1879] p. 52 | Proposition 60 | frege60a 42140 frege60b 42167 frege60c 42185 |
| [Frege1879] p. 52 | Proposition 61 | frege61a 42141 frege61b 42168 frege61c 42186 |
| [Frege1879] p. 52 | Proposition 62 | frege62a 42142 frege62b 42169 frege62c 42187 |
| [Frege1879] p. 52 | Proposition 63 | frege63a 42143 frege63b 42170 frege63c 42188 |
| [Frege1879] p. 53 | Proposition 64 | frege64a 42144 frege64b 42171 frege64c 42189 |
| [Frege1879] p. 53 | Proposition 65 | frege65a 42145 frege65b 42172 frege65c 42190 |
| [Frege1879] p. 54 | Proposition 66 | frege66a 42146 frege66b 42173 frege66c 42191 |
| [Frege1879] p. 54 | Proposition 67 | frege67a 42147 frege67b 42174 frege67c 42192 |
| [Frege1879] p. 54 | Proposition 68 | frege68a 42148 frege68b 42175 frege68c 42193 |
| [Frege1879] p. 55 | Definition 69 | dffrege69 42194 |
| [Frege1879] p. 58 | Proposition 70 | frege70 42195 |
| [Frege1879] p. 59 | Proposition 71 | frege71 42196 |
| [Frege1879] p. 59 | Proposition 72 | frege72 42197 |
| [Frege1879] p. 59 | Proposition 73 | frege73 42198 |
| [Frege1879] p. 60 | Definition 76 | dffrege76 42201 |
| [Frege1879] p. 60 | Proposition 74 | frege74 42199 |
| [Frege1879] p. 60 | Proposition 75 | frege75 42200 |
| [Frege1879] p. 62 | Proposition 77 | frege77 42202 frege77d 42008 |
| [Frege1879] p. 63 | Proposition 78 | frege78 42203 |
| [Frege1879] p. 63 | Proposition 79 | frege79 42204 |
| [Frege1879] p. 63 | Proposition 80 | frege80 42205 |
| [Frege1879] p. 63 | Proposition 81 | frege81 42206 frege81d 42009 |
| [Frege1879] p. 64 | Proposition 82 | frege82 42207 |
| [Frege1879] p. 65 | Proposition 83 | frege83 42208 frege83d 42010 |
| [Frege1879] p. 65 | Proposition 84 | frege84 42209 |
| [Frege1879] p. 66 | Proposition 85 | frege85 42210 |
| [Frege1879] p. 66 | Proposition 86 | frege86 42211 |
| [Frege1879] p. 66 | Proposition 87 | frege87 42212 frege87d 42012 |
| [Frege1879] p. 67 | Proposition 88 | frege88 42213 |
| [Frege1879] p. 68 | Proposition 89 | frege89 42214 |
| [Frege1879] p. 68 | Proposition 90 | frege90 42215 |
| [Frege1879] p. 68 | Proposition 91 | frege91 42216 frege91d 42013 |
| [Frege1879] p. 69 | Proposition 92 | frege92 42217 |
| [Frege1879] p. 70 | Proposition 93 | frege93 42218 |
| [Frege1879] p. 70 | Proposition 94 | frege94 42219 |
| [Frege1879] p. 70 | Proposition 95 | frege95 42220 |
| [Frege1879] p. 71 | Definition 99 | dffrege99 42224 |
| [Frege1879] p. 71 | Proposition 96 | frege96 42221 frege96d 42011 |
| [Frege1879] p. 71 | Proposition 97 | frege97 42222 frege97d 42014 |
| [Frege1879] p. 71 | Proposition 98 | frege98 42223 frege98d 42015 |
| [Frege1879] p. 72 | Proposition 100 | frege100 42225 |
| [Frege1879] p. 72 | Proposition 101 | frege101 42226 |
| [Frege1879] p. 72 | Proposition 102 | frege102 42227 frege102d 42016 |
| [Frege1879] p. 73 | Proposition 103 | frege103 42228 |
| [Frege1879] p. 73 | Proposition 104 | frege104 42229 |
| [Frege1879] p. 73 | Proposition 105 | frege105 42230 |
| [Frege1879] p. 73 | Proposition 106 | frege106 42231 frege106d 42017 |
| [Frege1879] p. 74 | Proposition 107 | frege107 42232 |
| [Frege1879] p. 74 | Proposition 108 | frege108 42233 frege108d 42018 |
| [Frege1879] p. 74 | Proposition 109 | frege109 42234 frege109d 42019 |
| [Frege1879] p. 75 | Proposition 110 | frege110 42235 |
| [Frege1879] p. 75 | Proposition 111 | frege111 42236 frege111d 42021 |
| [Frege1879] p. 76 | Proposition 112 | frege112 42237 |
| [Frege1879] p. 76 | Proposition 113 | frege113 42238 |
| [Frege1879] p. 76 | Proposition 114 | frege114 42239 frege114d 42020 |
| [Frege1879] p. 77 | Definition 115 | dffrege115 42240 |
| [Frege1879] p. 77 | Proposition 116 | frege116 42241 |
| [Frege1879] p. 78 | Proposition 117 | frege117 42242 |
| [Frege1879] p. 78 | Proposition 118 | frege118 42243 |
| [Frege1879] p. 78 | Proposition 119 | frege119 42244 |
| [Frege1879] p. 78 | Proposition 120 | frege120 42245 |
| [Frege1879] p. 79 | Proposition 121 | frege121 42246 |
| [Frege1879] p. 79 | Proposition 122 | frege122 42247 frege122d 42022 |
| [Frege1879] p. 79 | Proposition 123 | frege123 42248 |
| [Frege1879] p. 80 | Proposition 124 | frege124 42249 frege124d 42023 |
| [Frege1879] p. 81 | Proposition 125 | frege125 42250 |
| [Frege1879] p. 81 | Proposition 126 | frege126 42251 frege126d 42024 |
| [Frege1879] p. 82 | Proposition 127 | frege127 42252 |
| [Frege1879] p. 83 | Proposition 128 | frege128 42253 |
| [Frege1879] p. 83 | Proposition 129 | frege129 42254 frege129d 42025 |
| [Frege1879] p. 84 | Proposition 130 | frege130 42255 |
| [Frege1879] p. 85 | Proposition 131 | frege131 42256 frege131d 42026 |
| [Frege1879] p. 86 | Proposition 132 | frege132 42257 |
| [Frege1879] p. 86 | Proposition 133 | frege133 42258 frege133d 42027 |
| [Fremlin1] p. 13 | Definition 111G (b) | df-salgen 44544 |
| [Fremlin1] p. 13 | Definition 111G (d) | borelmbl 44867 |
| [Fremlin1] p. 13 | Proposition 111G (b) | salgenss 44567 |
| [Fremlin1] p. 14 | Definition 112A | ismea 44682 |
| [Fremlin1] p. 15 | Remark 112B (d) | psmeasure 44702 |
| [Fremlin1] p. 15 | Property 112C (a) | meadjun 44693 meadjunre 44707 |
| [Fremlin1] p. 15 | Property 112C (b) | meassle 44694 |
| [Fremlin1] p. 15 | Property 112C (c) | meaunle 44695 |
| [Fremlin1] p. 16 | Property 112C (d) | iundjiun 44691 meaiunle 44700 meaiunlelem 44699 |
| [Fremlin1] p. 16 | Proposition 112C (e) | meaiuninc 44712 meaiuninc2 44713 meaiuninc3 44716 meaiuninc3v 44715 meaiunincf 44714 meaiuninclem 44711 |
| [Fremlin1] p. 16 | Proposition 112C (f) | meaiininc 44718 meaiininc2 44719 meaiininclem 44717 |
| [Fremlin1] p. 19 | Theorem 113C | caragen0 44737 caragendifcl 44745 caratheodory 44759 omelesplit 44749 |
| [Fremlin1] p. 19 | Definition 113A | isome 44725 isomennd 44762 isomenndlem 44761 |
| [Fremlin1] p. 19 | Remark 113B (c) | omeunle 44747 |
| [Fremlin1] p. 19 | Definition 112Df | caragencmpl 44766 voncmpl 44852 |
| [Fremlin1] p. 19 | Definition 113A (ii) | omessle 44729 |
| [Fremlin1] p. 20 | Theorem 113C | carageniuncl 44754 carageniuncllem1 44752 carageniuncllem2 44753 caragenuncl 44744 caragenuncllem 44743 caragenunicl 44755 |
| [Fremlin1] p. 21 | Remark 113D | caragenel2d 44763 |
| [Fremlin1] p. 21 | Theorem 113C | caratheodorylem1 44757 caratheodorylem2 44758 |
| [Fremlin1] p. 21 | Exercise 113Xa | caragencmpl 44766 |
| [Fremlin1] p. 23 | Lemma 114B | hoidmv1le 44825 hoidmv1lelem1 44822 hoidmv1lelem2 44823 hoidmv1lelem3 44824 |
| [Fremlin1] p. 25 | Definition 114E | isvonmbl 44869 |
| [Fremlin1] p. 29 | Lemma 115B | hoidmv1le 44825 hoidmvle 44831 hoidmvlelem1 44826 hoidmvlelem2 44827 hoidmvlelem3 44828 hoidmvlelem4 44829 hoidmvlelem5 44830 hsphoidmvle2 44816 hsphoif 44807 hsphoival 44810 |
| [Fremlin1] p. 29 | Definition 1135 (b) | hoicvr 44779 |
| [Fremlin1] p. 29 | Definition 115A (b) | hoicvrrex 44787 |
| [Fremlin1] p. 29 | Definition 115A (c) | hoidmv0val 44814 hoidmvn0val 44815 hoidmvval 44808 hoidmvval0 44818 hoidmvval0b 44821 |
| [Fremlin1] p. 30 | Lemma 115B | hoiprodp1 44819 hsphoidmvle 44817 |
| [Fremlin1] p. 30 | Definition 115C | df-ovoln 44768 df-voln 44770 |
| [Fremlin1] p. 30 | Proposition 115D (a) | dmovn 44835 ovn0 44797 ovn0lem 44796 ovnf 44794 ovnome 44804 ovnssle 44792 ovnsslelem 44791 ovnsupge0 44788 |
| [Fremlin1] p. 30 | Proposition 115D (b) | ovnhoi 44834 ovnhoilem1 44832 ovnhoilem2 44833 vonhoi 44898 |
| [Fremlin1] p. 31 | Lemma 115F | hoidifhspdmvle 44851 hoidifhspf 44849 hoidifhspval 44839 hoidifhspval2 44846 hoidifhspval3 44850 hspmbl 44860 hspmbllem1 44857 hspmbllem2 44858 hspmbllem3 44859 |
| [Fremlin1] p. 31 | Definition 115E | voncmpl 44852 vonmea 44805 |
| [Fremlin1] p. 31 | Proposition 115D (a)(iv) | ovnsubadd 44803 ovnsubadd2 44877 ovnsubadd2lem 44876 ovnsubaddlem1 44801 ovnsubaddlem2 44802 |
| [Fremlin1] p. 32 | Proposition 115G (a) | hoimbl 44862 hoimbl2 44896 hoimbllem 44861 hspdifhsp 44847 opnvonmbl 44865 opnvonmbllem2 44864 |
| [Fremlin1] p. 32 | Proposition 115G (b) | borelmbl 44867 |
| [Fremlin1] p. 32 | Proposition 115G (c) | iccvonmbl 44910 iccvonmbllem 44909 ioovonmbl 44908 |
| [Fremlin1] p. 32 | Proposition 115G (d) | vonicc 44916 vonicclem2 44915 vonioo 44913 vonioolem2 44912 vonn0icc 44919 vonn0icc2 44923 vonn0ioo 44918 vonn0ioo2 44921 |
| [Fremlin1] p. 32 | Proposition 115G (e) | ctvonmbl 44920 snvonmbl 44917 vonct 44924 vonsn 44922 |
| [Fremlin1] p. 35 | Lemma 121A | subsalsal 44590 |
| [Fremlin1] p. 35 | Lemma 121A (iii) | subsaliuncl 44589 subsaliuncllem 44588 |
| [Fremlin1] p. 35 | Proposition 121B | salpreimagtge 44956 salpreimalegt 44940 salpreimaltle 44957 |
| [Fremlin1] p. 35 | Proposition 121B (i) | issmf 44959 issmff 44965 issmflem 44958 |
| [Fremlin1] p. 35 | Proposition 121B (ii) | issmfle 44976 issmflelem 44975 smfpreimale 44985 |
| [Fremlin1] p. 35 | Proposition 121B (iii) | issmfgt 44987 issmfgtlem 44986 |
| [Fremlin1] p. 36 | Definition 121C | df-smblfn 44927 issmf 44959 issmff 44965 issmfge 45001 issmfgelem 45000 issmfgt 44987 issmfgtlem 44986 issmfle 44976 issmflelem 44975 issmflem 44958 |
| [Fremlin1] p. 36 | Proposition 121B | salpreimagelt 44938 salpreimagtlt 44961 salpreimalelt 44960 |
| [Fremlin1] p. 36 | Proposition 121B (iv) | issmfge 45001 issmfgelem 45000 |
| [Fremlin1] p. 36 | Proposition 121D (a) | bormflebmf 44984 |
| [Fremlin1] p. 36 | Proposition 121D (b) | cnfrrnsmf 44982 cnfsmf 44971 |
| [Fremlin1] p. 36 | Proposition 121D (c) | decsmf 44998 decsmflem 44997 incsmf 44973 incsmflem 44972 |
| [Fremlin1] p. 37 | Proposition 121E (a) | pimconstlt0 44932 pimconstlt1 44933 smfconst 44980 |
| [Fremlin1] p. 37 | Proposition 121E (b) | smfadd 44996 smfaddlem1 44994 smfaddlem2 44995 |
| [Fremlin1] p. 37 | Proposition 121E (c) | smfmulc1 45027 |
| [Fremlin1] p. 37 | Proposition 121E (d) | smfmul 45026 smfmullem1 45022 smfmullem2 45023 smfmullem3 45024 smfmullem4 45025 |
| [Fremlin1] p. 37 | Proposition 121E (e) | smfdiv 45028 |
| [Fremlin1] p. 37 | Proposition 121E (f) | smfpimbor1 45031 smfpimbor1lem2 45030 |
| [Fremlin1] p. 37 | Proposition 121E (g) | smfco 45033 |
| [Fremlin1] p. 37 | Proposition 121E (h) | smfres 45021 |
| [Fremlin1] p. 38 | Proposition 121E (e) | smfrec 45020 |
| [Fremlin1] p. 38 | Proposition 121E (f) | smfpimbor1lem1 45029 smfresal 45019 |
| [Fremlin1] p. 38 | Proposition 121F (a) | smflim 45008 smflim2 45037 smflimlem1 45002 smflimlem2 45003 smflimlem3 45004 smflimlem4 45005 smflimlem5 45006 smflimlem6 45007 smflimmpt 45041 |
| [Fremlin1] p. 38 | Proposition 121F (b) | smfsup 45045 smfsuplem1 45042 smfsuplem2 45043 smfsuplem3 45044 smfsupmpt 45046 smfsupxr 45047 |
| [Fremlin1] p. 38 | Proposition 121F (c) | smfinf 45049 smfinflem 45048 smfinfmpt 45050 |
| [Fremlin1] p. 39 | Remark 121G | smflim 45008 smflim2 45037 smflimmpt 45041 |
| [Fremlin1] p. 39 | Proposition 121F | smfpimcc 45039 |
| [Fremlin1] p. 39 | Proposition 121H | smfdivdmmbl 45069 smfdivdmmbl2 45072 smfinfdmmbl 45080 smfinfdmmbllem 45079 smfsupdmmbl 45076 smfsupdmmbllem 45075 |
| [Fremlin1] p. 39 | Proposition 121F (d) | smflimsup 45059 smflimsuplem2 45052 smflimsuplem6 45056 smflimsuplem7 45057 smflimsuplem8 45058 smflimsupmpt 45060 |
| [Fremlin1] p. 39 | Proposition 121F (e) | smfliminf 45062 smfliminflem 45061 smfliminfmpt 45063 |
| [Fremlin1] p. 80 | Definition 135E (b) | df-smblfn 44927 |
| [Fremlin1], p. 38 | Proposition 121F (b) | fsupdm 45073 fsupdm2 45074 |
| [Fremlin1], p. 39 | Proposition 121H | adddmmbl 45064 adddmmbl2 45065 finfdm 45077 finfdm2 45078 fsupdm 45073 fsupdm2 45074 muldmmbl 45066 muldmmbl2 45067 |
| [Fremlin1], p. 39 | Proposition 121F (c) | finfdm 45077 finfdm2 45078 |
| [Fremlin5] p. 193 | Proposition 563Gb | nulmbl2 24900 |
| [Fremlin5] p. 213 | Lemma 565Ca | uniioovol 24943 |
| [Fremlin5] p. 214 | Lemma 565Ca | uniioombl 24953 |
| [Fremlin5] p. 218 | Lemma 565Ib | ftc1anclem6 36156 |
| [Fremlin5] p. 220 | Theorem 565Ma | ftc1anc 36159 |
| [FreydScedrov] p. 283 | Axiom of Infinity | ax-inf 9574 inf1 9558 inf2 9559 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 10847 enqer 10857 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nq 10852 df-nq 10848 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 10844 df-plq 10850 |
| [Gleason] p. 119 | Proposition 9-2.4 | caovmo 7591 df-mpq 10845 df-mq 10851 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 10853 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnq 10911 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 10912 ltbtwnnq 10914 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanq 10907 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnq 10908 |
| [Gleason] p. 120 | Proposition 9-2.6(iv) | ltrnq 10915 |
| [Gleason] p. 121 | Definition 9-3.1 | df-np 10917 |
| [Gleason] p. 121 | Definition 9-3.1 (ii) | prcdnq 10929 |
| [Gleason] p. 121 | Definition 9-3.1(iii) | prnmax 10931 |
| [Gleason] p. 122 | Definition | df-1p 10918 |
| [Gleason] p. 122 | Remark (1) | prub 10930 |
| [Gleason] p. 122 | Lemma 9-3.4 | prlem934 10969 |
| [Gleason] p. 122 | Proposition 9-3.2 | df-ltp 10921 |
| [Gleason] p. 122 | Proposition 9-3.3 | ltsopr 10968 psslinpr 10967 supexpr 10990 suplem1pr 10988 suplem2pr 10989 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 10954 addclprlem1 10952 addclprlem2 10953 df-plp 10919 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addasspr 10958 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcompr 10957 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 10970 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 10979 ltexprlem1 10972 ltexprlem2 10973 ltexprlem3 10974 ltexprlem4 10975 ltexprlem5 10976 ltexprlem6 10977 ltexprlem7 10978 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltapr 10981 ltaprlem 10980 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanpr 10982 |
| [Gleason] p. 124 | Lemma 9-3.6 | prlem936 10983 |
| [Gleason] p. 124 | Proposition 9-3.7 | df-mp 10920 mulclpr 10956 mulclprlem 10955 reclem2pr 10984 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 10965 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulasspr 10960 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcompr 10959 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrpr 10964 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 10987 reclem3pr 10985 reclem4pr 10986 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 10991 enrer 10999 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 10996 df-1r 10997 df-nr 10992 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 10994 df-plr 10993 negexsr 11038 recexsr 11043 recexsrlem 11039 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 10995 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 12148 creur 12147 cru 12145 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 11124 axcnre 11100 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 15000 crimd 15117 crimi 15078 crre 14999 crred 15116 crrei 15077 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 15002 remimd 15083 |
| [Gleason] p. 133 | Definition 10.36 | absval2 15169 absval2d 15330 absval2i 15282 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 15026 cjaddd 15105 cjaddi 15073 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 15027 cjmuld 15106 cjmuli 15074 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 15025 cjcjd 15084 cjcji 15056 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 15024 cjreb 15008 cjrebd 15087 cjrebi 15059 cjred 15111 rere 15007 rereb 15005 rerebd 15086 rerebi 15058 rered 15109 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 15033 addcjd 15097 addcji 15068 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 15123 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 15164 abscjd 15335 abscji 15286 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 15174 abs00d 15331 abs00i 15283 absne0d 15332 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 15206 releabsd 15336 releabsi 15287 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 15179 absmuld 15339 absmuli 15289 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 15167 sqabsaddi 15290 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 15215 abstrid 15341 abstrii 15293 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 13968 exp0 13971 expp1 13974 expp1d 14052 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | cxpadd 26034 cxpaddd 26072 expadd 14010 expaddd 14053 expaddz 14012 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 26043 cxpmuld 26091 expmul 14013 expmuld 14054 expmulz 14014 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulcxp 26040 mulcxpd 26083 mulexp 14007 mulexpd 14066 mulexpz 14008 |
| [Gleason] p. 140 | Exercise 1 | znnen 16094 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 13426 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 15514 rlimadd 15525 rlimdiv 15530 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 15516 rlimsub 15527 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 15515 rlimmul 15528 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 15519 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 15465 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 15486 climcj 15487 climim 15489 climre 15488 rlimabs 15491 rlimcj 15492 rlimim 15494 rlimre 15493 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 11194 df-xr 11193 ltxr 13036 |
| [Gleason] p. 175 | Definition 12-4.1 | df-limsup 15353 limsupval 15356 |
| [Gleason] p. 180 | Theorem 12-5.1 | climsup 15554 |
| [Gleason] p. 180 | Theorem 12-5.3 | caucvg 15563 caucvgb 15564 caucvgbf 43715 caucvgr 15560 climcau 15555 |
| [Gleason] p. 182 | Exercise 3 | cvgcmp 15701 |
| [Gleason] p. 182 | Exercise 4 | cvgrat 15768 |
| [Gleason] p. 195 | Theorem 13-2.12 | abs1m 15220 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 13733 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 20790 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 23696 xmet0 23695 |
| [Gleason] p. 223 | Definition 14-1.1(b) | metgt0 23712 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 23703 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 23705 mstri 23822 xmettri 23704 xmstri 23821 |
| [Gleason] p. 225 | Definition 14-1.5 | xpsmet 23735 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 22999 |
| [Gleason] p. 240 | Theorem 14-4.3 | metcnp4 24674 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 23896 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn 24228 addcn2 15476 mulcn 24230 mulcn2 15478 subcn 24229 subcn2 15477 |
| [Gleason] p. 295 | Remark | bcval3 14206 bcval4 14207 |
| [Gleason] p. 295 | Equation 2 | bcpasc 14221 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 14204 df-bc 14203 |
| [Gleason] p. 296 | Remark | bcn0 14210 bcnn 14212 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 15715 |
| [Gleason] p. 308 | Equation 2 | ef0 15973 |
| [Gleason] p. 308 | Equation 3 | efcj 15974 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 15979 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 15983 |
| [Gleason] p. 310 | Equation 14 | sinadd 16046 |
| [Gleason] p. 310 | Equation 15 | cosadd 16047 |
| [Gleason] p. 311 | Equation 17 | sincossq 16058 |
| [Gleason] p. 311 | Equation 18 | cosbnd 16063 sinbnd 16062 |
| [Gleason] p. 311 | Lemma 15-4.7 | sqeqor 14120 sqeqori 14118 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 15955 |
| [Godowski] p. 730 | Equation SF | goeqi 31215 |
| [GodowskiGreechie] p. 249 | Equation IV | 3oai 30610 |
| [Golan] p. 1 | Remark | srgisid 19940 |
| [Golan] p. 1 | Definition | df-srg 19918 |
| [Golan] p. 149 | Definition | df-slmd 32036 |
| [Gonshor] p. 7 | Definition | df-scut 27123 |
| [Gonshor] p. 9 | Theorem 2.5 | slerec 27158 |
| [Gonshor] p. 10 | Theorem 2.6 | cofcut1 27239 cofcut1d 27240 |
| [Gonshor] p. 10 | Theorem 2.7 | cofcut2 27241 cofcut2d 27242 |
| [Gonshor] p. 12 | Theorem 2.9 | cofcutr 27243 cofcutr1d 27244 cofcutr2d 27245 |
| [Gonshor] p. 13 | Definition | df-adds 27272 |
| [Gonshor] p. 14 | Theorem 3.1 | addsprop 27288 |
| [Gonshor] p. 15 | Theorem 3.2 | addsunif 27310 |
| [GramKnuthPat], p. 47 | Definition 2.42 | df-fwddif 34744 |
| [Gratzer] p. 23 | Section 0.6 | df-mre 17466 |
| [Gratzer] p. 27 | Section 0.6 | df-mri 17468 |
| [Hall] p. 1 | Section 1.1 | df-asslaw 46112 df-cllaw 46110 df-comlaw 46111 |
| [Hall] p. 2 | Section 1.2 | df-clintop 46124 |
| [Hall] p. 7 | Section 1.3 | df-sgrp2 46145 |
| [Halmos] p. 28 | Partition ` ` | df-parts 37227 dfmembpart2 37232 |
| [Halmos] p. 31 | Theorem 17.3 | riesz1 31007 riesz2 31008 |
| [Halmos] p. 41 | Definition of Hermitian | hmopadj2 30883 |
| [Halmos] p. 42 | Definition of projector ordering | pjordi 31115 |
| [Halmos] p. 43 | Theorem 26.1 | elpjhmop 31127 elpjidm 31126 pjnmopi 31090 |
| [Halmos] p. 44 | Remark | pjinormi 30629 pjinormii 30618 |
| [Halmos] p. 44 | Theorem 26.2 | elpjch 31131 pjrn 30649 pjrni 30644 pjvec 30638 |
| [Halmos] p. 44 | Theorem 26.3 | pjnorm2 30669 |
| [Halmos] p. 44 | Theorem 26.4 | hmopidmpj 31096 hmopidmpji 31094 |
| [Halmos] p. 45 | Theorem 27.1 | pjinvari 31133 |
| [Halmos] p. 45 | Theorem 27.3 | pjoci 31122 pjocvec 30639 |
| [Halmos] p. 45 | Theorem 27.4 | pjorthcoi 31111 |
| [Halmos] p. 48 | Theorem 29.2 | pjssposi 31114 |
| [Halmos] p. 48 | Theorem 29.3 | pjssdif1i 31117 pjssdif2i 31116 |
| [Halmos] p. 50 | Definition of spectrum | df-spec 30797 |
| [Hamilton] p. 28 | Definition 2.1 | ax-1 6 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 23 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1797 |
| [Hatcher] p. 25 | Definition | df-phtpc 24355 df-phtpy 24334 |
| [Hatcher] p. 26 | Definition | df-pco 24368 df-pi1 24371 |
| [Hatcher] p. 26 | Proposition 1.2 | phtpcer 24358 |
| [Hatcher] p. 26 | Proposition 1.3 | pi1grp 24413 |
| [Hefferon] p. 240 | Definition 3.12 | df-dmat 21839 df-dmatalt 46469 |
| [Helfgott] p. 2 | Theorem | tgoldbach 45999 |
| [Helfgott] p. 4 | Corollary 1.1 | wtgoldbnnsum4prm 45984 |
| [Helfgott] p. 4 | Section 1.2.2 | ax-hgprmladder 45996 bgoldbtbnd 45991 bgoldbtbnd 45991 tgblthelfgott 45997 |
| [Helfgott] p. 5 | Proposition 1.1 | circlevma 33255 |
| [Helfgott] p. 69 | Statement 7.49 | circlemethhgt 33256 |
| [Helfgott] p. 69 | Statement 7.50 | hgt750lema 33270 hgt750lemb 33269 hgt750leme 33271 hgt750lemf 33266 hgt750lemg 33267 |
| [Helfgott] p. 70 | Section 7.4 | ax-tgoldbachgt 45993 tgoldbachgt 33276 tgoldbachgtALTV 45994 tgoldbachgtd 33275 |
| [Helfgott] p. 70 | Statement 7.49 | ax-hgt749 33257 |
| [Herstein] p. 54 | Exercise 28 | df-grpo 29435 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 18759 grpoideu 29451 mndideu 18567 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 18785 grpoinveu 29461 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 18814 grpo2inv 29473 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 18825 grpoinvop 29475 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3e 18847 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1770 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1771 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1773 |
| [Holland] p. 1519 | Theorem 2 | sumdmdi 31362 |
| [Holland] p. 1520 | Lemma 5 | cdj1i 31375 cdj3i 31383 cdj3lem1 31376 cdjreui 31374 |
| [Holland] p. 1524 | Lemma 7 | mddmdin0i 31373 |
| [Holland95] p. 13 | Theorem 3.6 | hlathil 40428 |
| [Holland95] p. 14 | Line 15 | hgmapvs 40354 |
| [Holland95] p. 14 | Line 16 | hdmaplkr 40376 |
| [Holland95] p. 14 | Line 17 | hdmapellkr 40377 |
| [Holland95] p. 14 | Line 19 | hdmapglnm2 40374 |
| [Holland95] p. 14 | Line 20 | hdmapip0com 40380 |
| [Holland95] p. 14 | Theorem 3.6 | hdmapevec2 40299 |
| [Holland95] p. 14 | Lines 24 and 25 | hdmapoc 40394 |
| [Holland95] p. 204 | Definition of involution | df-srng 20305 |
| [Holland95] p. 212 | Definition of subspace | df-psubsp 37966 |
| [Holland95] p. 214 | Lemma 3.3 | lclkrlem2v 39991 |
| [Holland95] p. 214 | Definition 3.2 | df-lpolN 39944 |
| [Holland95] p. 214 | Definition of nonsingular | pnonsingN 38396 |
| [Holland95] p. 215 | Lemma 3.3(1) | dihoml4 39840 poml4N 38416 |
| [Holland95] p. 215 | Lemma 3.3(2) | dochexmid 39931 pexmidALTN 38441 pexmidN 38432 |
| [Holland95] p. 218 | Theorem 3.6 | lclkr 39996 |
| [Holland95] p. 218 | Definition of dual vector space | df-ldual 37586 ldualset 37587 |
| [Holland95] p. 222 | Item 1 | df-lines 37964 df-pointsN 37965 |
| [Holland95] p. 222 | Item 2 | df-polarityN 38366 |
| [Holland95] p. 223 | Remark | ispsubcl2N 38410 omllaw4 37708 pol1N 38373 polcon3N 38380 |
| [Holland95] p. 223 | Definition | df-psubclN 38398 |
| [Holland95] p. 223 | Equation for polarity | polval2N 38369 |
| [Holmes] p. 40 | Definition | df-xrn 36833 |
| [Hughes] p. 44 | Equation 1.21b | ax-his3 30026 |
| [Hughes] p. 47 | Definition of projection operator | dfpjop 31124 |
| [Hughes] p. 49 | Equation 1.30 | eighmre 30905 eigre 30777 eigrei 30776 |
| [Hughes] p. 49 | Equation 1.31 | eighmorth 30906 eigorth 30780 eigorthi 30779 |
| [Hughes] p. 137 | Remark (ii) | eigposi 30778 |
| [Huneke] p. 1 | Claim 1 | frgrncvvdeq 29253 |
| [Huneke] p. 1 | Statement 1 | frgrncvvdeqlem7 29249 |
| [Huneke] p. 1 | Statement 2 | frgrncvvdeqlem8 29250 |
| [Huneke] p. 1 | Statement 3 | frgrncvvdeqlem9 29251 |
| [Huneke] p. 2 | Claim 2 | frgrregorufr 29269 frgrregorufr0 29268 frgrregorufrg 29270 |
| [Huneke] p. 2 | Claim 3 | frgrhash2wsp 29276 frrusgrord 29285 frrusgrord0 29284 |
| [Huneke] p. 2 | Statement | df-clwwlknon 29032 |
| [Huneke] p. 2 | Statement 4 | frgrwopreglem4 29259 |
| [Huneke] p. 2 | Statement 5 | frgrwopreg1 29262 frgrwopreg2 29263 frgrwopregasn 29260 frgrwopregbsn 29261 |
| [Huneke] p. 2 | Statement 6 | frgrwopreglem5 29265 |
| [Huneke] p. 2 | Statement 7 | fusgreghash2wspv 29279 |
| [Huneke] p. 2 | Statement 8 | fusgreghash2wsp 29282 |
| [Huneke] p. 2 | Statement 9 | clwlksndivn 29030 numclwlk1 29315 numclwlk1lem1 29313 numclwlk1lem2 29314 numclwwlk1 29305 numclwwlk8 29336 |
| [Huneke] p. 2 | Definition 3 | frgrwopreglem1 29256 |
| [Huneke] p. 2 | Definition 4 | df-clwlks 28719 |
| [Huneke] p. 2 | Definition 6 | 2clwwlk 29291 |
| [Huneke] p. 2 | Definition 7 | numclwwlkovh 29317 numclwwlkovh0 29316 |
| [Huneke] p. 2 | Statement 10 | numclwwlk2 29325 |
| [Huneke] p. 2 | Statement 11 | rusgrnumwlkg 28922 |
| [Huneke] p. 2 | Statement 12 | numclwwlk3 29329 |
| [Huneke] p. 2 | Statement 13 | numclwwlk5 29332 |
| [Huneke] p. 2 | Statement 14 | numclwwlk7 29335 |
| [Indrzejczak] p. 33 | Definition ` `E | natded 29347 natded 29347 |
| [Indrzejczak] p. 33 | Definition ` `I | natded 29347 |
| [Indrzejczak] p. 34 | Definition ` `E | natded 29347 natded 29347 |
| [Indrzejczak] p. 34 | Definition ` `I | natded 29347 |
| [Jech] p. 4 | Definition of class | cv 1540 cvjust 2730 |
| [Jech] p. 42 | Lemma 6.1 | alephexp1 10515 |
| [Jech] p. 42 | Equation 6.1 | alephadd 10513 alephmul 10514 |
| [Jech] p. 43 | Lemma 6.2 | infmap 10512 infmap2 10154 |
| [Jech] p. 71 | Lemma 9.3 | jech9.3 9750 |
| [Jech] p. 72 | Equation 9.3 | scott0 9822 scottex 9821 |
| [Jech] p. 72 | Exercise 9.1 | rankval4 9803 |
| [Jech] p. 72 | Scheme "Collection Principle" | cp 9827 |
| [Jech] p. 78 | Note | opthprc 5696 |
| [JonesMatijasevic] p. 694 | Definition 2.3 | rmxyval 41225 |
| [JonesMatijasevic] p. 695 | Lemma 2.15 | jm2.15nn0 41313 |
| [JonesMatijasevic] p. 695 | Lemma 2.16 | jm2.16nn0 41314 |
| [JonesMatijasevic] p. 695 | Equation 2.7 | rmxadd 41237 |
| [JonesMatijasevic] p. 695 | Equation 2.8 | rmyadd 41241 |
| [JonesMatijasevic] p. 695 | Equation 2.9 | rmxp1 41242 rmyp1 41243 |
| [JonesMatijasevic] p. 695 | Equation 2.10 | rmxm1 41244 rmym1 41245 |
| [JonesMatijasevic] p. 695 | Equation 2.11 | rmx0 41235 rmx1 41236 rmxluc 41246 |
| [JonesMatijasevic] p. 695 | Equation 2.12 | rmy0 41239 rmy1 41240 rmyluc 41247 |
| [JonesMatijasevic] p. 695 | Equation 2.13 | rmxdbl 41249 |
| [JonesMatijasevic] p. 695 | Equation 2.14 | rmydbl 41250 |
| [JonesMatijasevic] p. 696 | Lemma 2.17 | jm2.17a 41270 jm2.17b 41271 jm2.17c 41272 |
| [JonesMatijasevic] p. 696 | Lemma 2.19 | jm2.19 41303 |
| [JonesMatijasevic] p. 696 | Lemma 2.20 | jm2.20nn 41307 |
| [JonesMatijasevic] p. 696 | Theorem 2.18 | jm2.18 41298 |
| [JonesMatijasevic] p. 697 | Lemma 2.24 | jm2.24 41273 jm2.24nn 41269 |
| [JonesMatijasevic] p. 697 | Lemma 2.26 | jm2.26 41312 |
| [JonesMatijasevic] p. 697 | Lemma 2.27 | jm2.27 41318 rmygeid 41274 |
| [JonesMatijasevic] p. 698 | Lemma 3.1 | jm3.1 41330 |
| [Juillerat] p. 11 | Section *5 | etransc 44514 etransclem47 44512 etransclem48 44513 |
| [Juillerat] p. 12 | Equation (7) | etransclem44 44509 |
| [Juillerat] p. 12 | Equation *(7) | etransclem46 44511 |
| [Juillerat] p. 12 | Proof of the derivative calculated | etransclem32 44497 |
| [Juillerat] p. 13 | Proof | etransclem35 44500 |
| [Juillerat] p. 13 | Part of case 2 proven in | etransclem38 44503 |
| [Juillerat] p. 13 | Part of case 2 proven | etransclem24 44489 |
| [Juillerat] p. 13 | Part of case 2: proven in | etransclem41 44506 |
| [Juillerat] p. 14 | Proof | etransclem23 44488 |
| [KalishMontague] p. 81 | Note 1 | ax-6 1971 |
| [KalishMontague] p. 85 | Lemma 2 | equid 2015 |
| [KalishMontague] p. 85 | Lemma 3 | equcomi 2020 |
| [KalishMontague] p. 86 | Lemma 7 | cbvalivw 2010 cbvaliw 2009 wl-cbvmotv 35972 wl-motae 35974 wl-moteq 35973 |
| [KalishMontague] p. 87 | Lemma 8 | spimvw 1999 spimw 1974 |
| [KalishMontague] p. 87 | Lemma 9 | spfw 2036 spw 2037 |
| [Kalmbach] p. 14 | Definition of lattice | chabs1 30458 chabs1i 30460 chabs2 30459 chabs2i 30461 chjass 30475 chjassi 30428 latabs1 18364 latabs2 18365 |
| [Kalmbach] p. 15 | Definition of atom | df-at 31280 ela 31281 |
| [Kalmbach] p. 15 | Definition of covers | cvbr2 31225 cvrval2 37736 |
| [Kalmbach] p. 16 | Definition | df-ol 37640 df-oml 37641 |
| [Kalmbach] p. 20 | Definition of commutes | cmbr 30526 cmbri 30532 cmtvalN 37673 df-cm 30525 df-cmtN 37639 |
| [Kalmbach] p. 22 | Remark | omllaw5N 37709 pjoml5 30555 pjoml5i 30530 |
| [Kalmbach] p. 22 | Definition | pjoml2 30553 pjoml2i 30527 |
| [Kalmbach] p. 22 | Theorem 2(v) | cmcm 30556 cmcmi 30534 cmcmii 30539 cmtcomN 37711 |
| [Kalmbach] p. 22 | Theorem 2(ii) | omllaw3 37707 omlsi 30346 pjoml 30378 pjomli 30377 |
| [Kalmbach] p. 22 | Definition of OML law | omllaw2N 37706 |
| [Kalmbach] p. 23 | Remark | cmbr2i 30538 cmcm3 30557 cmcm3i 30536 cmcm3ii 30541 cmcm4i 30537 cmt3N 37713 cmt4N 37714 cmtbr2N 37715 |
| [Kalmbach] p. 23 | Lemma 3 | cmbr3 30550 cmbr3i 30542 cmtbr3N 37716 |
| [Kalmbach] p. 25 | Theorem 5 | fh1 30560 fh1i 30563 fh2 30561 fh2i 30564 omlfh1N 37720 |
| [Kalmbach] p. 65 | Remark | chjatom 31299 chslej 30440 chsleji 30400 shslej 30322 shsleji 30312 |
| [Kalmbach] p. 65 | Proposition 1 | chocin 30437 chocini 30396 chsupcl 30282 chsupval2 30352 h0elch 30197 helch 30185 hsupval2 30351 ocin 30238 ococss 30235 shococss 30236 |
| [Kalmbach] p. 65 | Definition of subspace sum | shsval 30254 |
| [Kalmbach] p. 66 | Remark | df-pjh 30337 pjssmi 31107 pjssmii 30623 |
| [Kalmbach] p. 67 | Lemma 3 | osum 30587 osumi 30584 |
| [Kalmbach] p. 67 | Lemma 4 | pjci 31142 |
| [Kalmbach] p. 103 | Exercise 6 | atmd2 31342 |
| [Kalmbach] p. 103 | Exercise 12 | mdsl0 31252 |
| [Kalmbach] p. 140 | Remark | hatomic 31302 hatomici 31301 hatomistici 31304 |
| [Kalmbach] p. 140 | Proposition 1 | atlatmstc 37781 |
| [Kalmbach] p. 140 | Proposition 1(i) | atexch 31323 lsatexch 37505 |
| [Kalmbach] p. 140 | Proposition 1(ii) | chcv1 31297 cvlcvr1 37801 cvr1 37873 |
| [Kalmbach] p. 140 | Proposition 1(iii) | cvexch 31316 cvexchi 31311 cvrexch 37883 |
| [Kalmbach] p. 149 | Remark 2 | chrelati 31306 hlrelat 37865 hlrelat5N 37864 lrelat 37476 |
| [Kalmbach] p. 153 | Exercise 5 | lsmcv 20602 lsmsatcv 37472 spansncv 30595 spansncvi 30594 |
| [Kalmbach] p. 153 | Proposition 1(ii) | lsmcv2 37491 spansncv2 31235 |
| [Kalmbach] p. 266 | Definition | df-st 31153 |
| [Kalmbach2] p. 8 | Definition of adjoint | df-adjh 30791 |
| [KanamoriPincus] p. 415 | Theorem 1.1 | fpwwe 10582 fpwwe2 10579 |
| [KanamoriPincus] p. 416 | Corollary 1.3 | canth4 10583 |
| [KanamoriPincus] p. 417 | Corollary 1.6 | canthp1 10590 |
| [KanamoriPincus] p. 417 | Corollary 1.4(a) | canthnum 10585 |
| [KanamoriPincus] p. 417 | Corollary 1.4(b) | canthwe 10587 |
| [KanamoriPincus] p. 418 | Proposition 1.7 | pwfseq 10600 |
| [KanamoriPincus] p. 419 | Lemma 2.2 | gchdjuidm 10604 gchxpidm 10605 |
| [KanamoriPincus] p. 419 | Theorem 2.1 | gchacg 10616 gchhar 10615 |
| [KanamoriPincus] p. 420 | Lemma 2.3 | pwdjudom 10152 unxpwdom 9525 |
| [KanamoriPincus] p. 421 | Proposition 3.1 | gchpwdom 10606 |
| [Kreyszig] p. 3 | Property M1 | metcl 23685 xmetcl 23684 |
| [Kreyszig] p. 4 | Property M2 | meteq0 23692 |
| [Kreyszig] p. 8 | Definition 1.1-8 | dscmet 23928 |
| [Kreyszig] p. 12 | Equation 5 | conjmul 11872 muleqadd 11799 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 23791 |
| [Kreyszig] p. 19 | Remark | mopntopon 23792 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 23854 mopnm 23797 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 23852 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 23857 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 23898 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 22609 lmmbr 24622 lmmbr2 24623 |
| [Kreyszig] p. 26 | Lemma 1.4-2(a) | lmmo 22731 |
| [Kreyszig] p. 28 | Theorem 1.4-5 | lmcau 24677 |
| [Kreyszig] p. 28 | Definition 1.4-3 | iscau 24640 iscmet2 24658 |
| [Kreyszig] p. 30 | Theorem 1.4-7 | cmetss 24680 |
| [Kreyszig] p. 30 | Theorem 1.4-6(a) | 1stcelcls 22812 metelcls 24669 |
| [Kreyszig] p. 30 | Theorem 1.4-6(b) | metcld 24670 metcld2 24671 |
| [Kreyszig] p. 51 | Equation 2 | clmvneg1 24462 lmodvneg1 20365 nvinv 29581 vcm 29518 |
| [Kreyszig] p. 51 | Equation 1a | clm0vs 24458 lmod0vs 20355 slmd0vs 32059 vc0 29516 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 20356 slmdvs0 32060 vcz 29517 |
| [Kreyszig] p. 58 | Definition 2.2-1 | imsmet 29633 ngpmet 23959 nrmmetd 23930 |
| [Kreyszig] p. 59 | Equation 1 | imsdval 29628 imsdval2 29629 ncvspds 24525 ngpds 23960 |
| [Kreyszig] p. 63 | Problem 1 | nmval 23945 nvnd 29630 |
| [Kreyszig] p. 64 | Problem 2 | nmeq0 23974 nmge0 23973 nvge0 29615 nvz 29611 |
| [Kreyszig] p. 64 | Problem 3 | nmrtri 23980 nvabs 29614 |
| [Kreyszig] p. 91 | Definition 2.7-1 | isblo3i 29743 |
| [Kreyszig] p. 92 | Equation 2 | df-nmoo 29687 |
| [Kreyszig] p. 97 | Theorem 2.7-9(a) | blocn 29749 blocni 29747 |
| [Kreyszig] p. 97 | Theorem 2.7-9(b) | lnocni 29748 |
| [Kreyszig] p. 129 | Definition 3.1-1 | cphipeq0 24568 ipeq0 21042 ipz 29661 |
| [Kreyszig] p. 135 | Problem 2 | cphpyth 24580 pythi 29792 |
| [Kreyszig] p. 137 | Lemma 3-2.1(a) | sii 29796 |
| [Kreyszig] p. 137 | Lemma 3.2-1(a) | ipcau 24602 |
| [Kreyszig] p. 144 | Equation 4 | supcvg 15741 |
| [Kreyszig] p. 144 | Theorem 3.3-1 | minvec 24800 minveco 29826 |
| [Kreyszig] p. 196 | Definition 3.9-1 | df-aj 29692 |
| [Kreyszig] p. 247 | Theorem 4.7-2 | bcth 24693 |
| [Kreyszig] p. 249 | Theorem 4.7-3 | ubth 29815 |
| [Kreyszig] p. 470 | Definition of positive operator ordering | leop 31065 leopg 31064 |
| [Kreyszig] p. 476 | Theorem 9.4-2 | opsqrlem2 31083 |
| [Kreyszig] p. 525 | Theorem 10.1-1 | htth 29860 |
| [Kulpa] p. 547 | Theorem | poimir 36111 |
| [Kulpa] p. 547 | Equation (1) | poimirlem32 36110 |
| [Kulpa] p. 547 | Equation (2) | poimirlem31 36109 |
| [Kulpa] p. 548 | Theorem | broucube 36112 |
| [Kulpa] p. 548 | Equation (6) | poimirlem26 36104 |
| [Kulpa] p. 548 | Equation (7) | poimirlem27 36105 |
| [Kunen] p. 10 | Axiom 0 | ax6e 2381 axnul 5262 |
| [Kunen] p. 11 | Axiom 3 | axnul 5262 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 7887 |
| [Kunen] p. 24 | Definition 10.24 | mapval 8777 mapvalg 8775 |
| [Kunen] p. 30 | Lemma 10.20 | fodomg 10458 |
| [Kunen] p. 31 | Definition 10.24 | mapex 8771 |
| [Kunen] p. 95 | Definition 2.1 | df-r1 9700 |
| [Kunen] p. 97 | Lemma 2.10 | r1elss 9742 r1elssi 9741 |
| [Kunen] p. 107 | Exercise 4 | rankop 9794 rankopb 9788 rankuni 9799 rankxplim 9815 rankxpsuc 9818 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4966 |
| [Lang] , p. 225 | Corollary 1.3 | finexttrb 32351 |
| [Lang] p. | Definition | df-rn 5644 |
| [Lang] p. 3 | Statement | lidrideqd 18524 mndbn0 18572 |
| [Lang] p. 3 | Definition | df-mnd 18557 |
| [Lang] p. 4 | Definition of a (finite) product | gsumsplit1r 18542 |
| [Lang] p. 4 | Property of composites. Second formula | gsumccat 18651 |
| [Lang] p. 5 | Equation | gsumreidx 19694 |
| [Lang] p. 5 | Definition of an (infinite) product | gsumfsupp 46106 |
| [Lang] p. 6 | Example | nn0mnd 46103 |
| [Lang] p. 6 | Equation | gsumxp2 19757 |
| [Lang] p. 6 | Statement | cycsubm 18995 |
| [Lang] p. 6 | Definition | mulgnn0gsum 18882 |
| [Lang] p. 6 | Observation | mndlsmidm 19452 |
| [Lang] p. 7 | Definition | dfgrp2e 18776 |
| [Lang] p. 30 | Definition | df-tocyc 31956 |
| [Lang] p. 32 | Property (a) | cyc3genpm 32001 |
| [Lang] p. 32 | Property (b) | cyc3conja 32006 cycpmconjv 31991 |
| [Lang] p. 53 | Definition | df-cat 17548 |
| [Lang] p. 53 | Axiom CAT 1 | cat1 17983 cat1lem 17982 |
| [Lang] p. 54 | Definition | df-iso 17632 |
| [Lang] p. 57 | Definition | df-inito 17870 df-termo 17871 |
| [Lang] p. 58 | Example | irinitoringc 46357 |
| [Lang] p. 58 | Statement | initoeu1 17897 termoeu1 17904 |
| [Lang] p. 62 | Definition | df-func 17744 |
| [Lang] p. 65 | Definition | df-nat 17830 |
| [Lang] p. 91 | Note | df-ringc 46293 |
| [Lang] p. 92 | Statement | mxidlprm 32237 |
| [Lang] p. 92 | Definition | isprmidlc 32220 |
| [Lang] p. 128 | Remark | dsmmlmod 21151 |
| [Lang] p. 129 | Proof | lincscm 46501 lincscmcl 46503 lincsum 46500 lincsumcl 46502 |
| [Lang] p. 129 | Statement | lincolss 46505 |
| [Lang] p. 129 | Observation | dsmmfi 21144 |
| [Lang] p. 141 | Theorem 5.3 | dimkerim 32322 qusdimsum 32323 |
| [Lang] p. 141 | Corollary 5.4 | lssdimle 32305 |
| [Lang] p. 147 | Definition | snlindsntor 46542 |
| [Lang] p. 504 | Statement | mat1 21796 matring 21792 |
| [Lang] p. 504 | Definition | df-mamu 21733 |
| [Lang] p. 505 | Statement | mamuass 21749 mamutpos 21807 matassa 21793 mattposvs 21804 tposmap 21806 |
| [Lang] p. 513 | Definition | mdet1 21950 mdetf 21944 |
| [Lang] p. 513 | Theorem 4.4 | cramer 22040 |
| [Lang] p. 514 | Proposition 4.6 | mdetleib 21936 |
| [Lang] p. 514 | Proposition 4.8 | mdettpos 21960 |
| [Lang] p. 515 | Definition | df-minmar1 21984 smadiadetr 22024 |
| [Lang] p. 515 | Corollary 4.9 | mdetero 21959 mdetralt 21957 |
| [Lang] p. 517 | Proposition 4.15 | mdetmul 21972 |
| [Lang] p. 518 | Definition | df-madu 21983 |
| [Lang] p. 518 | Proposition 4.16 | madulid 21994 madurid 21993 matinv 22026 |
| [Lang] p. 561 | Theorem 3.1 | cayleyhamilton 22239 |
| [Lang], p. 224 | Proposition 1.2 | extdgmul 32350 fedgmul 32326 |
| [Lang], p. 561 | Remark | chpmatply1 22181 |
| [Lang], p. 561 | Definition | df-chpmat 22176 |
| [LarsonHostetlerEdwards] p. 278 | Section 4.1 | dvconstbi 42604 |
| [LarsonHostetlerEdwards] p. 311 | Example 1a | lhe4.4ex1a 42599 |
| [LarsonHostetlerEdwards] p. 375 | Theorem 5.1 | expgrowth 42605 |
| [LeBlanc] p. 277 | Rule R2 | axnul 5262 |
| [Levy] p. 12 | Axiom 4.3.1 | df-clab 2714 |
| [Levy] p. 59 | Definition | df-ttrcl 9644 |
| [Levy] p. 64 | Theorem 5.6(ii) | frinsg 9687 |
| [Levy] p. 338 | Axiom | df-clel 2814 df-cleq 2728 |
| [Levy] p. 357 | Proof sketch of conservativity; for details see Appendix | df-clel 2814 df-cleq 2728 |
| [Levy] p. 357 | Statements yield an eliminable and weakly (that is, object-level) conservative extension of FOL= plus ~ ax-ext , see Appendix | df-clab 2714 |
| [Levy] p. 358 | Axiom | df-clab 2714 |
| [Levy58] p. 2 | Definition I | isfin1-3 10322 |
| [Levy58] p. 2 | Definition II | df-fin2 10222 |
| [Levy58] p. 2 | Definition Ia | df-fin1a 10221 |
| [Levy58] p. 2 | Definition III | df-fin3 10224 |
| [Levy58] p. 3 | Definition V | df-fin5 10225 |
| [Levy58] p. 3 | Definition IV | df-fin4 10223 |
| [Levy58] p. 4 | Definition VI | df-fin6 10226 |
| [Levy58] p. 4 | Definition VII | df-fin7 10227 |
| [Levy58], p. 3 | Theorem 1 | fin1a2 10351 |
| [Lipparini] p. 3 | Lemma 2.1.1 | nosepssdm 27034 |
| [Lipparini] p. 3 | Lemma 2.1.4 | noresle 27045 |
| [Lipparini] p. 6 | Proposition 4.2 | noinfbnd1 27077 nosupbnd1 27062 |
| [Lipparini] p. 6 | Proposition 4.3 | noinfbnd2 27079 nosupbnd2 27064 |
| [Lipparini] p. 7 | Theorem 5.1 | noetasuplem3 27083 noetasuplem4 27084 |
| [Lipparini] p. 7 | Corollary 4.4 | nosupinfsep 27080 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1770 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1771 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1773 |
| [Maeda] p. 167 | Theorem 1(d) to (e) | mdsymlem6 31350 |
| [Maeda] p. 168 | Lemma 5 | mdsym 31354 mdsymi 31353 |
| [Maeda] p. 168 | Lemma 4(i) | mdsymlem4 31348 mdsymlem6 31350 mdsymlem7 31351 |
| [Maeda] p. 168 | Lemma 4(ii) | mdsymlem8 31352 |
| [MaedaMaeda] p. 1 | Remark | ssdmd1 31255 ssdmd2 31256 ssmd1 31253 ssmd2 31254 |
| [MaedaMaeda] p. 1 | Lemma 1.2 | mddmd2 31251 |
| [MaedaMaeda] p. 1 | Definition 1.1 | df-dmd 31223 df-md 31222 mdbr 31236 |
| [MaedaMaeda] p. 2 | Lemma 1.3 | mdsldmd1i 31273 mdslj1i 31261 mdslj2i 31262 mdslle1i 31259 mdslle2i 31260 mdslmd1i 31271 mdslmd2i 31272 |
| [MaedaMaeda] p. 2 | Lemma 1.4 | mdsl1i 31263 mdsl2bi 31265 mdsl2i 31264 |
| [MaedaMaeda] p. 2 | Lemma 1.6 | mdexchi 31277 |
| [MaedaMaeda] p. 2 | Lemma 1.5.1 | mdslmd3i 31274 |
| [MaedaMaeda] p. 2 | Lemma 1.5.2 | mdslmd4i 31275 |
| [MaedaMaeda] p. 2 | Lemma 1.5.3 | mdsl0 31252 |
| [MaedaMaeda] p. 2 | Theorem 1.3 | dmdsl3 31257 mdsl3 31258 |
| [MaedaMaeda] p. 3 | Theorem 1.9.1 | csmdsymi 31276 |
| [MaedaMaeda] p. 4 | Theorem 1.14 | mdcompli 31371 |
| [MaedaMaeda] p. 30 | Lemma 7.2 | atlrelat1 37783 hlrelat1 37863 |
| [MaedaMaeda] p. 31 | Lemma 7.5 | lcvexch 37501 |
| [MaedaMaeda] p. 31 | Lemma 7.5.1 | cvmd 31278 cvmdi 31266 cvnbtwn4 31231 cvrnbtwn4 37741 |
| [MaedaMaeda] p. 31 | Lemma 7.5.2 | cvdmd 31279 |
| [MaedaMaeda] p. 31 | Definition 7.4 | cvlcvrp 37802 cvp 31317 cvrp 37879 lcvp 37502 |
| [MaedaMaeda] p. 31 | Theorem 7.6(b) | atmd 31341 |
| [MaedaMaeda] p. 31 | Theorem 7.6(c) | atdmd 31340 |
| [MaedaMaeda] p. 32 | Definition 7.8 | cvlexch4N 37795 hlexch4N 37855 |
| [MaedaMaeda] p. 34 | Exercise 7.1 | atabsi 31343 |
| [MaedaMaeda] p. 41 | Lemma 9.2(delta) | cvrat4 37906 |
| [MaedaMaeda] p. 61 | Definition 15.1 | 0psubN 38212 atpsubN 38216 df-pointsN 37965 pointpsubN 38214 |
| [MaedaMaeda] p. 62 | Theorem 15.5 | df-pmap 37967 pmap11 38225 pmaple 38224 pmapsub 38231 pmapval 38220 |
| [MaedaMaeda] p. 62 | Theorem 15.5.1 | pmap0 38228 pmap1N 38230 |
| [MaedaMaeda] p. 62 | Theorem 15.5.2 | pmapglb 38233 pmapglb2N 38234 pmapglb2xN 38235 pmapglbx 38232 |
| [MaedaMaeda] p. 63 | Equation 15.5.3 | pmapjoin 38315 |
| [MaedaMaeda] p. 67 | Postulate PS1 | ps-1 37940 |
| [MaedaMaeda] p. 68 | Lemma 16.2 | df-padd 38259 paddclN 38305 paddidm 38304 |
| [MaedaMaeda] p. 68 | Condition PS2 | ps-2 37941 |
| [MaedaMaeda] p. 68 | Equation 16.2.1 | paddass 38301 |
| [MaedaMaeda] p. 69 | Lemma 16.4 | ps-1 37940 |
| [MaedaMaeda] p. 69 | Theorem 16.4 | ps-2 37941 |
| [MaedaMaeda] p. 70 | Theorem 16.9 | lsmmod 19457 lsmmod2 19458 lssats 37474 shatomici 31300 shatomistici 31303 shmodi 30332 shmodsi 30331 |
| [MaedaMaeda] p. 130 | Remark 29.6 | dmdmd 31242 mdsymlem7 31351 |
| [MaedaMaeda] p. 132 | Theorem 29.13(e) | pjoml6i 30531 |
| [MaedaMaeda] p. 136 | Lemma 31.1.5 | shjshseli 30435 |
| [MaedaMaeda] p. 139 | Remark | sumdmdii 31357 |
| [Margaris] p. 40 | Rule C | exlimiv 1933 |
| [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 397 df-ex 1782 df-or 846 dfbi2 475 |
| [Margaris] p. 51 | Theorem 1 | idALT 23 |
| [Margaris] p. 56 | Theorem 3 | conventions 29344 |
| [Margaris] p. 59 | Section 14 | notnotrALTVD 43187 |
| [Margaris] p. 60 | Theorem 8 | jcn 162 |
| [Margaris] p. 60 | Section 14 | con3ALTVD 43188 |
| [Margaris] p. 79 | Rule C | exinst01 42897 exinst11 42898 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1980 19.2g 2181 r19.2z 4452 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 2195 rr19.3v 3619 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 2156 |
| [Margaris] p. 89 | Theorem 19.6 | alex 1828 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1783 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 2174 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 2198 19.9h 2282 exlimd 2211 exlimdh 2286 |
| [Margaris] p. 89 | Theorem 19.11 | excom 2162 excomim 2163 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 2320 |
| [Margaris] p. 90 | Section 19 | conventions-labels 29345 conventions-labels 29345 conventions-labels 29345 conventions-labels 29345 |
| [Margaris] p. 90 | Theorem 19.14 | exnal 1829 |
| [Margaris] p. 90 | Theorem 19.15 | 2albi 42648 albi 1820 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 2218 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 2219 |
| [Margaris] p. 90 | Theorem 19.18 | 2exbi 42650 exbi 1849 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 2222 |
| [Margaris] p. 90 | Theorem 19.20 | 2alim 42647 2alimdv 1921 alimd 2205 alimdh 1819 alimdv 1919 ax-4 1811 ralimdaa 3243 ralimdv 3166 ralimdva 3164 ralimdvva 3201 sbcimdv 3813 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21 2200 19.21h 2283 19.21t 2199 19.21vv 42646 alrimd 2208 alrimdd 2207 alrimdh 1866 alrimdv 1932 alrimi 2206 alrimih 1826 alrimiv 1930 alrimivv 1931 hbralrimi 3141 r19.21be 3235 r19.21bi 3234 ralrimd 3247 ralrimdv 3149 ralrimdva 3151 ralrimdvv 3198 ralrimdvva 3203 ralrimi 3240 ralrimia 3241 ralrimiv 3142 ralrimiva 3143 ralrimivv 3195 ralrimivva 3197 ralrimivvva 3200 ralrimivw 3147 |
| [Margaris] p. 90 | Theorem 19.22 | 2exim 42649 2eximdv 1922 exim 1836 eximd 2209 eximdh 1867 eximdv 1920 rexim 3090 reximd2a 3252 reximdai 3244 reximdd 43352 reximddv 3168 reximddv2 3206 reximddv3 43351 reximdv 3167 reximdv2 3161 reximdva 3165 reximdvai 3162 reximdvva 3202 reximi2 3082 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 2204 19.23bi 2184 19.23h 2284 19.23t 2203 exlimdv 1936 exlimdvv 1937 exlimexi 42796 exlimiv 1933 exlimivv 1935 rexlimd3 43344 rexlimdv 3150 rexlimdv3a 3156 rexlimdva 3152 rexlimdva2 3154 rexlimdvaa 3153 rexlimdvv 3204 rexlimdvva 3205 rexlimdvw 3157 rexlimiv 3145 rexlimiva 3144 rexlimivv 3196 |
| [Margaris] p. 90 | Theorem 19.24 | 19.24 1989 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1883 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26 1873 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 2220 r19.27z 4462 r19.27zv 4463 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 2221 19.28vv 42656 r19.28z 4455 r19.28zf 43364 r19.28zv 4458 rr19.28v 3620 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1876 r19.29d2r 3137 r19.29imd 3121 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30 1884 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31 2227 19.31vv 42654 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32 2226 r19.32 45320 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33-2 42652 19.33 1887 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1990 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35 1880 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36 2223 19.36vv 42653 r19.36zv 4464 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37 2225 19.37vv 42655 r19.37zv 4459 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1841 |
| [Margaris] p. 90 | Theorem 19.39 | 19.39 1988 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1890 19.40 1889 r19.40 3122 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 2228 19.41rg 42822 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 2229 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1885 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 2230 r19.44zv 4461 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 2231 r19.45zv 4460 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2610 |
| [Mayet] p. 370 | Remark | jpi 31212 largei 31209 stri 31199 |
| [Mayet3] p. 9 | Definition of CH-states | df-hst 31154 ishst 31156 |
| [Mayet3] p. 10 | Theorem | hstrbi 31208 hstri 31207 |
| [Mayet3] p. 1223 | Theorem 4.1 | mayete3i 30670 |
| [Mayet3] p. 1240 | Theorem 7.1 | mayetes3i 30671 |
| [MegPav2000] p. 2344 | Theorem 3.3 | stcltrthi 31220 |
| [MegPav2000] p. 2345 | Definition 3.4-1 | chintcl 30274 chsupcl 30282 |
| [MegPav2000] p. 2345 | Definition 3.4-2 | hatomic 31302 |
| [MegPav2000] p. 2345 | Definition 3.4-3(a) | superpos 31296 |
| [MegPav2000] p. 2345 | Definition 3.4-3(b) | atexch 31323 |
| [MegPav2000] p. 2366 | Figure 7 | pl42N 38446 |
| [MegPav2002] p. 362 | Lemma 2.2 | latj31 18376 latj32 18374 latjass 18372 |
| [Megill] p. 444 | Axiom C5 | ax-5 1913 ax5ALT 37369 |
| [Megill] p. 444 | Section 7 | conventions 29344 |
| [Megill] p. 445 | Lemma L12 | aecom-o 37363 ax-c11n 37350 axc11n 2424 |
| [Megill] p. 446 | Lemma L17 | equtrr 2025 |
| [Megill] p. 446 | Lemma L18 | ax6fromc10 37358 |
| [Megill] p. 446 | Lemma L19 | hbnae-o 37390 hbnae 2430 |
| [Megill] p. 447 | Remark 9.1 | dfsb1 2483 sbid 2247 sbidd-misc 47154 sbidd 47153 |
| [Megill] p. 448 | Remark 9.6 | axc14 2461 |
| [Megill] p. 448 | Scheme C4' | ax-c4 37346 |
| [Megill] p. 448 | Scheme C5' | ax-c5 37345 sp 2176 |
| [Megill] p. 448 | Scheme C6' | ax-11 2154 |
| [Megill] p. 448 | Scheme C7' | ax-c7 37347 |
| [Megill] p. 448 | Scheme C8' | ax-7 2011 |
| [Megill] p. 448 | Scheme C9' | ax-c9 37352 |
| [Megill] p. 448 | Scheme C10' | ax-6 1971 ax-c10 37348 |
| [Megill] p. 448 | Scheme C11' | ax-c11 37349 |
| [Megill] p. 448 | Scheme C12' | ax-8 2108 |
| [Megill] p. 448 | Scheme C13' | ax-9 2116 |
| [Megill] p. 448 | Scheme C14' | ax-c14 37353 |
| [Megill] p. 448 | Scheme C15' | ax-c15 37351 |
| [Megill] p. 448 | Scheme C16' | ax-c16 37354 |
| [Megill] p. 448 | Theorem 9.4 | dral1-o 37366 dral1 2437 dral2-o 37392 dral2 2436 drex1 2439 drex2 2440 drsb1 2497 drsb2 2257 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2161 sbequ 2086 sbid2v 2511 |
| [Megill] p. 450 | Example in Appendix | hba1-o 37359 hba1 2289 |
| [Mendelson] p. 35 | Axiom A3 | hirstL-ax3 45117 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 23 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3835 rspsbca 3836 stdpc4 2071 |
| [Mendelson] p. 69 | Axiom 5 | ax-c4 37346 ra4 3842 stdpc5 2201 |
| [Mendelson] p. 81 | Rule C | exlimiv 1933 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 2031 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 2242 |
| [Mendelson] p. 225 | Axiom system NBG | ru 3738 |
| [Mendelson] p. 230 | Exercise 4.8(b) | opthwiener 5471 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 4354 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 4355 |
| [Mendelson] p. 231 | Exercise 4.10(n) | dfin3 4226 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 4283 |
| [Mendelson] p. 231 | Exercise 4.10(q) | dfin4 4227 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddif 4096 |
| [Mendelson] p. 231 | Definition of union | dfun3 4225 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 5408 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 4862 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 5527 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4578 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssun 5528 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 4892 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 5782 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 6220 |
| [Mendelson] p. 244 | Proposition 4.8(g) | epweon 7709 |
| [Mendelson] p. 246 | Definition of successor | df-suc 6323 |
| [Mendelson] p. 250 | Exercise 4.36 | oelim2 8542 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 9084 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 8999 xpsneng 9000 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 9007 xpcomeng 9008 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 9010 |
| [Mendelson] p. 255 | Definition | brsdom 8915 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 9002 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 8769 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 8981 mapsnend 8980 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 9090 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 9089 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 8820 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 8984 |
| [Mendelson] p. 257 | Proposition 4.24(a) | undom 9003 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 10114 djucomen 10113 |
| [Mendelson] p. 258 | Exercise 4.56(f) | djudom1 10118 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 10112 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 8477 |
| [Mendelson] p. 266 | Proposition 4.34(f) | oaordex 8505 |
| [Mendelson] p. 275 | Proposition 4.42(d) | entri3 10495 |
| [Mendelson] p. 281 | Definition | df-r1 9700 |
| [Mendelson] p. 281 | Proposition 4.45 (b) to (a) | unir1 9749 |
| [Mendelson] p. 287 | Axiom system MK | ru 3738 |
| [MertziosUnger] p. 152 | Definition | df-frgr 29203 |
| [MertziosUnger] p. 153 | Remark 1 | frgrconngr 29238 |
| [MertziosUnger] p. 153 | Remark 2 | vdgn1frgrv2 29240 vdgn1frgrv3 29241 |
| [MertziosUnger] p. 153 | Remark 3 | vdgfrgrgt2 29242 |
| [MertziosUnger] p. 153 | Proposition 1(a) | n4cyclfrgr 29235 |
| [MertziosUnger] p. 153 | Proposition 1(b) | 2pthfrgr 29228 2pthfrgrrn 29226 2pthfrgrrn2 29227 |
| [Mittelstaedt] p. 9 | Definition | df-oc 30194 |
| [Monk1] p. 22 | Remark | conventions 29344 |
| [Monk1] p. 22 | Theorem 3.1 | conventions 29344 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 4190 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 5738 ssrelf 31534 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 5740 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 5168 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 6214 coi2 6215 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 5876 rn0 5881 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 6094 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 5651 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxp 5884 rnxp 6122 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 5730 xp0 6110 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 6029 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 6026 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 7853 imaexALTV 36791 imaexg 7852 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 6024 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 7026 funfvop 7000 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 6898 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 6908 |
| [Monk1] p. 43 | Theorem 4.6 | funun 6547 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 7202 dff13f 7203 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 7169 funrnex 7886 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 7194 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 6179 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 4925 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 7938 df-1st 7921 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 7939 df-2nd 7922 |
| [Monk1] p. 112 | Theorem 15.17(v) | ranksn 9790 ranksnb 9763 |
| [Monk1] p. 112 | Theorem 15.17(iv) | rankuni2 9791 |
| [Monk1] p. 112 | Theorem 15.17(iii) | rankun 9792 rankunb 9786 |
| [Monk1] p. 113 | Theorem 15.18 | r1val3 9774 |
| [Monk1] p. 113 | Definition 15.19 | df-r1 9700 r1val2 9773 |
| [Monk1] p. 117 | Lemma | zorn2 10442 zorn2g 10439 |
| [Monk1] p. 133 | Theorem 18.11 | cardom 9922 |
| [Monk1] p. 133 | Theorem 18.12 | canth3 10497 |
| [Monk1] p. 133 | Theorem 18.14 | carduni 9917 |
| [Monk2] p. 105 | Axiom C4 | ax-4 1811 |
| [Monk2] p. 105 | Axiom C7 | ax-7 2011 |
| [Monk2] p. 105 | Axiom C8 | ax-12 2171 ax-c15 37351 ax12v2 2173 |
| [Monk2] p. 108 | Lemma 5 | ax-c4 37346 |
| [Monk2] p. 109 | Lemma 12 | ax-11 2154 |
| [Monk2] p. 109 | Lemma 15 | equvini 2453 equvinv 2032 eqvinop 5444 |
| [Monk2] p. 113 | Axiom C5-1 | ax-5 1913 ax5ALT 37369 |
| [Monk2] p. 113 | Axiom C5-2 | ax-10 2137 |
| [Monk2] p. 113 | Axiom C5-3 | ax-11 2154 |
| [Monk2] p. 114 | Lemma 21 | sp 2176 |
| [Monk2] p. 114 | Lemma 22 | axc4 2314 hba1-o 37359 hba1 2289 |
| [Monk2] p. 114 | Lemma 23 | nfia1 2150 |
| [Monk2] p. 114 | Lemma 24 | nfa2 2170 nfra2 3349 nfra2w 3282 |
| [Moore] p. 53 | Part I | df-mre 17466 |
| [Munkres] p. 77 | Example 2 | distop 22345 indistop 22352 indistopon 22351 |
| [Munkres] p. 77 | Example 3 | fctop 22354 fctop2 22355 |
| [Munkres] p. 77 | Example 4 | cctop 22356 |
| [Munkres] p. 78 | Definition of basis | df-bases 22296 isbasis3g 22299 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 17325 tgval2 22306 |
| [Munkres] p. 79 | Remark | tgcl 22319 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 22313 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 22337 tgss3 22336 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 22338 basgen2 22339 |
| [Munkres] p. 83 | Exercise 3 | topdifinf 35820 topdifinfeq 35821 topdifinffin 35819 topdifinfindis 35817 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 22511 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 22389 topcld 22386 |
| [Munkres] p. 93 | Theorem 6.1(2) | iincld 22390 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 22392 |
| [Munkres] p. 94 | Definition of closure | clsval 22388 |
| [Munkres] p. 94 | Definition of interior | ntrval 22387 |
| [Munkres] p. 95 | Theorem 6.5(a) | clsndisj 22426 elcls 22424 |
| [Munkres] p. 95 | Theorem 6.5(b) | elcls3 22434 |
| [Munkres] p. 97 | Theorem 6.6 | clslp 22499 neindisj 22468 |
| [Munkres] p. 97 | Corollary 6.7 | cldlp 22501 |
| [Munkres] p. 97 | Definition of limit point | islp2 22496 lpval 22490 |
| [Munkres] p. 98 | Definition of Hausdorff space | df-haus 22666 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 22578 iscn 22586 iscn2 22589 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 22631 cncnp2 22632 cncnpi 22629 df-cnp 22579 iscnp 22588 iscnp2 22590 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 23899 |
| [Munkres] p. 128 | Theorem 10.3 | metcn4 24675 |
| [Nathanson] p. 123 | Remark | reprgt 33234 reprinfz1 33235 reprlt 33232 |
| [Nathanson] p. 123 | Definition | df-repr 33222 |
| [Nathanson] p. 123 | Chapter 5.1 | circlemethnat 33254 |
| [Nathanson] p. 123 | Proposition | breprexp 33246 breprexpnat 33247 itgexpif 33219 |
| [NielsenChuang] p. 195 | Equation 4.73 | unierri 31046 |
| [OeSilva] p. 2042 | Section 2 | ax-bgbltosilva 45992 |
| [Pfenning] p. 17 | Definition XM | natded 29347 |
| [Pfenning] p. 17 | Definition NNC | natded 29347 notnotrd 133 |
| [Pfenning] p. 17 | Definition ` `C | natded 29347 |
| [Pfenning] p. 18 | Rule" | natded 29347 |
| [Pfenning] p. 18 | Definition /\I | natded 29347 |
| [Pfenning] p. 18 | Definition ` `E | natded 29347 natded 29347 natded 29347 natded 29347 natded 29347 |
| [Pfenning] p. 18 | Definition ` `I | natded 29347 natded 29347 natded 29347 natded 29347 natded 29347 |
| [Pfenning] p. 18 | Definition ` `EL | natded 29347 |
| [Pfenning] p. 18 | Definition ` `ER | natded 29347 |
| [Pfenning] p. 18 | Definition ` `Ea,u | natded 29347 |
| [Pfenning] p. 18 | Definition ` `IR | natded 29347 |
| [Pfenning] p. 18 | Definition ` `Ia | natded 29347 |
| [Pfenning] p. 127 | Definition =E | natded 29347 |
| [Pfenning] p. 127 | Definition =I | natded 29347 |
| [Ponnusamy] p. 361 | Theorem 6.44 | cphip0l 24566 df-dip 29643 dip0l 29660 ip0l 21040 |
| [Ponnusamy] p. 361 | Equation 6.45 | cphipval 24607 ipval 29645 |
| [Ponnusamy] p. 362 | Equation I1 | dipcj 29656 ipcj 21038 |
| [Ponnusamy] p. 362 | Equation I3 | cphdir 24569 dipdir 29784 ipdir 21043 ipdiri 29772 |
| [Ponnusamy] p. 362 | Equation I4 | ipidsq 29652 nmsq 24558 |
| [Ponnusamy] p. 362 | Equation 6.46 | ip0i 29767 |
| [Ponnusamy] p. 362 | Equation 6.47 | ip1i 29769 |
| [Ponnusamy] p. 362 | Equation 6.48 | ip2i 29770 |
| [Ponnusamy] p. 363 | Equation I2 | cphass 24575 dipass 29787 ipass 21049 ipassi 29783 |
| [Prugovecki] p. 186 | Definition of bra | braval 30886 df-bra 30792 |
| [Prugovecki] p. 376 | Equation 8.1 | df-kb 30793 kbval 30896 |
| [PtakPulmannova] p. 66 | Proposition 3.2.17 | atomli 31324 |
| [PtakPulmannova] p. 68 | Lemma 3.1.4 | df-pclN 38351 |
| [PtakPulmannova] p. 68 | Lemma 3.2.20 | atcvat3i 31338 atcvat4i 31339 cvrat3 37905 cvrat4 37906 lsatcvat3 37514 |
| [PtakPulmannova] p. 68 | Definition 3.2.18 | cvbr 31224 cvrval 37731 df-cv 31221 df-lcv 37481 lspsncv0 20607 |
| [PtakPulmannova] p. 72 | Lemma 3.3.6 | pclfinN 38363 |
| [PtakPulmannova] p. 74 | Lemma 3.3.10 | pclcmpatN 38364 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2714 rabid 3427 rabidd 43360 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2275 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2728 |
| [Quine] p. 19 | Definition 2.9 | conventions 29344 df-v 3447 |
| [Quine] p. 34 | Theorem 5.1 | eqab 2877 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2874 abid2f 2939 |
| [Quine] p. 40 | Theorem 6.1 | sb5 2267 |
| [Quine] p. 40 | Theorem 6.2 | sb6 2088 sbalex 2235 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2814 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2736 eqid1 29411 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2743 |
| [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 3449 |
| [Quine] p. 43 | Theorem 6.9 | isset 3458 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 3550 spcgv 3555 spcimgf 3548 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3752 spsbcd 3753 |
| [Quine] p. 44 | Theorem 6.12 | elex 3463 |
| [Quine] p. 44 | Theorem 6.13 | elab 3630 elabg 3628 elabgf 3626 |
| [Quine] p. 44 | Theorem 6.14 | noel 4290 |
| [Quine] p. 48 | Theorem 7.2 | snprc 4678 |
| [Quine] p. 48 | Definition 7.1 | df-pr 4589 df-sn 4587 |
| [Quine] p. 49 | Theorem 7.4 | snss 4746 snssg 4744 |
| [Quine] p. 49 | Theorem 7.5 | prss 4780 prssg 4779 |
| [Quine] p. 49 | Theorem 7.6 | prid1 4723 prid1g 4721 prid2 4724 prid2g 4722 snid 4622 snidg 4620 |
| [Quine] p. 51 | Theorem 7.12 | snex 5388 |
| [Quine] p. 51 | Theorem 7.13 | prex 5389 |
| [Quine] p. 53 | Theorem 8.2 | unisn 4887 unisnALT 43198 unisng 4886 |
| [Quine] p. 53 | Theorem 8.3 | uniun 4891 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 4898 |
| [Quine] p. 54 | Theorem 8.7 | uni0 4896 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 6463 |
| [Quine] p. 56 | Definition 8.18 | dfaiota2 45308 dfiota2 6449 |
| [Quine] p. 57 | Theorem 8.19 | aiotaval 45317 iotaval 6467 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 6474 |
| [Quine] p. 58 | Theorem 8.23 | iotaex 6469 |
| [Quine] p. 58 | Definition 9.1 | df-op 4593 |
| [Quine] p. 61 | Theorem 9.5 | opabid 5482 opabidw 5481 opelopab 5499 opelopaba 5493 opelopabaf 5501 opelopabf 5502 opelopabg 5495 opelopabga 5490 opelopabgf 5497 oprabid 7389 oprabidw 7388 |
| [Quine] p. 64 | Definition 9.11 | df-xp 5639 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 5641 |
| [Quine] p. 64 | Definition 9.15 | df-id 5531 |
| [Quine] p. 65 | Theorem 10.3 | fun0 6566 |
| [Quine] p. 65 | Theorem 10.4 | funi 6533 |
| [Quine] p. 65 | Theorem 10.5 | funsn 6554 funsng 6552 |
| [Quine] p. 65 | Definition 10.1 | df-fun 6498 |
| [Quine] p. 65 | Definition 10.2 | args 6044 dffv4 6839 |
| [Quine] p. 68 | Definition 10.11 | conventions 29344 df-fv 6504 fv2 6837 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 14172 nn0opth2i 14171 nn0opthi 14170 omopthi 8607 |
| [Quine] p. 177 | Definition 25.2 | df-rdg 8356 |
| [Quine] p. 232 | Equation i | carddom 10490 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 6589 funimaexg 6587 |
| [Quine] p. 331 | Axiom system NF | ru 3738 |
| [ReedSimon] p. 36 | Definition (iii) | ax-his3 30026 |
| [ReedSimon] p. 63 | Exercise 4(a) | df-dip 29643 polid 30101 polid2i 30099 polidi 30100 |
| [ReedSimon] p. 63 | Exercise 4(b) | df-ph 29755 |
| [ReedSimon] p. 195 | Remark | lnophm 30961 lnophmi 30960 |
| [Retherford] p. 49 | Exercise 1(i) | leopadd 31074 |
| [Retherford] p. 49 | Exercise 1(ii) | leopmul 31076 leopmuli 31075 |
| [Retherford] p. 49 | Exercise 1(iv) | leoptr 31079 |
| [Retherford] p. 49 | Definition VI.1 | df-leop 30794 leoppos 31068 |
| [Retherford] p. 49 | Exercise 1(iii) | leoptri 31078 |
| [Retherford] p. 49 | Definition of operator ordering | leop3 31067 |
| [Roman] p. 4 | Definition | df-dmat 21839 df-dmatalt 46469 |
| [Roman] p. 18 | Part Preliminaries | df-rng 46163 |
| [Roman] p. 19 | Part Preliminaries | df-ring 19966 |
| [Roman] p. 46 | Theorem 1.6 | isldepslvec2 46556 |
| [Roman] p. 112 | Note | isldepslvec2 46556 ldepsnlinc 46579 zlmodzxznm 46568 |
| [Roman] p. 112 | Example | zlmodzxzequa 46567 zlmodzxzequap 46570 zlmodzxzldep 46575 |
| [Roman] p. 170 | Theorem 7.8 | cayleyhamilton 22239 |
| [Rosenlicht] p. 80 | Theorem | heicant 36113 |
| [Rosser] p. 281 | Definition | df-op 4593 |
| [RosserSchoenfeld] p. 71 | Theorem 12. | ax-ros335 33258 |
| [RosserSchoenfeld] p. 71 | Theorem 13. | ax-ros336 33259 |
| [Rotman] p. 28 | Remark | pgrpgt2nabl 46432 pmtr3ncom 19257 |
| [Rotman] p. 31 | Theorem 3.4 | symggen2 19253 |
| [Rotman] p. 42 | Theorem 3.15 | cayley 19196 cayleyth 19197 |
| [Rudin] p. 164 | Equation 27 | efcan 15978 |
| [Rudin] p. 164 | Equation 30 | efzval 15984 |
| [Rudin] p. 167 | Equation 48 | absefi 16078 |
| [Sanford] p. 39 | Remark | ax-mp 5 mto 196 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1773 |
| [Sanford] p. 39 | Rule 4 | mptxor 1771 |
| [Sanford] p. 40 | Rule 1 | mptnan 1770 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 6069 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 6072 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 6066 |
| [Schechter] p. 51 | Definition of transitivity | cotr 6064 |
| [Schechter] p. 78 | Definition of Moore collection of sets | df-mre 17466 |
| [Schechter] p. 79 | Definition of Moore closure | df-mrc 17467 |
| [Schechter] p. 82 | Section 4.5 | df-mrc 17467 |
| [Schechter] p. 84 | Definition (A) of an algebraic closure system | df-acs 17469 |
| [Schechter] p. 139 | Definition AC3 | dfac9 10072 |
| [Schechter] p. 141 | Definition (MC) | dfac11 41375 |
| [Schechter] p. 149 | Axiom DC1 | ax-dc 10382 axdc3 10390 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 19968 isrngo 36356 |
| [Schechter] p. 276 | Remark 11.6.e | span0 30484 |
| [Schechter] p. 276 | Definition of span | df-span 30251 spanval 30275 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 22343 |
| [Schloeder] p. 1 | Lemma 1.3 | onelon 6342 onelord 41571 ordelon 6341 ordelord 6339 |
| [Schloeder] p. 1 | Lemma 1.7 | onepsuc 41572 sucidg 6398 |
| [Schloeder] p. 1 | Remark 1.5 | 0elon 6371 onsuc 7746 ord0 6370 ordsuci 7743 |
| [Schloeder] p. 1 | Theorem 1.9 | epsoon 41573 |
| [Schloeder] p. 1 | Definition 1.1 | dftr5 5226 |
| [Schloeder] p. 1 | Definition 1.2 | dford3 41338 elon2 6328 |
| [Schloeder] p. 1 | Definition 1.4 | df-suc 6323 |
| [Schloeder] p. 1 | Definition 1.6 | epel 5540 epelg 5538 |
| [Schloeder] p. 1 | Theorem 1.9(i) | elirr 9533 epirron 41574 ordirr 6335 |
| [Schloeder] p. 1 | Theorem 1.9(ii) | oneltr 41576 oneptr 41575 ontr1 6363 |
| [Schloeder] p. 1 | Theorem 1.9(iii) | oneltri 41578 oneptri 41577 ordtri3or 6349 |
| [Schloeder] p. 2 | Lemma 1.10 | ondif1 8447 ord0eln0 6372 |
| [Schloeder] p. 2 | Lemma 1.13 | elsuci 6384 onsucss 41587 trsucss 6405 |
| [Schloeder] p. 2 | Lemma 1.14 | ordsucss 7753 |
| [Schloeder] p. 2 | Lemma 1.15 | onnbtwn 6411 ordnbtwn 6410 |
| [Schloeder] p. 2 | Lemma 1.16 | orddif0suc 41589 ordnexbtwnsuc 41588 |
| [Schloeder] p. 2 | Lemma 1.17 | fin1a2lem2 10337 onsucf1lem 41590 onsucf1o 41593 onsucf1olem 41591 onsucrn 41592 |
| [Schloeder] p. 2 | Lemma 1.18 | dflim7 41594 |
| [Schloeder] p. 2 | Remark 1.12 | ordzsl 7781 |
| [Schloeder] p. 2 | Theorem 1.10 | ondif1i 41583 ordne0gt0 41582 |
| [Schloeder] p. 2 | Definition 1.11 | dflim6 41585 limnsuc 41586 onsucelab 41584 |
| [Schloeder] p. 3 | Remark 1.21 | omex 9579 |
| [Schloeder] p. 3 | Theorem 1.19 | tfinds 7796 |
| [Schloeder] p. 3 | Theorem 1.22 | omelon 9582 ordom 7812 |
| [Schloeder] p. 3 | Definition 1.20 | dfom3 9583 |
| [Schloeder] p. 4 | Lemma 2.2 | 1onn 8586 |
| [Schloeder] p. 4 | Lemma 2.7 | ssonuni 7714 ssorduni 7713 |
| [Schloeder] p. 4 | Remark 2.4 | oa1suc 8477 |
| [Schloeder] p. 4 | Theorem 1.23 | dfom5 9586 limom 7818 |
| [Schloeder] p. 4 | Definition 2.1 | df-1o 8412 df1o2 8419 |
| [Schloeder] p. 4 | Definition 2.3 | oa0 8462 oa0suclim 41596 oalim 8478 oasuc 8470 |
| [Schloeder] p. 4 | Definition 2.5 | om0 8463 om0suclim 41597 omlim 8479 omsuc 8472 |
| [Schloeder] p. 4 | Definition 2.6 | oe0 8468 oe0m1 8467 oe0suclim 41598 oelim 8480 oesuc 8473 |
| [Schloeder] p. 5 | Lemma 2.10 | onsupuni 41549 |
| [Schloeder] p. 5 | Lemma 2.11 | onsupsucismax 41600 |
| [Schloeder] p. 5 | Lemma 2.12 | onsssupeqcond 41601 |
| [Schloeder] p. 5 | Lemma 2.13 | limexissup 41602 limexissupab 41604 limiun 41603 limuni 6378 |
| [Schloeder] p. 5 | Lemma 2.14 | oa0r 8484 |
| [Schloeder] p. 5 | Lemma 2.15 | om1 8489 om1om1r 41605 om1r 8490 |
| [Schloeder] p. 5 | Remark 2.8 | oacl 8481 oaomoecl 41599 oecl 8483 omcl 8482 |
| [Schloeder] p. 5 | Definition 2.9 | onsupintrab 41551 |
| [Schloeder] p. 6 | Lemma 2.16 | oe1 8491 |
| [Schloeder] p. 6 | Lemma 2.17 | oe1m 8492 |
| [Schloeder] p. 6 | Lemma 2.18 | oe0rif 41606 |
| [Schloeder] p. 6 | Theorem 2.19 | oasubex 41607 |
| [Schloeder] p. 6 | Theorem 2.20 | nnacl 8558 nnamecl 41608 nnecl 8560 nnmcl 8559 |
| [Schloeder] p. 7 | Lemma 3.1 | onsucwordi 41609 |
| [Schloeder] p. 7 | Lemma 3.2 | oaword1 8499 |
| [Schloeder] p. 7 | Lemma 3.3 | oaword2 8500 |
| [Schloeder] p. 7 | Lemma 3.4 | oalimcl 8507 |
| [Schloeder] p. 7 | Lemma 3.5 | oaltublim 41611 |
| [Schloeder] p. 8 | Lemma 3.6 | oaordi3 41612 |
| [Schloeder] p. 8 | Lemma 3.8 | 1oaomeqom 41614 |
| [Schloeder] p. 8 | Lemma 3.10 | oa00 8506 |
| [Schloeder] p. 8 | Lemma 3.11 | omge1 41617 omword1 8520 |
| [Schloeder] p. 8 | Remark 3.9 | oaordnr 41616 oaordnrex 41615 |
| [Schloeder] p. 8 | Theorem 3.7 | oaord3 41613 |
| [Schloeder] p. 9 | Lemma 3.12 | omge2 41618 omword2 8521 |
| [Schloeder] p. 9 | Lemma 3.13 | omlim2 41619 |
| [Schloeder] p. 9 | Lemma 3.14 | omord2lim 41620 |
| [Schloeder] p. 9 | Lemma 3.15 | omord2i 41621 omordi 8513 |
| [Schloeder] p. 9 | Theorem 3.16 | omord 8515 omord2com 41622 |
| [Schloeder] p. 10 | Lemma 3.17 | 2omomeqom 41623 df-2o 8413 |
| [Schloeder] p. 10 | Lemma 3.19 | oege1 41626 oewordi 8538 |
| [Schloeder] p. 10 | Lemma 3.20 | oege2 41627 oeworde 8540 |
| [Schloeder] p. 10 | Lemma 3.21 | rp-oelim2 41628 |
| [Schloeder] p. 10 | Lemma 3.22 | oeord2lim 41629 |
| [Schloeder] p. 10 | Remark 3.18 | omnord1 41625 omnord1ex 41624 |
| [Schloeder] p. 11 | Lemma 3.23 | oeord2i 41630 |
| [Schloeder] p. 11 | Lemma 3.25 | nnoeomeqom 41632 |
| [Schloeder] p. 11 | Remark 3.26 | oenord1 41636 oenord1ex 41635 |
| [Schloeder] p. 11 | Theorem 4.1 | oaomoencom 41637 |
| [Schloeder] p. 11 | Theorem 4.2 | oaass 8508 |
| [Schloeder] p. 11 | Theorem 3.24 | oeord2com 41631 |
| [Schloeder] p. 12 | Theorem 4.3 | odi 8526 |
| [Schloeder] p. 13 | Theorem 4.4 | omass 8527 |
| [Schloeder] p. 14 | Remark 4.6 | oenass 41639 |
| [Schloeder] p. 14 | Theorem 4.7 | oeoa 8544 |
| [Schloeder] p. 15 | Lemma 5.1 | cantnftermord 41640 |
| [Schloeder] p. 15 | Lemma 5.2 | cantnfub 41641 cantnfub2 41642 |
| [Schloeder] p. 16 | Theorem 5.3 | cantnf2 41645 |
| [Schwabhauser] p. 10 | Axiom A1 | axcgrrflx 27863 axtgcgrrflx 27404 |
| [Schwabhauser] p. 10 | Axiom A2 | axcgrtr 27864 |
| [Schwabhauser] p. 10 | Axiom A3 | axcgrid 27865 axtgcgrid 27405 |
| [Schwabhauser] p. 10 | Axioms A1 to A3 | df-trkgc 27390 |
| [Schwabhauser] p. 11 | Axiom A4 | axsegcon 27876 axtgsegcon 27406 df-trkgcb 27392 |
| [Schwabhauser] p. 11 | Axiom A5 | ax5seg 27887 axtg5seg 27407 df-trkgcb 27392 |
| [Schwabhauser] p. 11 | Axiom A6 | axbtwnid 27888 axtgbtwnid 27408 df-trkgb 27391 |
| [Schwabhauser] p. 12 | Axiom A7 | axpasch 27890 axtgpasch 27409 df-trkgb 27391 |
| [Schwabhauser] p. 12 | Axiom A8 | axlowdim2 27909 df-trkg2d 33278 |
| [Schwabhauser] p. 13 | Axiom A8 | axtglowdim2 27412 |
| [Schwabhauser] p. 13 | Axiom A9 | axtgupdim2 27413 df-trkg2d 33278 |
| [Schwabhauser] p. 13 | Axiom A10 | axeuclid 27912 axtgeucl 27414 df-trkge 27393 |
| [Schwabhauser] p. 13 | Axiom A11 | axcont 27925 axtgcont 27411 axtgcont1 27410 df-trkgb 27391 |
| [Schwabhauser] p. 27 | Theorem 2.1 | cgrrflx 34572 |
| [Schwabhauser] p. 27 | Theorem 2.2 | cgrcomim 34574 |
| [Schwabhauser] p. 27 | Theorem 2.3 | cgrtr 34577 |
| [Schwabhauser] p. 27 | Theorem 2.4 | cgrcoml 34581 |
| [Schwabhauser] p. 27 | Theorem 2.5 | cgrcomr 34582 tgcgrcomimp 27419 tgcgrcoml 27421 tgcgrcomr 27420 |
| [Schwabhauser] p. 28 | Theorem 2.8 | cgrtriv 34587 tgcgrtriv 27426 |
| [Schwabhauser] p. 28 | Theorem 2.10 | 5segofs 34591 tg5segofs 33286 |
| [Schwabhauser] p. 28 | Definition 2.10 | df-afs 33283 df-ofs 34568 |
| [Schwabhauser] p. 29 | Theorem 2.11 | cgrextend 34593 tgcgrextend 27427 |
| [Schwabhauser] p. 29 | Theorem 2.12 | segconeq 34595 tgsegconeq 27428 |
| [Schwabhauser] p. 30 | Theorem 3.1 | btwnouttr2 34607 btwntriv2 34597 tgbtwntriv2 27429 |
| [Schwabhauser] p. 30 | Theorem 3.2 | btwncomim 34598 tgbtwncom 27430 |
| [Schwabhauser] p. 30 | Theorem 3.3 | btwntriv1 34601 tgbtwntriv1 27433 |
| [Schwabhauser] p. 30 | Theorem 3.4 | btwnswapid 34602 tgbtwnswapid 27434 |
| [Schwabhauser] p. 30 | Theorem 3.5 | btwnexch2 34608 btwnintr 34604 tgbtwnexch2 27438 tgbtwnintr 27435 |
| [Schwabhauser] p. 30 | Theorem 3.6 | btwnexch 34610 btwnexch3 34605 tgbtwnexch 27440 tgbtwnexch3 27436 |
| [Schwabhauser] p. 30 | Theorem 3.7 | btwnouttr 34609 tgbtwnouttr 27439 tgbtwnouttr2 27437 |
| [Schwabhauser] p. 32 | Theorem 3.13 | axlowdim1 27908 |
| [Schwabhauser] p. 32 | Theorem 3.14 | btwndiff 34612 tgbtwndiff 27448 |
| [Schwabhauser] p. 33 | Theorem 3.17 | tgtrisegint 27441 trisegint 34613 |
| [Schwabhauser] p. 34 | Theorem 4.2 | ifscgr 34629 tgifscgr 27450 |
| [Schwabhauser] p. 34 | Theorem 4.11 | colcom 27500 colrot1 27501 colrot2 27502 lncom 27564 lnrot1 27565 lnrot2 27566 |
| [Schwabhauser] p. 34 | Definition 4.1 | df-ifs 34625 |
| [Schwabhauser] p. 35 | Theorem 4.3 | cgrsub 34630 tgcgrsub 27451 |
| [Schwabhauser] p. 35 | Theorem 4.5 | cgrxfr 34640 tgcgrxfr 27460 |
| [Schwabhauser] p. 35 | Statement 4.4 | ercgrg 27459 |
| [Schwabhauser] p. 35 | Definition 4.4 | df-cgr3 34626 df-cgrg 27453 |
| [Schwabhauser] p. 35 | Definition instead (given | df-cgrg 27453 |
| [Schwabhauser] p. 36 | Theorem 4.6 | btwnxfr 34641 tgbtwnxfr 27472 |
| [Schwabhauser] p. 36 | Theorem 4.11 | colinearperm1 34647 colinearperm2 34649 colinearperm3 34648 colinearperm4 34650 colinearperm5 34651 |
| [Schwabhauser] p. 36 | Definition 4.8 | df-ismt 27475 |
| [Schwabhauser] p. 36 | Definition 4.10 | df-colinear 34624 tgellng 27495 tglng 27488 |
| [Schwabhauser] p. 37 | Theorem 4.12 | colineartriv1 34652 |
| [Schwabhauser] p. 37 | Theorem 4.13 | colinearxfr 34660 lnxfr 27508 |
| [Schwabhauser] p. 37 | Theorem 4.14 | lineext 34661 lnext 27509 |
| [Schwabhauser] p. 37 | Theorem 4.16 | fscgr 34665 tgfscgr 27510 |
| [Schwabhauser] p. 37 | Theorem 4.17 | linecgr 34666 lncgr 27511 |
| [Schwabhauser] p. 37 | Definition 4.15 | df-fs 34627 |
| [Schwabhauser] p. 38 | Theorem 4.18 | lineid 34668 lnid 27512 |
| [Schwabhauser] p. 38 | Theorem 4.19 | idinside 34669 tgidinside 27513 |
| [Schwabhauser] p. 39 | Theorem 5.1 | btwnconn1 34686 tgbtwnconn1 27517 |
| [Schwabhauser] p. 41 | Theorem 5.2 | btwnconn2 34687 tgbtwnconn2 27518 |
| [Schwabhauser] p. 41 | Theorem 5.3 | btwnconn3 34688 tgbtwnconn3 27519 |
| [Schwabhauser] p. 41 | Theorem 5.5 | brsegle2 34694 |
| [Schwabhauser] p. 41 | Definition 5.4 | df-segle 34692 legov 27527 |
| [Schwabhauser] p. 41 | Definition 5.5 | legov2 27528 |
| [Schwabhauser] p. 42 | Remark 5.13 | legso 27541 |
| [Schwabhauser] p. 42 | Theorem 5.6 | seglecgr12im 34695 |
| [Schwabhauser] p. 42 | Theorem 5.7 | seglerflx 34697 |
| [Schwabhauser] p. 42 | Theorem 5.8 | segletr 34699 |
| [Schwabhauser] p. 42 | Theorem 5.9 | segleantisym 34700 |
| [Schwabhauser] p. 42 | Theorem 5.10 | seglelin 34701 |
| [Schwabhauser] p. 42 | Theorem 5.11 | seglemin 34698 |
| [Schwabhauser] p. 42 | Theorem 5.12 | colinbtwnle 34703 |
| [Schwabhauser] p. 42 | Proposition 5.7 | legid 27529 |
| [Schwabhauser] p. 42 | Proposition 5.8 | legtrd 27531 |
| [Schwabhauser] p. 42 | Proposition 5.9 | legtri3 27532 |
| [Schwabhauser] p. 42 | Proposition 5.10 | legtrid 27533 |
| [Schwabhauser] p. 42 | Proposition 5.11 | leg0 27534 |
| [Schwabhauser] p. 43 | Theorem 6.2 | btwnoutside 34710 |
| [Schwabhauser] p. 43 | Theorem 6.3 | broutsideof3 34711 |
| [Schwabhauser] p. 43 | Theorem 6.4 | broutsideof 34706 df-outsideof 34705 |
| [Schwabhauser] p. 43 | Definition 6.1 | broutsideof2 34707 ishlg 27544 |
| [Schwabhauser] p. 44 | Theorem 6.4 | hlln 27549 |
| [Schwabhauser] p. 44 | Theorem 6.5 | hlid 27551 outsideofrflx 34712 |
| [Schwabhauser] p. 44 | Theorem 6.6 | hlcomb 27545 hlcomd 27546 outsideofcom 34713 |
| [Schwabhauser] p. 44 | Theorem 6.7 | hltr 27552 outsideoftr 34714 |
| [Schwabhauser] p. 44 | Theorem 6.11 | hlcgreu 27560 outsideofeu 34716 |
| [Schwabhauser] p. 44 | Definition 6.8 | df-ray 34723 |
| [Schwabhauser] p. 45 | Part 2 | df-lines2 34724 |
| [Schwabhauser] p. 45 | Theorem 6.13 | outsidele 34717 |
| [Schwabhauser] p. 45 | Theorem 6.15 | lineunray 34732 |
| [Schwabhauser] p. 45 | Theorem 6.16 | lineelsb2 34733 tglineelsb2 27574 |
| [Schwabhauser] p. 45 | Theorem 6.17 | linecom 34735 linerflx1 34734 linerflx2 34736 tglinecom 27577 tglinerflx1 27575 tglinerflx2 27576 |
| [Schwabhauser] p. 45 | Theorem 6.18 | linethru 34738 tglinethru 27578 |
| [Schwabhauser] p. 45 | Definition 6.14 | df-line2 34722 tglng 27488 |
| [Schwabhauser] p. 45 | Proposition 6.13 | legbtwn 27536 |
| [Schwabhauser] p. 46 | Theorem 6.19 | linethrueu 34741 tglinethrueu 27581 |
| [Schwabhauser] p. 46 | Theorem 6.21 | lineintmo 34742 tglineineq 27585 tglineinteq 27587 tglineintmo 27584 |
| [Schwabhauser] p. 46 | Theorem 6.23 | colline 27591 |
| [Schwabhauser] p. 46 | Theorem 6.24 | tglowdim2l 27592 |
| [Schwabhauser] p. 46 | Theorem 6.25 | tglowdim2ln 27593 |
| [Schwabhauser] p. 49 | Theorem 7.3 | mirinv 27608 |
| [Schwabhauser] p. 49 | Theorem 7.7 | mirmir 27604 |
| [Schwabhauser] p. 49 | Theorem 7.8 | mirreu3 27596 |
| [Schwabhauser] p. 49 | Definition 7.5 | df-mir 27595 ismir 27601 mirbtwn 27600 mircgr 27599 mirfv 27598 mirval 27597 |
| [Schwabhauser] p. 50 | Theorem 7.8 | mirreu 27606 |
| [Schwabhauser] p. 50 | Theorem 7.9 | mireq 27607 |
| [Schwabhauser] p. 50 | Theorem 7.10 | mirinv 27608 |
| [Schwabhauser] p. 50 | Theorem 7.11 | mirf1o 27611 |
| [Schwabhauser] p. 50 | Theorem 7.13 | miriso 27612 |
| [Schwabhauser] p. 51 | Theorem 7.14 | mirmot 27617 |
| [Schwabhauser] p. 51 | Theorem 7.15 | mirbtwnb 27614 mirbtwni 27613 |
| [Schwabhauser] p. 51 | Theorem 7.16 | mircgrs 27615 |
| [Schwabhauser] p. 51 | Theorem 7.17 | miduniq 27627 |
| [Schwabhauser] p. 52 | Lemma 7.21 | symquadlem 27631 |
| [Schwabhauser] p. 52 | Theorem 7.18 | miduniq1 27628 |
| [Schwabhauser] p. 52 | Theorem 7.19 | miduniq2 27629 |
| [Schwabhauser] p. 52 | Theorem 7.20 | colmid 27630 |
| [Schwabhauser] p. 53 | Lemma 7.22 | krippen 27633 |
| [Schwabhauser] p. 55 | Lemma 7.25 | midexlem 27634 |
| [Schwabhauser] p. 57 | Theorem 8.2 | ragcom 27640 |
| [Schwabhauser] p. 57 | Definition 8.1 | df-rag 27636 israg 27639 |
| [Schwabhauser] p. 58 | Theorem 8.3 | ragcol 27641 |
| [Schwabhauser] p. 58 | Theorem 8.4 | ragmir 27642 |
| [Schwabhauser] p. 58 | Theorem 8.5 | ragtrivb 27644 |
| [Schwabhauser] p. 58 | Theorem 8.6 | ragflat2 27645 |
| [Schwabhauser] p. 58 | Theorem 8.7 | ragflat 27646 |
| [Schwabhauser] p. 58 | Theorem 8.8 | ragtriva 27647 |
| [Schwabhauser] p. 58 | Theorem 8.9 | ragflat3 27648 ragncol 27651 |
| [Schwabhauser] p. 58 | Theorem 8.10 | ragcgr 27649 |
| [Schwabhauser] p. 59 | Theorem 8.12 | perpcom 27655 |
| [Schwabhauser] p. 59 | Theorem 8.13 | ragperp 27659 |
| [Schwabhauser] p. 59 | Theorem 8.14 | perpneq 27656 |
| [Schwabhauser] p. 59 | Definition 8.11 | df-perpg 27638 isperp 27654 |
| [Schwabhauser] p. 59 | Definition 8.13 | isperp2 27657 |
| [Schwabhauser] p. 60 | Theorem 8.18 | foot 27664 |
| [Schwabhauser] p. 62 | Lemma 8.20 | colperpexlem1 27672 colperpexlem2 27673 |
| [Schwabhauser] p. 63 | Theorem 8.21 | colperpex 27675 colperpexlem3 27674 |
| [Schwabhauser] p. 64 | Theorem 8.22 | mideu 27680 midex 27679 |
| [Schwabhauser] p. 66 | Lemma 8.24 | opphllem 27677 |
| [Schwabhauser] p. 67 | Theorem 9.2 | oppcom 27686 |
| [Schwabhauser] p. 67 | Definition 9.1 | islnopp 27681 |
| [Schwabhauser] p. 68 | Lemma 9.3 | opphllem2 27690 |
| [Schwabhauser] p. 68 | Lemma 9.4 | opphllem5 27693 opphllem6 27694 |
| [Schwabhauser] p. 69 | Theorem 9.5 | opphl 27696 |
| [Schwabhauser] p. 69 | Theorem 9.6 | axtgpasch 27409 |
| [Schwabhauser] p. 70 | Theorem 9.6 | outpasch 27697 |
| [Schwabhauser] p. 71 | Theorem 9.8 | lnopp2hpgb 27705 |
| [Schwabhauser] p. 71 | Definition 9.7 | df-hpg 27700 hpgbr 27702 |
| [Schwabhauser] p. 72 | Lemma 9.10 | hpgerlem 27707 |
| [Schwabhauser] p. 72 | Theorem 9.9 | lnoppnhpg 27706 |
| [Schwabhauser] p. 72 | Theorem 9.11 | hpgid 27708 |
| [Schwabhauser] p. 72 | Theorem 9.12 | hpgcom 27709 |
| [Schwabhauser] p. 72 | Theorem 9.13 | hpgtr 27710 |
| [Schwabhauser] p. 73 | Theorem 9.18 | colopp 27711 |
| [Schwabhauser] p. 73 | Theorem 9.19 | colhp 27712 |
| [Schwabhauser] p. 88 | Theorem 10.2 | lmieu 27726 |
| [Schwabhauser] p. 88 | Definition 10.1 | df-mid 27716 |
| [Schwabhauser] p. 89 | Theorem 10.4 | lmicom 27730 |
| [Schwabhauser] p. 89 | Theorem 10.5 | lmilmi 27731 |
| [Schwabhauser] p. 89 | Theorem 10.6 | lmireu 27732 |
| [Schwabhauser] p. 89 | Theorem 10.7 | lmieq 27733 |
| [Schwabhauser] p. 89 | Theorem 10.8 | lmiinv 27734 |
| [Schwabhauser] p. 89 | Theorem 10.9 | lmif1o 27737 |
| [Schwabhauser] p. 89 | Theorem 10.10 | lmiiso 27739 |
| [Schwabhauser] p. 89 | Definition 10.3 | df-lmi 27717 |
| [Schwabhauser] p. 90 | Theorem 10.11 | lmimot 27740 |
| [Schwabhauser] p. 91 | Theorem 10.12 | hypcgr 27743 |
| [Schwabhauser] p. 92 | Theorem 10.14 | lmiopp 27744 |
| [Schwabhauser] p. 92 | Theorem 10.15 | lnperpex 27745 |
| [Schwabhauser] p. 92 | Theorem 10.16 | trgcopy 27746 trgcopyeu 27748 |
| [Schwabhauser] p. 95 | Definition 11.2 | dfcgra2 27772 |
| [Schwabhauser] p. 95 | Definition 11.3 | iscgra 27751 |
| [Schwabhauser] p. 95 | Proposition 11.4 | cgracgr 27760 |
| [Schwabhauser] p. 95 | Proposition 11.10 | cgrahl1 27758 cgrahl2 27759 |
| [Schwabhauser] p. 96 | Theorem 11.6 | cgraid 27761 |
| [Schwabhauser] p. 96 | Theorem 11.9 | cgraswap 27762 |
| [Schwabhauser] p. 97 | Theorem 11.7 | cgracom 27764 |
| [Schwabhauser] p. 97 | Theorem 11.8 | cgratr 27765 |
| [Schwabhauser] p. 97 | Theorem 11.21 | cgrabtwn 27768 cgrahl 27769 |
| [Schwabhauser] p. 98 | Theorem 11.13 | sacgr 27773 |
| [Schwabhauser] p. 98 | Theorem 11.14 | oacgr 27774 |
| [Schwabhauser] p. 98 | Theorem 11.15 | acopy 27775 acopyeu 27776 |
| [Schwabhauser] p. 101 | Theorem 11.24 | inagswap 27783 |
| [Schwabhauser] p. 101 | Theorem 11.25 | inaghl 27787 |
| [Schwabhauser] p. 101 | Definition 11.23 | isinag 27780 |
| [Schwabhauser] p. 102 | Lemma 11.28 | cgrg3col4 27795 |
| [Schwabhauser] p. 102 | Definition 11.27 | df-leag 27788 isleag 27789 |
| [Schwabhauser] p. 107 | Theorem 11.49 | tgsas 27797 tgsas1 27796 tgsas2 27798 tgsas3 27799 |
| [Schwabhauser] p. 108 | Theorem 11.50 | tgasa 27801 tgasa1 27800 |
| [Schwabhauser] p. 109 | Theorem 11.51 | tgsss1 27802 tgsss2 27803 tgsss3 27804 |
| [Shapiro] p. 230 | Theorem 6.5.1 | dchrhash 26619 dchrsum 26617 dchrsum2 26616 sumdchr 26620 |
| [Shapiro] p. 232 | Theorem 6.5.2 | dchr2sum 26621 sum2dchr 26622 |
| [Shapiro], p. 199 | Lemma 6.1C.2 | ablfacrp 19845 ablfacrp2 19846 |
| [Shapiro], p. 328 | Equation 9.2.4 | vmasum 26564 |
| [Shapiro], p. 329 | Equation 9.2.7 | logfac2 26565 |
| [Shapiro], p. 329 | Equation 9.2.9 | logfacrlim 26572 |
| [Shapiro], p. 331 | Equation 9.2.13 | vmadivsum 26830 |
| [Shapiro], p. 331 | Equation 9.2.14 | rplogsumlem2 26833 |
| [Shapiro], p. 336 | Exercise 9.1.7 | vmalogdivsum 26887 vmalogdivsum2 26886 |
| [Shapiro], p. 375 | Theorem 9.4.1 | dirith 26877 dirith2 26876 |
| [Shapiro], p. 375 | Equation 9.4.3 | rplogsum 26875 rpvmasum 26874 rpvmasum2 26860 |
| [Shapiro], p. 376 | Equation 9.4.7 | rpvmasumlem 26835 |
| [Shapiro], p. 376 | Equation 9.4.8 | dchrvmasum 26873 |
| [Shapiro], p. 377 | Lemma 9.4.1 | dchrisum 26840 dchrisumlem1 26837 dchrisumlem2 26838 dchrisumlem3 26839 dchrisumlema 26836 |
| [Shapiro], p. 377 | Equation 9.4.11 | dchrvmasumlem1 26843 |
| [Shapiro], p. 379 | Equation 9.4.16 | dchrmusum 26872 dchrmusumlem 26870 dchrvmasumlem 26871 |
| [Shapiro], p. 380 | Lemma 9.4.2 | dchrmusum2 26842 |
| [Shapiro], p. 380 | Lemma 9.4.3 | dchrvmasum2lem 26844 |
| [Shapiro], p. 382 | Lemma 9.4.4 | dchrisum0 26868 dchrisum0re 26861 dchrisumn0 26869 |
| [Shapiro], p. 382 | Equation 9.4.27 | dchrisum0fmul 26854 |
| [Shapiro], p. 382 | Equation 9.4.29 | dchrisum0flb 26858 |
| [Shapiro], p. 383 | Equation 9.4.30 | dchrisum0fno1 26859 |
| [Shapiro], p. 403 | Equation 10.1.16 | pntrsumbnd 26914 pntrsumbnd2 26915 pntrsumo1 26913 |
| [Shapiro], p. 405 | Equation 10.2.1 | mudivsum 26878 |
| [Shapiro], p. 406 | Equation 10.2.6 | mulogsum 26880 |
| [Shapiro], p. 407 | Equation 10.2.7 | mulog2sumlem1 26882 |
| [Shapiro], p. 407 | Equation 10.2.8 | mulog2sum 26885 |
| [Shapiro], p. 418 | Equation 10.4.6 | logsqvma 26890 |
| [Shapiro], p. 418 | Equation 10.4.8 | logsqvma2 26891 |
| [Shapiro], p. 419 | Equation 10.4.10 | selberg 26896 |
| [Shapiro], p. 420 | Equation 10.4.12 | selberg2lem 26898 |
| [Shapiro], p. 420 | Equation 10.4.14 | selberg2 26899 |
| [Shapiro], p. 422 | Equation 10.6.7 | selberg3 26907 |
| [Shapiro], p. 422 | Equation 10.4.20 | selberg4lem1 26908 |
| [Shapiro], p. 422 | Equation 10.4.21 | selberg3lem1 26905 selberg3lem2 26906 |
| [Shapiro], p. 422 | Equation 10.4.23 | selberg4 26909 |
| [Shapiro], p. 427 | Theorem 10.5.2 | chpdifbnd 26903 |
| [Shapiro], p. 428 | Equation 10.6.2 | selbergr 26916 |
| [Shapiro], p. 429 | Equation 10.6.8 | selberg3r 26917 |
| [Shapiro], p. 430 | Equation 10.6.11 | selberg4r 26918 |
| [Shapiro], p. 431 | Equation 10.6.15 | pntrlog2bnd 26932 |
| [Shapiro], p. 434 | Equation 10.6.27 | pntlema 26944 pntlemb 26945 pntlemc 26943 pntlemd 26942 pntlemg 26946 |
| [Shapiro], p. 435 | Equation 10.6.29 | pntlema 26944 |
| [Shapiro], p. 436 | Lemma 10.6.1 | pntpbnd 26936 |
| [Shapiro], p. 436 | Lemma 10.6.2 | pntibnd 26941 |
| [Shapiro], p. 436 | Equation 10.6.34 | pntlema 26944 |
| [Shapiro], p. 436 | Equation 10.6.35 | pntlem3 26957 pntleml 26959 |
| [Stoll] p. 13 | Definition corresponds to | dfsymdif3 4256 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 4361 dif0 4332 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdir 4449 |
| [Stoll] p. 17 | Theorem 5.1(5) | unvdif 4434 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 4247 |
| [Stoll] p. 19 | Theorem 5.2(13') | indm 4248 |
| [Stoll] p. 20 | Remark | invdif 4228 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 4595 |
| [Stoll] p. 43 | Definition | uniiun 5018 |
| [Stoll] p. 44 | Definition | intiin 5019 |
| [Stoll] p. 45 | Definition | df-iin 4957 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4956 |
| [Stoll] p. 176 | Theorem 3.4(27) | iman 402 |
| [Stoll] p. 262 | Example 4.1 | dfsymdif3 4256 |
| [Strang] p. 242 | Section 6.3 | expgrowth 42605 |
| [Suppes] p. 22 | Theorem 2 | eq0 4303 eq0f 4300 |
| [Suppes] p. 22 | Theorem 4 | eqss 3959 eqssd 3961 eqssi 3960 |
| [Suppes] p. 23 | Theorem 5 | ss0 4358 ss0b 4357 |
| [Suppes] p. 23 | Theorem 6 | sstr 3952 sstrALT2 43107 |
| [Suppes] p. 23 | Theorem 7 | pssirr 4060 |
| [Suppes] p. 23 | Theorem 8 | pssn2lp 4061 |
| [Suppes] p. 23 | Theorem 9 | psstr 4064 |
| [Suppes] p. 23 | Theorem 10 | pssss 4055 |
| [Suppes] p. 25 | Theorem 12 | elin 3926 elun 4108 |
| [Suppes] p. 26 | Theorem 15 | inidm 4178 |
| [Suppes] p. 26 | Theorem 16 | in0 4351 |
| [Suppes] p. 27 | Theorem 23 | unidm 4112 |
| [Suppes] p. 27 | Theorem 24 | un0 4350 |
| [Suppes] p. 27 | Theorem 25 | ssun1 4132 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 4140 |
| [Suppes] p. 27 | Theorem 27 | unss 4144 |
| [Suppes] p. 27 | Theorem 28 | indir 4235 |
| [Suppes] p. 27 | Theorem 29 | undir 4236 |
| [Suppes] p. 28 | Theorem 32 | difid 4330 |
| [Suppes] p. 29 | Theorem 33 | difin 4221 |
| [Suppes] p. 29 | Theorem 34 | indif 4229 |
| [Suppes] p. 29 | Theorem 35 | undif1 4435 |
| [Suppes] p. 29 | Theorem 36 | difun2 4440 |
| [Suppes] p. 29 | Theorem 37 | difin0 4433 |
| [Suppes] p. 29 | Theorem 38 | disjdif 4431 |
| [Suppes] p. 29 | Theorem 39 | difundi 4239 |
| [Suppes] p. 29 | Theorem 40 | difindi 4241 |
| [Suppes] p. 30 | Theorem 41 | nalset 5270 |
| [Suppes] p. 39 | Theorem 61 | uniss 4873 |
| [Suppes] p. 39 | Theorem 65 | uniop 5472 |
| [Suppes] p. 41 | Theorem 70 | intsn 4947 |
| [Suppes] p. 42 | Theorem 71 | intpr 4943 intprg 4942 |
| [Suppes] p. 42 | Theorem 73 | op1stb 5428 |
| [Suppes] p. 42 | Theorem 78 | intun 4941 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4993 dfiun2g 4990 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4994 |
| [Suppes] p. 47 | Theorem 86 | elpw 4564 elpw2 5302 elpw2g 5301 elpwg 4563 elpwgdedVD 43189 |
| [Suppes] p. 47 | Theorem 87 | pwid 4582 |
| [Suppes] p. 47 | Theorem 89 | pw0 4772 |
| [Suppes] p. 48 | Theorem 90 | pwpw0 4773 |
| [Suppes] p. 52 | Theorem 101 | xpss12 5648 |
| [Suppes] p. 52 | Theorem 102 | xpindi 5789 xpindir 5790 |
| [Suppes] p. 52 | Theorem 103 | xpundi 5700 xpundir 5701 |
| [Suppes] p. 54 | Theorem 105 | elirrv 9532 |
| [Suppes] p. 58 | Theorem 2 | relss 5737 |
| [Suppes] p. 59 | Theorem 4 | eldm 5856 eldm2 5857 eldm2g 5855 eldmg 5854 |
| [Suppes] p. 59 | Definition 3 | df-dm 5643 |
| [Suppes] p. 60 | Theorem 6 | dmin 5867 |
| [Suppes] p. 60 | Theorem 8 | rnun 6098 |
| [Suppes] p. 60 | Theorem 9 | rnin 6099 |
| [Suppes] p. 60 | Definition 4 | dfrn2 5844 |
| [Suppes] p. 61 | Theorem 11 | brcnv 5838 brcnvg 5835 |
| [Suppes] p. 62 | Equation 5 | elcnv 5832 elcnv2 5833 |
| [Suppes] p. 62 | Theorem 12 | relcnv 6056 |
| [Suppes] p. 62 | Theorem 15 | cnvin 6097 |
| [Suppes] p. 62 | Theorem 16 | cnvun 6095 |
| [Suppes] p. 63 | Definition | dftrrels2 37037 |
| [Suppes] p. 63 | Theorem 20 | co02 6212 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5926 |
| [Suppes] p. 63 | Definition 7 | df-co 5642 |
| [Suppes] p. 64 | Theorem 26 | cnvco 5841 |
| [Suppes] p. 64 | Theorem 27 | coass 6217 |
| [Suppes] p. 65 | Theorem 31 | resundi 5951 |
| [Suppes] p. 65 | Theorem 34 | elima 6018 elima2 6019 elima3 6020 elimag 6017 |
| [Suppes] p. 65 | Theorem 35 | imaundi 6102 |
| [Suppes] p. 66 | Theorem 40 | dminss 6105 |
| [Suppes] p. 66 | Theorem 41 | imainss 6106 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 6109 |
| [Suppes] p. 81 | Definition 34 | dfec2 8651 |
| [Suppes] p. 82 | Theorem 72 | elec 8692 elecALTV 36726 elecg 8691 |
| [Suppes] p. 82 | Theorem 73 | eqvrelth 37073 erth 8697 erth2 8698 |
| [Suppes] p. 83 | Theorem 74 | eqvreldisj 37076 erdisj 8700 |
| [Suppes] p. 83 | Definition 35, | df-parts 37227 dfmembpart2 37232 |
| [Suppes] p. 89 | Theorem 96 | map0b 8821 |
| [Suppes] p. 89 | Theorem 97 | map0 8825 map0g 8822 |
| [Suppes] p. 89 | Theorem 98 | mapsn 8826 mapsnd 8824 |
| [Suppes] p. 89 | Theorem 99 | mapss 8827 |
| [Suppes] p. 91 | Definition 12(ii) | alephsuc 10004 |
| [Suppes] p. 91 | Definition 12(iii) | alephlim 10003 |
| [Suppes] p. 92 | Theorem 1 | enref 8925 enrefg 8924 |
| [Suppes] p. 92 | Theorem 2 | ensym 8943 ensymb 8942 ensymi 8944 |
| [Suppes] p. 92 | Theorem 3 | entr 8946 |
| [Suppes] p. 92 | Theorem 4 | unen 8990 |
| [Suppes] p. 94 | Theorem 15 | endom 8919 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 8940 |
| [Suppes] p. 94 | Theorem 17 | domtr 8947 |
| [Suppes] p. 95 | Theorem 18 | sbth 9037 |
| [Suppes] p. 97 | Theorem 23 | canth2 9074 canth2g 9075 |
| [Suppes] p. 97 | Definition 3 | brsdom2 9041 df-sdom 8886 dfsdom2 9040 |
| [Suppes] p. 97 | Theorem 21(i) | sdomirr 9058 |
| [Suppes] p. 97 | Theorem 22(i) | domnsym 9043 |
| [Suppes] p. 97 | Theorem 21(ii) | sdomnsym 9042 |
| [Suppes] p. 97 | Theorem 22(ii) | domsdomtr 9056 |
| [Suppes] p. 97 | Theorem 22(iv) | brdom2 8922 |
| [Suppes] p. 97 | Theorem 21(iii) | sdomtr 9059 |
| [Suppes] p. 97 | Theorem 22(iii) | sdomdomtr 9054 |
| [Suppes] p. 98 | Exercise 4 | fundmen 8975 fundmeng 8976 |
| [Suppes] p. 98 | Exercise 6 | xpdom3 9014 |
| [Suppes] p. 98 | Exercise 11 | sdomentr 9055 |
| [Suppes] p. 104 | Theorem 37 | fofi 9282 |
| [Suppes] p. 104 | Theorem 38 | pwfi 9122 |
| [Suppes] p. 105 | Theorem 40 | pwfi 9122 |
| [Suppes] p. 111 | Axiom for cardinal numbers | carden 10487 |
| [Suppes] p. 130 | Definition 3 | df-tr 5223 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 7714 |
| [Suppes] p. 134 | Definition 6 | df-suc 6323 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 7839 finds 7835 finds1 7838 finds2 7837 |
| [Suppes] p. 151 | Theorem 42 | isfinite 9588 isfinite2 9245 isfiniteg 9248 unbnn 9243 |
| [Suppes] p. 162 | Definition 5 | df-ltnq 10854 df-ltpq 10846 |
| [Suppes] p. 197 | Theorem Schema 4 | tfindes 7799 tfinds 7796 tfinds2 7800 |
| [Suppes] p. 209 | Theorem 18 | oaord1 8498 |
| [Suppes] p. 209 | Theorem 21 | oaword2 8500 |
| [Suppes] p. 211 | Theorem 25 | oaass 8508 |
| [Suppes] p. 225 | Definition 8 | iscard2 9912 |
| [Suppes] p. 227 | Theorem 56 | ondomon 10499 |
| [Suppes] p. 228 | Theorem 59 | harcard 9914 |
| [Suppes] p. 228 | Definition 12(i) | aleph0 10002 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 6368 |
| [Suppes] p. 228 | Theorem Schema 62 | onminesb 7728 onminsb 7729 |
| [Suppes] p. 229 | Theorem 64 | alephval2 10508 |
| [Suppes] p. 229 | Theorem 65 | alephcard 10006 |
| [Suppes] p. 229 | Theorem 66 | alephord2i 10013 |
| [Suppes] p. 229 | Theorem 67 | alephnbtwn 10007 |
| [Suppes] p. 229 | Definition 12 | df-aleph 9876 |
| [Suppes] p. 242 | Theorem 6 | weth 10431 |
| [Suppes] p. 242 | Theorem 8 | entric 10493 |
| [Suppes] p. 242 | Theorem 9 | carden 10487 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2707 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2728 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2814 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2730 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2759 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 7361 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3738 |
| [TakeutiZaring] p. 15 | Axiom 2 | zfpair 5376 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 4609 elpr2 4611 elpr2g 4610 elprg 4607 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 4601 elsn2 4625 elsn2g 4624 elsng 4600 velsn 4602 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 5424 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 4596 sneqr 4798 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 4605 dfsn2 4599 dfsn2ALT 4606 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 7678 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 5433 |
| [TakeutiZaring] p. 16 | Exercise 7 | opex 5421 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 5405 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 7680 unexg 7683 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 4650 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 4866 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3917 df-un 3915 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 4883 uniprg 4882 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 5332 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 4649 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 6387 elsucg 6385 sstr2 3951 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 4113 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 4161 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 4126 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 4179 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 4233 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 4234 |
| [TakeutiZaring] p. 17 | Definition 5.9 | df-pss 3929 dfss2 3930 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 4562 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 4141 |
| [TakeutiZaring] p. 18 | Exercise 9 | df-ss 3927 sseqin2 4175 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3966 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 4188 inss2 4189 |
| [TakeutiZaring] p. 18 | Exercise 13 | nss 4006 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 4876 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 5406 sspwimp 43190 sspwimpALT 43197 sspwimpALT2 43200 sspwimpcf 43192 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 5413 |
| [TakeutiZaring] p. 19 | Axiom 5 | ax-rep 5242 |
| [TakeutiZaring] p. 20 | Definition | df-rab 3408 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 5264 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3913 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 4285 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 4330 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0 4306 n0f 4302 neq0 4305 neq0f 4301 |
| [TakeutiZaring] p. 21 | Axiom 6 | zfreg 9531 |
| [TakeutiZaring] p. 21 | Axiom 6' | zfregs 9668 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 9670 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 3447 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 5272 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 4356 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 5278 ssexg 5280 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 5274 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 9538 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 9533 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0 4323 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 4090 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3 4250 undif3VD 43154 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 4091 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 4098 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 3065 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 3074 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 7687 xpexg 7684 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 5640 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 6572 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 6748 fun11 6575 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 6512 svrelfun 6573 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 5843 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 5845 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 5645 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 5646 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 5642 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 6146 dfrel2 6141 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 5649 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 5767 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 5774 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 5788 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5966 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5943 opelresi 5945 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5959 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5962 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5967 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 6543 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 6060 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 6541 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 6750 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2609 |
| [TakeutiZaring] p. 26 | Definition 6.11 | conventions 29344 df-fv 6504 fv3 6860 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 7862 cnvexg 7861 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 7848 dmexg 7840 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 7849 rnexg 7841 |
| [TakeutiZaring] p. 26 | Corollary 6.9(1) | xpexb 42724 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnv 7857 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | fvex 6855 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1-afv 45396 tz6.12-1-afv2 45463 tz6.12-1 6865 tz6.12-afv 45395 tz6.12-afv2 45462 tz6.12 6867 tz6.12c-afv2 45464 tz6.12c 6864 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2-afv2 45459 tz6.12-2 6830 tz6.12i-afv2 45465 tz6.12i 6870 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 6499 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 6500 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 6502 wfo 6494 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 6501 wf1 6493 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 6503 wf1o 6495 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 6982 eqfnfv2 6983 eqfnfv2f 6986 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 6939 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 7167 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 7165 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 6589 funimaexg 6587 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 5106 |
| [TakeutiZaring] p. 29 | Definition 6.19(1) | df-so 5546 |
| [TakeutiZaring] p. 30 | Definition 6.21 | dffr2 5597 dffr3 6051 eliniseg 6046 iniseg 6049 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 5537 |
| [TakeutiZaring] p. 30 | Proposition 6.23 | fr2nr 5611 fr3nr 7706 frirr 5610 |
| [TakeutiZaring] p. 30 | Definition 6.24(1) | df-fr 5588 |
| [TakeutiZaring] p. 30 | Definition 6.24(2) | dfwe2 7708 |
| [TakeutiZaring] p. 31 | Exercise 1 | frss 5600 |
| [TakeutiZaring] p. 31 | Exercise 4 | wess 5620 |
| [TakeutiZaring] p. 31 | Proposition 6.26 | tz6.26 6301 tz6.26i 6303 wefrc 5627 wereu2 5630 |
| [TakeutiZaring] p. 32 | Theorem 6.27 | wfi 6304 wfii 6306 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 6505 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 7274 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 7275 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 7281 |
| [TakeutiZaring] p. 33 | Proposition 6.31(1) | isomin 7282 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 7283 |
| [TakeutiZaring] p. 33 | Proposition 6.32(1) | isofr 7287 |
| [TakeutiZaring] p. 33 | Proposition 6.32(3) | isowe 7294 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 7296 |
| [TakeutiZaring] p. 35 | Notation | wtr 5222 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | trelpss 42725 tz7.2 5617 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 5228 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 6330 |
| [TakeutiZaring] p. 36 | Proposition 7.5 | tz7.5 6338 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 6339 ordelordALT 42809 ordelordALTVD 43139 |
| [TakeutiZaring] p. 37 | Corollary 7.8 | ordelpss 6345 ordelssne 6344 |
| [TakeutiZaring] p. 37 | Proposition 7.7 | tz7.7 6343 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 6347 |
| [TakeutiZaring] p. 38 | Corollary 7.14 | ordeleqon 7716 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 7717 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 6321 |
| [TakeutiZaring] p. 38 | Proposition 7.10 | ordtri3or 6349 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | onfrALT 42821 ordon 7711 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 7712 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 7789 |
| [TakeutiZaring] p. 40 | Exercise 3 | ontr2 6364 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 5224 |
| [TakeutiZaring] p. 40 | Exercise 9 | onssmin 7727 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 7766 |
| [TakeutiZaring] p. 40 | Exercise 12 | ordun 6421 |
| [TakeutiZaring] p. 40 | Exercise 14 | ordequn 6420 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 7713 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 4898 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 6323 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 6397 sucidg 6398 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 7746 |
| [TakeutiZaring] p. 41 | Proposition 7.25 | onnbtwn 6411 ordnbtwn 6410 |
| [TakeutiZaring] p. 41 | Proposition 7.26 | onsucuni 7763 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-lim 6322 |
| [TakeutiZaring] p. 42 | Exercise 4 | omssnlim 7817 |
| [TakeutiZaring] p. 42 | Exercise 7 | ssnlim 7822 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 7777 ordelsuc 7755 |
| [TakeutiZaring] p. 42 | Exercise 9 | ordsucelsuc 7757 |
| [TakeutiZaring] p. 42 | Definition 7.27 | nlimon 7787 |
| [TakeutiZaring] p. 42 | Definition 7.28 | dfom2 7804 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 7825 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 7827 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 7828 |
| [TakeutiZaring] p. 43 | Remark | omon 7814 |
| [TakeutiZaring] p. 43 | Axiom 7 | inf3 9571 omex 9579 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 7812 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 7833 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 7829 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 7830 |
| [TakeutiZaring] p. 44 | Exercise 1 | limomss 7807 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 4923 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintss 5241 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 4924 |
| [TakeutiZaring] p. 44 | Exercise 5 | intex 5294 |
| [TakeutiZaring] p. 44 | Exercise 6 | oninton 7730 |
| [TakeutiZaring] p. 44 | Exercise 11 | ordintdif 6367 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 4908 |
| [TakeutiZaring] p. 44 | Proposition 7.34 | noinfep 9596 |
| [TakeutiZaring] p. 45 | Exercise 4 | onint 7725 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 8322 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfr1 8343 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfr2 8344 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfr3 8345 |
| [TakeutiZaring] p. 49 | Theorem 7.44 | tz7.44-1 8352 tz7.44-2 8353 tz7.44-3 8354 |
| [TakeutiZaring] p. 50 | Exercise 1 | smogt 8313 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 8308 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 8292 |
| [TakeutiZaring] p. 51 | Proposition 7.49 | tz7.49 8391 tz7.49c 8392 |
| [TakeutiZaring] p. 51 | Proposition 7.48(1) | tz7.48-1 8389 |
| [TakeutiZaring] p. 51 | Proposition 7.48(2) | tz7.48-2 8388 |
| [TakeutiZaring] p. 51 | Proposition 7.48(3) | tz7.48-3 8390 |
| [TakeutiZaring] p. 53 | Proposition 7.53 | 2eu5 2655 |
| [TakeutiZaring] p. 54 | Proposition 7.56(1) | leweon 9947 |
| [TakeutiZaring] p. 54 | Proposition 7.58(1) | r0weon 9948 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oalim 8478 oasuc 8470 |
| [TakeutiZaring] p. 57 | Remark | tfindsg 7797 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 8481 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 8462 oa0r 8484 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 8482 |
| [TakeutiZaring] p. 58 | Corollary 8.5 | oacan 8495 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 8566 nnaordi 8565 oaord 8494 oaordi 8493 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 5009 uniss2 4902 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordri 8497 |
| [TakeutiZaring] p. 59 | Proposition 8.8 | oawordeu 8502 oawordex 8504 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 8558 |
| [TakeutiZaring] p. 59 | Proposition 8.10 | oaabs 8594 |
| [TakeutiZaring] p. 60 | Remark | oancom 9587 |
| [TakeutiZaring] p. 60 | Proposition 8.11 | oalimcl 8507 |
| [TakeutiZaring] p. 62 | Exercise 1 | nnarcl 8563 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 8499 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0x 8465 omlim 8479 omsuc 8472 |
| [TakeutiZaring] p. 62 | Definition 8.15(a) | om0 8463 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnecl 8560 nnmcl 8559 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 8579 nnmordi 8578 omord 8515 omordi 8513 |
| [TakeutiZaring] p. 63 | Proposition 8.20 | omcan 8516 |
| [TakeutiZaring] p. 63 | Proposition 8.21 | nnmwordri 8583 omwordri 8519 |
| [TakeutiZaring] p. 63 | Proposition 8.18(1) | om0r 8485 |
| [TakeutiZaring] p. 63 | Proposition 8.18(2) | om1 8489 om1r 8490 |
| [TakeutiZaring] p. 64 | Proposition 8.22 | om00 8522 |
| [TakeutiZaring] p. 64 | Proposition 8.23 | omordlim 8524 |
| [TakeutiZaring] p. 64 | Proposition 8.24 | omlimcl 8525 |
| [TakeutiZaring] p. 64 | Proposition 8.25 | odi 8526 |
| [TakeutiZaring] p. 65 | Theorem 8.26 | omass 8527 |
| [TakeutiZaring] p. 67 | Definition 8.30 | nnesuc 8555 oe0 8468 oelim 8480 oesuc 8473 onesuc 8476 |
| [TakeutiZaring] p. 67 | Proposition 8.31 | oe0m0 8466 |
| [TakeutiZaring] p. 67 | Proposition 8.32 | oen0 8533 |
| [TakeutiZaring] p. 67 | Proposition 8.33 | oeordi 8534 |
| [TakeutiZaring] p. 67 | Proposition 8.31(2) | oe0m1 8467 |
| [TakeutiZaring] p. 67 | Proposition 8.31(3) | oe1m 8492 |
| [TakeutiZaring] p. 68 | Corollary 8.34 | oeord 8535 |
| [TakeutiZaring] p. 68 | Corollary 8.36 | oeordsuc 8541 |
| [TakeutiZaring] p. 68 | Proposition 8.35 | oewordri 8539 |
| [TakeutiZaring] p. 68 | Proposition 8.37 | oeworde 8540 |
| [TakeutiZaring] p. 69 | Proposition 8.41 | oeoa 8544 |
| [TakeutiZaring] p. 70 | Proposition 8.42 | oeoe 8546 |
| [TakeutiZaring] p. 73 | Theorem 9.1 | trcl 9664 tz9.1 9665 |
| [TakeutiZaring] p. 76 | Definition 9.9 | df-r1 9700 r10 9704 r1lim 9708 r1limg 9707 r1suc 9706 r1sucg 9705 |
| [TakeutiZaring] p. 77 | Proposition 9.10(2) | r1ord 9716 r1ord2 9717 r1ordg 9714 |
| [TakeutiZaring] p. 78 | Proposition 9.12 | tz9.12 9726 |
| [TakeutiZaring] p. 78 | Proposition 9.13 | rankwflem 9751 tz9.13 9727 tz9.13g 9728 |
| [TakeutiZaring] p. 79 | Definition 9.14 | df-rank 9701 rankval 9752 rankvalb 9733 rankvalg 9753 |
| [TakeutiZaring] p. 79 | Proposition 9.16 | rankel 9775 rankelb 9760 |
| [TakeutiZaring] p. 79 | Proposition 9.17 | rankuni2b 9789 rankval3 9776 rankval3b 9762 |
| [TakeutiZaring] p. 79 | Proposition 9.18 | rankonid 9765 |
| [TakeutiZaring] p. 79 | Proposition 9.15(1) | rankon 9731 |
| [TakeutiZaring] p. 79 | Proposition 9.15(2) | rankr1 9770 rankr1c 9757 rankr1g 9768 |
| [TakeutiZaring] p. 79 | Proposition 9.15(3) | ssrankr1 9771 |
| [TakeutiZaring] p. 80 | Exercise 1 | rankss 9785 rankssb 9784 |
| [TakeutiZaring] p. 80 | Exercise 2 | unbndrank 9778 |
| [TakeutiZaring] p. 80 | Proposition 9.19 | bndrank 9777 |
| [TakeutiZaring] p. 83 | Axiom of Choice | ac4 10411 dfac3 10057 |
| [TakeutiZaring] p. 84 | Theorem 10.3 | dfac8a 9966 numth 10408 numth2 10407 |
| [TakeutiZaring] p. 85 | Definition 10.4 | cardval 10482 |
| [TakeutiZaring] p. 85 | Proposition 10.5 | cardid 10483 cardid2 9889 |
| [TakeutiZaring] p. 85 | Proposition 10.9 | oncard 9896 |
| [TakeutiZaring] p. 85 | Proposition 10.10 | carden 10487 |
| [TakeutiZaring] p. 85 | Proposition 10.11 | cardidm 9895 |
| [TakeutiZaring] p. 85 | Proposition 10.6(1) | cardon 9880 |
| [TakeutiZaring] p. 85 | Proposition 10.6(2) | cardne 9901 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 9893 |
| [TakeutiZaring] p. 87 | Proposition 10.15 | pwen 9094 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 8957 |
| [TakeutiZaring] p. 88 | Exercise 7 | infensuc 9099 |
| [TakeutiZaring] p. 89 | Exercise 10 | omxpen 9018 |
| [TakeutiZaring] p. 90 | Corollary 10.23 | cardnn 9899 |
| [TakeutiZaring] p. 90 | Definition 10.27 | alephiso 10034 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 9153 |
| [TakeutiZaring] p. 90 | Proposition 10.22 | onomeneq 9172 |
| [TakeutiZaring] p. 90 | Proposition 10.26 | alephprc 10035 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 9158 |
| [TakeutiZaring] p. 91 | Exercise 2 | alephle 10024 |
| [TakeutiZaring] p. 91 | Exercise 3 | aleph0 10002 |
| [TakeutiZaring] p. 91 | Exercise 4 | cardlim 9908 |
| [TakeutiZaring] p. 91 | Exercise 7 | infpss 10153 |
| [TakeutiZaring] p. 91 | Exercise 8 | infcntss 9265 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 8887 isfi 8916 |
| [TakeutiZaring] p. 92 | Proposition 10.32 | onfin 9174 |
| [TakeutiZaring] p. 92 | Proposition 10.34 | imadomg 10470 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 9011 |
| [TakeutiZaring] p. 93 | Proposition 10.35 | fodomb 10462 |
| [TakeutiZaring] p. 93 | Proposition 10.36 | djuxpdom 10121 unxpdom 9197 |
| [TakeutiZaring] p. 93 | Proposition 10.37 | cardsdomel 9910 cardsdomelir 9909 |
| [TakeutiZaring] p. 93 | Proposition 10.38 | sucxpdom 9199 |
| [TakeutiZaring] p. 94 | Proposition 10.39 | infxpen 9950 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 8767 |
| [TakeutiZaring] p. 95 | Proposition 10.40 | infxpidm 10498 infxpidm2 9953 |
| [TakeutiZaring] p. 95 | Proposition 10.41 | infdju 10144 infxp 10151 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2en 9023 pw2f1o 9021 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 9087 |
| [TakeutiZaring] p. 97 | Theorem 10.46 | ac6s3 10423 |
| [TakeutiZaring] p. 98 | Theorem 10.46 | ac6c5 10418 ac6s5 10427 |
| [TakeutiZaring] p. 98 | Theorem 10.47 | unidom 10479 |
| [TakeutiZaring] p. 99 | Theorem 10.48 | uniimadom 10480 uniimadomf 10481 |
| [TakeutiZaring] p. 100 | Definition 11.1 | cfcof 10210 |
| [TakeutiZaring] p. 101 | Proposition 11.7 | cofsmo 10205 |
| [TakeutiZaring] p. 102 | Exercise 1 | cfle 10190 |
| [TakeutiZaring] p. 102 | Exercise 2 | cf0 10187 |
| [TakeutiZaring] p. 102 | Exercise 3 | cfsuc 10193 |
| [TakeutiZaring] p. 102 | Exercise 4 | cfom 10200 |
| [TakeutiZaring] p. 102 | Proposition 11.9 | coftr 10209 |
| [TakeutiZaring] p. 103 | Theorem 11.15 | alephreg 10518 |
| [TakeutiZaring] p. 103 | Proposition 11.11 | cardcf 10188 |
| [TakeutiZaring] p. 103 | Proposition 11.13 | alephsing 10212 |
| [TakeutiZaring] p. 104 | Corollary 11.17 | cardinfima 10033 |
| [TakeutiZaring] p. 104 | Proposition 11.16 | carduniima 10032 |
| [TakeutiZaring] p. 104 | Proposition 11.18 | alephfp 10044 alephfp2 10045 |
| [TakeutiZaring] p. 106 | Theorem 11.20 | gchina 10635 |
| [TakeutiZaring] p. 106 | Theorem 11.21 | mappwen 10048 |
| [TakeutiZaring] p. 107 | Theorem 11.26 | konigth 10505 |
| [TakeutiZaring] p. 108 | Theorem 11.28 | pwcfsdom 10519 |
| [TakeutiZaring] p. 108 | Theorem 11.29 | cfpwsdom 10520 |
| [Tarski] p. 67 | Axiom B5 | ax-c5 37345 |
| [Tarski] p. 67 | Scheme B5 | sp 2176 |
| [Tarski] p. 68 | Lemma 6 | avril1 29407 equid 2015 |
| [Tarski] p. 69 | Lemma 7 | equcomi 2020 |
| [Tarski] p. 70 | Lemma 14 | spim 2385 spime 2387 spimew 1975 |
| [Tarski] p. 70 | Lemma 16 | ax-12 2171 ax-c15 37351 ax12i 1970 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 2088 |
| [Tarski] p. 75 | Axiom B7 | ax6v 1972 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-5 1913 ax5ALT 37369 |
| [Tarski], p. 75 | Scheme B8 of system S2 | ax-7 2011 ax-8 2108 ax-9 2116 |
| [Tarski1999] p. 178 | Axiom 4 | axtgsegcon 27406 |
| [Tarski1999] p. 178 | Axiom 5 | axtg5seg 27407 |
| [Tarski1999] p. 179 | Axiom 7 | axtgpasch 27409 |
| [Tarski1999] p. 180 | Axiom 7.1 | axtgpasch 27409 |
| [Tarski1999] p. 185 | Axiom 11 | axtgcont1 27410 |
| [Truss] p. 114 | Theorem 5.18 | ruc 16125 |
| [Viaclovsky7] p. 3 | Corollary 0.3 | mblfinlem3 36117 |
| [Viaclovsky8] p. 3 | Proposition 7 | ismblfin 36119 |
| [Weierstrass] p. 272 | Definition | df-mdet 21934 mdetuni 21971 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 | pm1.2 902 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 866 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 867 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 918 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 966 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 188 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 135 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 90 wl-luk-pm2.04 35916 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | frege5 42062 imim2 58 wl-luk-imim2 35911 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | adh-minimp-imim1 45244 imim1 83 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1 895 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2662 syl 17 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 901 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 22 wl-luk-id 35914 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmid 893 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 142 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13 896 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotr 130 notnotrALT2 43199 wl-luk-notnotr 35915 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1 146 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | ax-frege28 42092 axfrege28 42091 con3 153 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | ax-3 8 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18 128 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 865 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 923 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 123 wl-luk-pm2.21 35908 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 124 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25 888 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26 938 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | conventions-labels 29345 pm2.27 42 wl-luk-pm2.27 35906 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 921 |
| [WhiteheadRussell] p. 104 | Proof begins with references *2.21 ( ~ pm2.21 ) and *14.26 ( ~ eupickbi ) | mopickr 36824 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 922 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 968 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 969 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 967 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1088 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 905 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 906 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 941 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 56 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 880 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 881 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5 169 pm2.5g 168 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6 190 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 882 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 883 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 884 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 172 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 173 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 849 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54 850 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 887 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 889 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61 191 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 898 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 939 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 940 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 192 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 890 pm2.67 891 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521 176 pm2.521g 174 pm2.521g2 175 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 897 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 971 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68 899 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinv 202 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 972 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 973 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 932 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 930 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 970 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 974 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 84 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85 931 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 109 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 990 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 470 pm3.2im 160 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11 991 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12 992 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13 993 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 994 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 472 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 460 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 403 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 801 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 449 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 450 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 483 simplim 167 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 485 simprim 166 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 763 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 764 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 806 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 622 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 808 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 493 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 494 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 959 pm3.44 958 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 807 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 474 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 962 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34b 315 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 260 |
| [WhiteheadRussell] p. 117 | Theorem *4.11 | notbi 318 |
| [WhiteheadRussell] p. 117 | Theorem *4.12 | con2bi 353 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotb 314 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14 805 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 831 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 221 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 804 bitr 803 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 564 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 903 pm4.25 904 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 461 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 1006 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 868 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 469 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 920 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 632 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 916 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 636 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 975 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1089 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 1004 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42 1052 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 1021 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 995 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 997 pm4.45 996 pm4.45im 826 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anor 981 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imor 851 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 546 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianor 980 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52 983 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53 984 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54 985 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55 986 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 982 pm4.56 987 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | oran 988 pm4.57 989 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | pm4.61 405 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62 854 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63 398 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64 847 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65 406 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66 848 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67 399 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 558 pm4.71d 562 pm4.71i 560 pm4.71r 559 pm4.71rd 563 pm4.71ri 561 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 948 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 528 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 935 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 518 pm4.76 519 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 960 pm4.77 961 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78 933 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79 1002 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 393 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81 394 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 1022 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83 1023 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 347 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 348 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 351 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 388 impexp 451 pm4.87 841 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 822 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11 943 pm5.11g 942 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12 944 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13 946 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14 945 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15 1011 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 1012 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17 1010 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbn 384 pm5.18 382 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 387 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 823 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xor 1013 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3 1048 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24 1049 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2 900 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 573 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 389 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 361 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6 1000 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7 952 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 829 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 574 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 834 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 824 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 832 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 390 pm5.41 391 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 544 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 543 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 1003 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54 1016 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55 947 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 999 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62 1017 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63 1018 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71 1026 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 366 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 269 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 1027 |
| [WhiteheadRussell] p. 146 | Theorem *10.12 | pm10.12 42628 |
| [WhiteheadRussell] p. 146 | Theorem *10.14 | pm10.14 42629 |
| [WhiteheadRussell] p. 147 | Theorem *10.22 | 19.26 1873 |
| [WhiteheadRussell] p. 149 | Theorem *10.251 | pm10.251 42630 |
| [WhiteheadRussell] p. 149 | Theorem *10.252 | pm10.252 42631 |
| [WhiteheadRussell] p. 149 | Theorem *10.253 | pm10.253 42632 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1896 |
| [WhiteheadRussell] p. 151 | Theorem *10.301 | albitr 42633 |
| [WhiteheadRussell] p. 155 | Theorem *10.42 | pm10.42 42634 |
| [WhiteheadRussell] p. 155 | Theorem *10.52 | pm10.52 42635 |
| [WhiteheadRussell] p. 155 | Theorem *10.53 | pm10.53 42636 |
| [WhiteheadRussell] p. 155 | Theorem *10.541 | pm10.541 42637 |
| [WhiteheadRussell] p. 156 | Theorem *10.55 | pm10.55 42639 |
| [WhiteheadRussell] p. 156 | Theorem *10.56 | pm10.56 42640 |
| [WhiteheadRussell] p. 156 | Theorem *10.57 | pm10.57 42641 |
| [WhiteheadRussell] p. 156 | Theorem *10.542 | pm10.542 42638 |
| [WhiteheadRussell] p. 159 | Axiom *11.07 | pm11.07 2093 |
| [WhiteheadRussell] p. 159 | Theorem *11.11 | pm11.11 42644 |
| [WhiteheadRussell] p. 159 | Theorem *11.12 | pm11.12 42645 |
| [WhiteheadRussell] p. 159 | Theorem PM*11.1 | 2stdpc4 2073 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 2157 |
| [WhiteheadRussell] p. 160 | Theorem *11.22 | 2exnaln 1831 |
| [WhiteheadRussell] p. 160 | Theorem *11.25 | 2nexaln 1832 |
| [WhiteheadRussell] p. 161 | Theorem *11.3 | 19.21vv 42646 |
| [WhiteheadRussell] p. 162 | Theorem *11.32 | 2alim 42647 |
| [WhiteheadRussell] p. 162 | Theorem *11.33 | 2albi 42648 |
| [WhiteheadRussell] p. 162 | Theorem *11.34 | 2exim 42649 |
| [WhiteheadRussell] p. 162 | Theorem *11.36 | spsbce-2 42651 |
| [WhiteheadRussell] p. 162 | Theorem *11.341 | 2exbi 42650 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1890 |
| [WhiteheadRussell] p. 163 | Theorem *11.43 | 19.36vv 42653 |
| [WhiteheadRussell] p. 163 | Theorem *11.44 | 19.31vv 42654 |
| [WhiteheadRussell] p. 163 | Theorem *11.421 | 19.33-2 42652 |
| [WhiteheadRussell] p. 164 | Theorem *11.5 | 2nalexn 1830 |
| [WhiteheadRussell] p. 164 | Theorem *11.46 | 19.37vv 42655 |
| [WhiteheadRussell] p. 164 | Theorem *11.47 | 19.28vv 42656 |
| [WhiteheadRussell] p. 164 | Theorem *11.51 | 2exnexn 1848 |
| [WhiteheadRussell] p. 164 | Theorem *11.52 | pm11.52 42657 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 2342 |
| [WhiteheadRussell] p. 164 | Theorem *11.521 | 2exanali 1863 |
| [WhiteheadRussell] p. 165 | Theorem *11.6 | pm11.6 42662 |
| [WhiteheadRussell] p. 165 | Theorem *11.56 | aaanv 42658 |
| [WhiteheadRussell] p. 165 | Theorem *11.57 | pm11.57 42659 |
| [WhiteheadRussell] p. 165 | Theorem *11.58 | pm11.58 42660 |
| [WhiteheadRussell] p. 165 | Theorem *11.59 | pm11.59 42661 |
| [WhiteheadRussell] p. 166 | Theorem *11.7 | pm11.7 42666 |
| [WhiteheadRussell] p. 166 | Theorem *11.61 | pm11.61 42663 |
| [WhiteheadRussell] p. 166 | Theorem *11.62 | pm11.62 42664 |
| [WhiteheadRussell] p. 166 | Theorem *11.63 | pm11.63 42665 |
| [WhiteheadRussell] p. 166 | Theorem *11.71 | pm11.71 42667 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2567 |
| [WhiteheadRussell] p. 178 | Theorem *13.13 | pm13.13a 42677 pm13.13b 42678 |
| [WhiteheadRussell] p. 178 | Theorem *13.14 | pm13.14 42679 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 3025 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 3026 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 3618 |
| [WhiteheadRussell] p. 179 | Theorem *13.21 | 2sbc6g 42685 |
| [WhiteheadRussell] p. 179 | Theorem *13.22 | 2sbc5g 42686 |
| [WhiteheadRussell] p. 179 | Theorem *13.192 | pm13.192 42680 |
| [WhiteheadRussell] p. 179 | Theorem *13.193 | 2pm13.193 42824 pm13.193 42681 |
| [WhiteheadRussell] p. 179 | Theorem *13.194 | pm13.194 42682 |
| [WhiteheadRussell] p. 179 | Theorem *13.195 | pm13.195 42683 |
| [WhiteheadRussell] p. 179 | Theorem *13.196 | pm13.196a 42684 |
| [WhiteheadRussell] p. 184 | Theorem *14.12 | pm14.12 42691 |
| [WhiteheadRussell] p. 184 | Theorem *14.111 | iotasbc2 42690 |
| [WhiteheadRussell] p. 184 | Definition *14.01 | iotasbc 42689 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3807 |
| [WhiteheadRussell] p. 185 | Theorem *14.122 | pm14.122a 42692 pm14.122b 42693 pm14.122c 42694 |
| [WhiteheadRussell] p. 185 | Theorem *14.123 | pm14.123a 42695 pm14.123b 42696 pm14.123c 42697 |
| [WhiteheadRussell] p. 189 | Theorem *14.2 | iotaequ 42699 |
| [WhiteheadRussell] p. 189 | Theorem *14.18 | pm14.18 42698 |
| [WhiteheadRussell] p. 189 | Theorem *14.202 | iotavalb 42700 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 6477 |
| [WhiteheadRussell] p. 190 | Theorem *14.205 | iotasbc5 42701 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 6478 |
| [WhiteheadRussell] p. 191 | Theorem *14.24 | pm14.24 42702 |
| [WhiteheadRussell] p. 192 | Theorem *14.25 | sbiota1 42704 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2633 eupickbi 2636 sbaniota 42705 |
| [WhiteheadRussell] p. 192 | Theorem *14.242 | iotavalsb 42703 |
| [WhiteheadRussell] p. 192 | Theorem *14.271 | eubi 2582 |
| [WhiteheadRussell] p. 193 | Theorem *14.272 | iotasbcq 42707 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | conventions 29344 df-fv 6504 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 9937 pm54.43lem 9936 |
| [Young] p. 141 | Definition of operator ordering | leop2 31066 |
| [Young] p. 142 | Example 12.2(i) | 0leop 31072 idleop 31073 |
| [vandenDries] p. 42 | Lemma 61 | irrapx1 41137 |
| [vandenDries] p. 43 | Theorem 62 | pellex 41144 pellexlem1 41138 |