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Mirrors > Home > MPE Home > Th. List > reldmopsr | Structured version Visualization version GIF version |
Description: Lemma for ordered power series. (Contributed by Stefan O'Rear, 2-Oct-2015.) |
Ref | Expression |
---|---|
reldmopsr | β’ Rel dom ordPwSer |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-opsr 21239 | . 2 β’ ordPwSer = (π β V, π β V β¦ (π β π« (π Γ π) β¦ β¦(π mPwSer π ) / πβ¦(π sSet β¨(leβndx), {β¨π₯, π¦β© β£ ({π₯, π¦} β (Baseβπ) β§ ([{β β (β0 βm π) β£ (β‘β β β) β Fin} / π]βπ§ β π ((π₯βπ§)(ltβπ )(π¦βπ§) β§ βπ€ β π (π€(π <bag π)π§ β (π₯βπ€) = (π¦βπ€))) β¨ π₯ = π¦))}β©))) | |
2 | 1 | reldmmpo 7483 | 1 β’ Rel dom ordPwSer |
Colors of variables: wff setvar class |
Syntax hints: β wi 4 β§ wa 397 β¨ wo 846 = wceq 1542 β wcel 2107 βwral 3063 βwrex 3072 {crab 3406 Vcvv 3444 [wsbc 3738 β¦csb 3854 β wss 3909 π« cpw 4559 {cpr 4587 β¨cop 4591 class class class wbr 5104 {copab 5166 β¦ cmpt 5187 Γ cxp 5629 β‘ccnv 5630 dom cdm 5631 β cima 5634 Rel wrel 5636 βcfv 6492 (class class class)co 7350 βm cmap 8699 Fincfn 8817 βcn 12087 β0cn0 12347 sSet csts 16970 ndxcnx 17000 Basecbs 17018 lecple 17075 ltcplt 18132 mPwSer cmps 21230 <bag cltb 21233 ordPwSer copws 21234 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2709 ax-sep 5255 ax-nul 5262 ax-pr 5383 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2540 df-eu 2569 df-clab 2716 df-cleq 2730 df-clel 2816 df-nfc 2888 df-rab 3407 df-v 3446 df-dif 3912 df-un 3914 df-in 3916 df-ss 3926 df-nul 4282 df-if 4486 df-sn 4586 df-pr 4588 df-op 4592 df-br 5105 df-opab 5167 df-xp 5637 df-rel 5638 df-dm 5641 df-oprab 7354 df-mpo 7355 df-opsr 21239 |
This theorem is referenced by: opsrle 21371 opsrbaslem 21373 opsrbaslemOLD 21374 psr1val 21480 |
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