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Theorem efgcpbllema 16751
 Description: Lemma for efgrelex 16748. Define an auxiliary equivalence relation such that if there are sequences from to passing through the same reduced word. (Contributed by Mario Carneiro, 1-Oct-2015.)
Hypotheses
Ref Expression
efgval.w Word
efgval.r ~FG
efgval2.m
efgval2.t splice
efgred.d
efgred.s Word ..^
efgcpbllem.1 concat concat concat concat
Assertion
Ref Expression
efgcpbllema concat concat concat concat
Distinct variable groups:   ,,   ,   ,,,,,   ,,,,,,,,   ,,,,,,   ,,   ,,,,   ,,,,,,,,,   ,,,,,,,   ,,   ,,   ,,   ,,,,,,,,,,   ,,,,
Allowed substitution hints:   (,,,,,,,,)   (,,,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,,,)   (,,,,)   ()   (,,,,,,,,,,)   (,,)   (,,,,,,,,)   (,,,,,,,,)

Proof of Theorem efgcpbllema
StepHypRef Expression
1 oveq2 6289 . . . . 5 concat concat
21oveq1d 6296 . . . 4 concat concat concat concat
3 oveq2 6289 . . . . 5 concat concat
43oveq1d 6296 . . . 4 concat concat concat concat
52, 4breqan12d 4452 . . 3 concat concat concat concat concat concat concat concat
6 efgcpbllem.1 . . . 4 concat concat concat concat
7 vex 3098 . . . . . . 7
8 vex 3098 . . . . . . 7
97, 8prss 4169 . . . . . 6
109anbi1i 695 . . . . 5 concat concat concat concat concat concat concat concat
1110opabbii 4501 . . . 4 concat concat concat concat concat concat concat concat
126, 11eqtr4i 2475 . . 3 concat concat concat concat
135, 12brab2ga 5065 . 2 concat concat concat concat
14 df-3an 976 . 2 concat concat concat concat concat concat concat concat
1513, 14bitr4i 252 1 concat concat concat concat
 Colors of variables: wff setvar class Syntax hints:   wb 184   wa 369   w3a 974   wceq 1383   wcel 1804  wral 2793  crab 2797   cdif 3458   wss 3461  c0 3770  csn 4014  cpr 4016  cop 4020  cotp 4022  ciun 4315   class class class wbr 4437  copab 4494   cmpt 4495   cid 4780   cxp 4987   crn 4990  cfv 5578  (class class class)co 6281   cmpt2 6283  c1o 7125  c2o 7126  cc0 9495  c1 9496   cmin 9810  cfz 11683  ..^cfzo 11806  chash 12387  Word cword 12516   concat cconcat 12518   splice csplice 12521  cs2 12788   ~FG cefg 16703 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-9 1808  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421  ax-sep 4558  ax-nul 4566  ax-pr 4676 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-eu 2272  df-mo 2273  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-ne 2640  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021  df-uni 4235  df-br 4438  df-opab 4496  df-xp 4995  df-iota 5541  df-fv 5586  df-ov 6284 This theorem is referenced by:  efgcpbllemb  16752  efgcpbl  16753
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