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Theorem finfrag-repla-sametrace

⊦ nounsharedextR(cren, cext, ren) ∧ nounsharedextR(aren, aext, ren) ∧ Πok(ext, cext, ren, cren) ∧ Πok(ext, aext, ren, aren) ∧ frag*(IOAut(Π(start, cstart), Π(step, cstep, ren, cren, ext, cext), Π(ext, cext, ren, cren)))((s, cs) ' + pcsl, pal) ∧ frag(IOAut(astart, astep, aext))(⌜as '⌝ + aσ, aα) ∧ ⌜cext !(πra(step, cstep, ren, cren, (s, cs) ' + pcsl, pal))⌝ ⊑ aext !(aα) → Π(ext, aext, ren, aren) !(repla(step, cstep, cren, ren, aren, cext, aext, (s, cs) ' + pcsl, pal, ⌜as '⌝ + aσ, aα)) = Π(ext, cext, ren, cren) !(pal)

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