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Theorem frag-repla-sametrace

⊦ nounsharedextR(cren, cext, ren) ∧ nounsharedextR(aren, aext, ren) ∧ Πok(ext, cext, ren, cren) ∧ Πok(ext, aext, ren, aren) ∧ oinj(cext) ∧ oinj(aext) ∧ oinj(ext) ∧ sameshared(cren, aren, ren) ∧ frag(IOAut(Π(start, cstart), Π(step, cstep, ren, cren, ext, cext), Π(ext, cext, ren, cren)))(pcσ, pα) ∧ frag(IOAut(astart, astep, aext))(⌜as '⌝ + aσ, aα) ∧ cext !(πra(step, cstep, ren, cren, pcσ, pα)) = aext !(aα) → Π(ext, aext, ren, aren) !(repla(step, cstep, cren, ren, aren, cext, aext, pcσ, pα, ⌜as '⌝ + aσ, aα)) = Π(ext, cext, ren, cren) !(pα)

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