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Theorem finfrag-repl-frag

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

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