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Theorem repls-infrec-skip

⊦ nounsharedextR(cren, cext, ren) ∧ Πok(ext, cext, ren, cren) ∧ cext !(πra(step, cstep, ren, cren, ⌜(s, cs) '⌝ + ⌜(s, cs0) '⌝ + ⌜pcsf⌝ , ⌜cren(ca) '⌝ + ⌜paf⌝ )) ⊑ aext !(aα) ∧ frag(IOAut(astart, astep, aext))(⌜as '⌝ + aσ, aα) ∧ fragω(IOAut(Π(start, cstart), Π(step, cstep, ren, cren, ext, cext), Π(ext, cext, ren, cren)))((s, cs0) ' + pcsf, paf) ∧ cstep(cs, ca, cs0) ∧ ¬ cod(ren)(cren(ca)) → repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s, cs) '⌝ + ⌜(s, cs0) '⌝ + ⌜pcsf⌝ , ⌜cren(ca) '⌝ + ⌜paf⌝ , ⌜as '⌝ + aσ, aα) = repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s, cs0) '⌝ + ⌜pcsf⌝ , ⌜paf⌝ , ⌜as '⌝ + aσ, aα)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: frag-repls-head,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 15
Used lemmas: repls-rec-skip, mon-repls, replstate-inf-def, nounsharedextR-notcodren-internal, replstate-inf,
Used spec theorems:
Used simplifier rules: