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Theorem frag-repls-head

nounsharedextR(cren, cext, ren), Πok(ext, cext, ren, cren), frag(IOAut(Π(start, cstart), Π(step, cstep, ren, cren, ext, cext), Π(ext, cext, ren, cren)))(⌜(s, cs) '⌝ + pcσ, pα), frag(IOAut(astart, astep, aext))(⌜as '⌝ + aσ, aα), cext !(πra(step, cstep, ren, cren, ⌜(s, cs) '⌝ + pcσ, pα)) ⊑ aext !(aα) ⊦ repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s, cs) '⌝ + pcσ, pα, ⌜as '⌝ + aσ, aα) ≠ [] ∧ hd(repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s, cs) '⌝ + pcσ, pα, ⌜as '⌝ + aσ, aα)) = (s, as)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: repl-exec,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 38
Proof steps: 73
Used lemmas: lift-rec, lift-base, repls-infrec-addboth, repls-base, mon-repls, replstate-inf, nounsharedextR-notcodren-internal, repls-infrec-skip, repls-infrec-addS, finfrag-repls-head, replstate-fin-def,
Used spec theorems:
Used simplifier rules: