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Theorem repls-infrec-addboth

⊦ nounsharedextR(cren, cext, ren) ∧ Πok(ext, cext, ren, cren) ∧ cext !(πra(step, cstep, ren, cren, ⌜(s, cs) '⌝ + ⌜(s0, cs0) '⌝ + ⌜pcsf⌝ , ⌜ren(a) '⌝ + ⌜paf⌝ )) ⊑ aext !(⌜aa '⌝ + aα) ∧ frag(IOAut(astart, astep, aext))(aσ, ⌜aal⌝ + ⌜aa '⌝ + aα) ∧ aext !(⌜aal⌝ ) = [] ∧ n = # aal ∧ fragω(IOAut(Π(start, cstart), Π(step, cstep, ren, cren, ext, cext), Π(ext, cext, ren, cren)))((s0, cs0) ' + pcsf, paf) ∧ step(s, a, s0) ∧ cstep(cs, ca, cs0) ∧ ren(a) = cren(ca) ∧ cext(ca) = aext(aa) → repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s, cs) '⌝ + ⌜(s0, cs0) '⌝ + ⌜pcsf⌝ , ⌜ren(a) '⌝ + ⌜paf⌝ , aσ, ⌜aal⌝ + ⌜aa '⌝ + aα) = ⌜lift(aσ.take(n), s)⌝ + ⌜(s, aσ[n]) '⌝ + repls(step, cstep, cren, ren, aren, cext, aext, ⌜(s0, cs0) '⌝ + ⌜pcsf⌝ , ⌜paf⌝ , aσ.drop(n + 1), 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: 22
Proof steps: 42
Used lemmas: repls-rec-addboth, repls-mon, replstate-inf-def, replstate-inf,
Used spec theorems:
Used simplifier rules: