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Proof step 25 from proof ac-in-10 (previous step)

r -- sk ∈ addclass(class, fv ' + fis0, st), r ∈ addclass(class, fv ' + fis0, st), ∀ sk0, class0, r0, st0. ¬ sk0 ∈ fis0 ∧ sk0 ≠ mkfs(class0, void_type, `initstate' .field) ' → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ sk = mkfs(class, void_type, `initstate' .field) ', r -- sk ∈ st, sk ∈ fv ', sk ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 21:
¬ is_indexkey(fv .1), r -- sk ∈ addclass(class, fv ' + fis0, st), r ∈ addclass(class, fv ' + fis0, st), ∀ sk0, class0, r0, st0. ¬ sk0 ∈ fis0 ∧ sk0 ≠ mkfs(class0, void_type, `initstate' .field) ' → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ sk = mkfs(class, void_type, `initstate' .field) ', r -- sk ∈ st, sk ∈ fv ', sk ∈ fis0
Proof step 24:
is_indexkey(fv .1), r -- sk ∈ addclass(class, fis0, st), r ∈ addclass(class, fis0, st), ∀ sk0, class0, r0, st0. ¬ sk0 ∈ fis0 ∧ sk0 ≠ mkfs(class0, void_type, `initstate' .field) ' → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ sk = mkfs(class, void_type, `initstate' .field) ', r -- sk ∈ st, sk ∈ fv ', sk ∈ fis0

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, fv, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, fv, class)]]