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Proof step 21 from proof ac-lookup-06 (previous step)

∀ sk, class, st, r. sk = mkfs(class, void_type, `initstate' .field) ' ∨ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = mkfs(class, void_type, `initstate' .field) ', (addclass(class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], sk = sk0, sk ∈ fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 18:
¬ is_indexkey((sk0 × val) .1), ∀ sk, class, st, r. sk = mkfs(class, void_type, `initstate' .field) ' ∨ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = mkfs(class, void_type, `initstate' .field) ', (addclass(class, (sk0 × val) ' + fis0, st)[r -- sk]) = st[r -- sk], sk = sk0, sk ∈ fis0
Proof step 20:
is_indexkey((sk0 × val) .1), ∀ sk, class, st, r. sk = mkfs(class, void_type, `initstate' .field) ' ∨ (addclass(class, fis0, st)[r -- sk]) = st[r -- sk] ∨ sk ∈ fis0 ⊦ sk = mkfs(class, void_type, `initstate' .field) ', (addclass(class, fis0, st)[r -- sk]) = st[r -- sk], sk = sk0, sk ∈ fis0

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, sk0 × val, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, sk0 × val, class)]]