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Proof step 20 from proof ac-lookup-06 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
is_indexkey(sk0), ∀ 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

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]