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Proof step 19 from proof ac-lookup-03 (previous step)

fv = sk × val, is_fskey(sk), ∀ class1, st. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done) ∨ mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ (addclass(class1, fv ' + fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done), mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
is_fskey(sk), ∀ class1, st. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done) ∨ mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ (addclass(class1, (sk × val) ' + fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done), mkfs(class1, void_type, `initstate' .field) ' = sk, mkfs(class1, void_type, `initstate' .field) ' ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' + fis ↔ sk = sk0 ∨ sk ∈ fis])]]