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Proof step 9 from proof ac-lookup-03 (previous step)

sk = fs ', 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, ¬ is_indexkey(sk) ∧ fs .class ≠ class1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ class1, st. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done) ∨ mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(fs .class, void_type, `initstate' .field) = fs, (addclass(fs .class, (fs ' × val) ' + fis0, st)[jvmref -- mkfs(fs .class, void_type, `initstate' .field) ']) = initval(done), mkfs(fs .class, void_type, `initstate' .field) ' ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')], [CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0])]]