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Proof step 8 from proof ac-lookup-02 (previous step)

sk = fs ', is_fskey(sk), ∀ class1, class2, st, ty, fieldvar. class1 = class2 ∨ (addclass(class2, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '] ⊦ class1 = class2, (addclass(class2, (sk × val) ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '], ¬ is_indexkey(sk) ∧ fs .class ≠ class2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
∀ class1, class2, st, ty, fieldvar. class1 = class2 ∨ (addclass(class2, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '] ⊦ (addclass(fs .class, (fs ' × val) ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = st[jvmref -- mkfs(class1, ty, fieldvar) '], class1 = fs .class

Rule argument

[emptyarg]

Additional information

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