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Proof step 10 from proof ac-lookup (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
mkfs(fs .class, ty, fieldvar) ' ∈ fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(fs .class, (fs ' × val) ' + fis0, st)[jvmref -- mkfs(fs .class, ty, fieldvar) ']) = ((fs ' × val) ' + fis0)[mkfs(fs .class, ty, fieldvar) ']

Rule argument

[emptyarg]

Additional information

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