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

is_indexkey((sk × val) .1), sk .fs = mkfs(class, ty, fieldvar), ∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ class1 = `java.lang.Object' .class, (addclass(class1, fis0, st)[_mode]) = st[_mode], ¬ is_indexkey(sk) ∧ class ≠ class1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
sk .fs = mkfs(class, ty, fieldvar), is_indexkey(sk), ∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ class1 = `java.lang.Object' .class, (addclass(class1, fis0, st)[_mode]) = st[_mode]

Rule argument

[emptyarg]

Additional information

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