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Proof step 12 from proof ac-mode-01 (previous step)

is_indexkey((sk × val) .1), sk .fs = mkfs(class1, ty, fieldvar), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ class1 ≠ class

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
sk .fs = mkfs(class1, ty, fieldvar), is_indexkey(sk), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0

Rule argument

[emptyarg]

Additional information

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