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Proof step 15 from proof ac-mode-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, (sk × val) ' + 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) ∧ sk .fs .class ≠ class

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0])]]