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Proof step 11 from proof ac-in-10 (previous step)

¬ (is_fskey((sk1 × val) .1) ∧ (sk1 × val) .1 .fs .class ≠ class), r -- sk ∈ addclass(class, (sk1 × val) ' + fis0, st), is_fskey(sk1), r ∈ addclass(class, (sk1 × val) ' + fis0, st), ∀ sk0, class0, r0, st0. ¬ sk0 ∈ fis0 ∧ sk0 ≠ mkfs(class0, void_type, `initstate' .field) ' → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ sk = mkfs(class, void_type, `initstate' .field) ', sk = sk1, sk ∈ fis0, r -- sk ∈ st

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
is_fskey(sk1), r -- sk ∈ addclass(sk1 .fs .class, (sk1 × val) ' + fis0, st), r ∈ addclass(sk1 .fs .class, (sk1 × val) ' + fis0, st), ∀ sk0, class0, r0, st0. ¬ sk0 ∈ fis0 ∧ sk0 ≠ mkfs(class0, void_type, `initstate' .field) ' → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ sk = sk1, sk = mkfs(sk1 .fs .class, void_type, `initstate' .field) ', r -- sk ∈ st, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]