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Proof step 14 from proof ac-shift-02 (previous step)

¬ is_indexkey((sk × val0) .1), sk .fs = mkfs(class, ty0, fieldvar0), ∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, (sk × val0) ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((sk × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st), ¬ is_indexkey(sk) ∧ class ≠ class1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
sk .fs = mkfs(class1, ty0, fieldvar0), is_fskey(sk), ∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, (sk × val0) ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((sk × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

Rule argument

[emptyarg]

Additional information

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