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Proof step 19 from proof ac-shift-03 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
is_fskey(sk), ∀ class, st, ty, fieldvar, val. (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st) ⊦ (addclass(sk .fs .class, (sk × val0) ' + fis0, st)[jvmref -- mkfs(sk .fs .class, ty, fieldvar) ', val]) = addclass(sk .fs .class, ((sk × val0) ' + fis0)[mkfs(sk .fs .class, 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 : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]