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Proof step 33 from proof ac-shift-03 (previous step)

is_indexkey((sk × val0) .1), is_indexkey(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, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
is_indexkey(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, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]) = addclass(class, fis0[mkfs(class, ty, fieldvar) ', val], st)

Rule argument

[emptyarg]

Additional information

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