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Proof step 22 from proof ac-lookup (previous step)

¬ is_indexkey(fv .1), mkfs(class1, ty, fieldvar) ' ∈ fv ' + fis0, ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class1, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv ' + fis0)[mkfs(class1, ty, fieldvar) ']

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
mkfs(class1, ty, fieldvar) ' ∈ fv ' + fis0, is_fskey(fv .1), ∀ class1, ty, fieldvar, st. mkfs(class1, ty, fieldvar) ' ∈ fis0 → (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = fis0[mkfs(class1, ty, fieldvar) '] ⊦ (addclass(class1, fv ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ']) = (fv ' + fis0)[mkfs(class1, ty, fieldvar) ']

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)])]]