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Proof step 35 from proof ac-init-01 (previous step)

initundone(class1, addclass(class1, fv ' + fis0, st)), ∀ class1, st. initundone(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 31:
¬ is_indexkey(fv .1), initundone(class1, addclass(class1, fv ' + fis0, st)), ∀ class1, st. initundone(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0
Proof step 34:
is_indexkey(fv .1), initundone(class1, addclass(class1, fis0, st)), ∀ class1, st. initundone(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st, fis0, fv, class1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fis0, fv, class1)]]