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Proof step 45 from proof ac-init (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 41:
¬ is_indexkey(fv .1), ∀ class1, st. mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ∨ initdone(class1, addclass(class1, fis0, st)) ⊦ mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0, initdone(class1, addclass(class1, fv ' + fis0, st))
Proof step 44:
is_indexkey(fv .1), ∀ class1, st. mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ∨ initdone(class1, addclass(class1, fis0, st)) ⊦ mkfs(class1, void_type, `initstate' .field) ' ∈ fv ' + fis0, initdone(class1, addclass(class1, fis0, st))

Rule argument

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

Additional information

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