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Proof step 34 from proof ac-init-01 (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 33:
fv = sk × val, is_indexkey(sk), 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

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val)]]