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Proof step 16 from proof ac-init-02 (previous step)

initerror(fs .class, addclass(fs .class, (fs ' × val) ' + fis0, st)), ∀ class1, st. initerror(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(fs .class, void_type, `initstate' .field) = fs, mkfs(fs .class, void_type, `initstate' .field) ' ∈ fis0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
fs = mkfs(class, ty, fieldvar), initerror(class, addclass(class, (fs ' × val) ' + fis0, st)), ∀ class1, st. initerror(class1, addclass(class1, fis0, st)) → mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class, void_type, `initstate' .field) = fs, mkfs(class, void_type, `initstate' .field) ' ∈ fis0

Rule argument

[speclemmaarg: , class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar) ,[fs, class, ty, fieldvar] → [fs, class, ty, fieldvar] ,T ,fieldspec , ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ class = fs .class ∧ ty = fs .type ∧ fieldvar = fs .field ↔ fs = mkfs(class, ty, fieldvar)])], [EXTRATERMS : (fs, class, ty, fieldvar)]]