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Proof step 12 from proof ac-mode (previous step)

∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ class1 = `java.lang.Object' .class, (addclass(class1, (sk × val) ' + fis0, st)[_mode]) = st[_mode], ¬ is_indexkey(sk) ∧ sk .fs .class ≠ class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
sk .fs = mkfs(class, ty, fieldvar), ∀ class1, st. class1 = `java.lang.Object' .class ∨ (addclass(class1, fis0, st)[_mode]) = st[_mode] ⊦ class1 = `java.lang.Object' .class, (addclass(class1, (sk × val) ' + fis0, st)[_mode]) = st[_mode], ¬ is_indexkey(sk) ∧ class ≠ class1

Rule argument

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