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Proof step 18 from proof ac-out (previous step)

∀ class1, st, val. class1 = `java.lang.Object' .class ∨ addclass(class1, fis0, st[_out, val]) = (addclass(class1, fis0, st)[_out, val]) ⊦ class1 = `java.lang.Object' .class, addclass(class1, fv ' + fis0, st[_out, val]) = (addclass(class1, fv ' + fis0, st)[_out, val]), ¬ is_indexkey(fv .1) ∧ fv .1 .fs .class ≠ class1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 17:
fv = sk × val0, ∀ class1, st, val. class1 = `java.lang.Object' .class ∨ addclass(class1, fis0, st[_out, val]) = (addclass(class1, fis0, st)[_out, val]) ⊦ class1 = `java.lang.Object' .class, addclass(class1, fv ' + fis0, st[_out, val]) = (addclass(class1, fv ' + fis0, st)[_out, val]), ¬ is_indexkey(sk) ∧ sk .fs .class ≠ class1

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk, val0] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk, val0)]]