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Proof step 15 from proof ac-out (previous step)

sk .fs = mkfs(class, ty, fieldvar), ∀ 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, (sk × val0) ' + fis0, st[_out, val]) = (addclass(class1, (sk × val0) ' + fis0, st)[_out, val]), ¬ is_indexkey(sk) ∧ class ≠ class1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 11:
¬ is_indexkey((sk × val0) .1), sk .fs = mkfs(class, ty, fieldvar), ∀ 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, (sk × val0) ' + fis0, st[_out, val]) = (addclass(class1, (sk × val0) ' + fis0, st)[_out, val]), ¬ is_indexkey(sk) ∧ class ≠ class1
Proof step 14:
is_indexkey((sk × val0) .1), sk .fs = mkfs(class, ty, fieldvar), ∀ 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, fis0, st[_out, val]) = (addclass(class1, (sk × val0) ' + fis0, st)[_out, val]), ¬ is_indexkey(sk) ∧ class ≠ class1

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st[_out, val], fis0, sk × val0, class1] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[_out, val], fis0, sk × val0, class1)]]