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Proof step 11 from proof ac-mode (previous step)

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

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 8:
¬ is_indexkey((sk × val) .1), 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
Proof step 10:
is_indexkey((sk × val) .1), 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, fis0, st)[_mode]) = st[_mode], ¬ is_indexkey(sk) ∧ class ≠ class1

Rule argument

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

Additional information

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