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Proof step 13 from proof ac-mode-01 (previous step)

sk .fs = mkfs(class1, ty, fieldvar), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, (sk × val) ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ class1 ≠ class

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 10:
¬ is_indexkey((sk × val) .1), sk .fs = mkfs(class1, ty, fieldvar), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, (sk × val) ' + fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ class1 ≠ class
Proof step 12:
is_indexkey((sk × val) .1), sk .fs = mkfs(class1, ty, fieldvar), ∀ class0, st0. (addclass(class0, fis0, st0)[_mode]) = st0[_mode] ⊦ (addclass(class, fis0, st)[_mode]) = st[_mode], mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' = sk, mkfs(`java.lang.Object' .class, void_type, `mode' .field) ' ∈ fis0, ¬ is_indexkey(sk) ∧ class1 ≠ class

Rule argument

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

Additional information

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