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Proof step 18 from proof addclass-switch-01 (previous step)

sk0 .fs = mkfs(class0, ty, fieldvar), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ r = jvmref, addclass(class, (sk0 × val0) ' + fis0, st[r -- sk, val]) = (addclass(class, (sk0 × val0) ' + fis0, st)[r -- sk, val]), ¬ is_indexkey(sk0) ∧ class0 ≠ class

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 14:
¬ is_indexkey((sk0 × val0) .1), sk0 .fs = mkfs(class0, ty, fieldvar), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ r = jvmref, addclass(class, (sk0 × val0) ' + fis0, st[r -- sk, val]) = (addclass(class, (sk0 × val0) ' + fis0, st)[r -- sk, val]), ¬ is_indexkey(sk0) ∧ class0 ≠ class
Proof step 17:
is_indexkey((sk0 × val0) .1), sk0 .fs = mkfs(class0, ty, fieldvar), ∀ r, class, st, sk, val. r = jvmref ∨ addclass(class, fis0, st[r -- sk, val]) = (addclass(class, fis0, st)[r -- sk, val]) ⊦ r = jvmref, addclass(class, fis0, st[r -- sk, val]) = (addclass(class, (sk0 × val0) ' + fis0, st)[r -- sk, val]), ¬ is_indexkey(sk0) ∧ class0 ≠ class

Rule argument

[crewrite-arg: ac-no2 , F , [st, fis, fv, class] → [st[r -- sk, val], fis0, sk0 × val0, class] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r -- sk, val], fis0, sk0 × val0, class)]]