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Proof step 11 from proof ac-lookup-05 (previous step)

fs = mkfs(class, ty, fieldvar), is_indexkey(sk), ∀ sk0, class0, st0, r0. ¬ is_fskey(sk0) → (addclass(class0, fis0, st0)[r0 -- sk0]) = st0[r0 -- sk0] ⊦ (addclass(class, (fs ' × val) ' + fis0, st)[r -- sk]) = st[r -- sk]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 10:
is_indexkey(sk), ∀ sk0, class0, st0, r0. ¬ is_fskey(sk0) → (addclass(class0, fis0, st0)[r0 -- sk0]) = st0[r0 -- sk0] ⊦ (((r = jvmref ∧ sk = mkfs(class, ty, fieldvar) ') ⊃ val; addclass(class, fis0, st)[r -- sk])) = st[r -- sk]

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]