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Proof step 7 from proof ac-in-11 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 6:
is_indexkey(sk), r -- sk ∈ (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]), r ∈ (addclass(class, fis0, st)[jvmref -- mkfs(class, ty, fieldvar) ', val]), ∀ sk0, r0, class0, st0. ¬ is_fskey(sk0) → (r0 -- sk0 ∈ addclass(class0, fis0, st0) → r0 -- sk0 ∈ st0) ⊦ r -- sk ∈ st

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]