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Proof step 17 from proof ac-shift-02 (previous step)

is_indexkey((sk × val0) .1), sk .fs = mkfs(class, ty0, fieldvar0), ∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((sk × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st), ¬ is_indexkey(sk) ∧ class ≠ class1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
⊦ is_indexkey(fv .1) → addclass(class, fv ' + fis, st) = addclass(class, fis, st)
Proof step 16:
sk .fs = mkfs(class, ty0, fieldvar0), is_indexkey(sk), ∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st) ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : sk0 ≠ sk ⊦ ((sk0 × val0) ' + fis)[sk, val] = (sk0 × val0) ' + fis[sk, val]], [CSIMPSEQ : ⊦ fs ' .fs = fs], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ (sk × val) .1 = sk], [CSIMPSEQ : ⊦ ¬ is_indexkey(fs ')])]]