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Proof step 29 from proof ac-shift-02 (previous step)

fv = sk × val0, is_fskey(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) ⊦ sk .fs .class = class1, (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, (fv ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
is_fskey(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) ⊦ sk .fs .class = class1, (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, (sk × val0) ' + 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) .class = class])]]