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Proof step 12 from proof ac-shift-02 (previous step)

sk = fs ', fs = mkfs(class1, ty0, fieldvar0), 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) ⊦ (addclass(class1, (sk × val0) ' + fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((sk × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], 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 11:
∀ 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, ty0, fieldvar0) ', val0][jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, ((mkfs(class1, ty0, fieldvar0) ' × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_fskey(fs ')], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1])]]