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Proof step 10 from proof ac-shift-02 (previous step)

jvmref -- mkfs(class1, ty, fieldvar) ' ≠ jvmref -- mkfs(class1, 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][jvmref -- mkfs(class1, ty0, fieldvar0) ', val0]) = addclass(class1, ((mkfs(class1, ty0, fieldvar0) ' × val0) ' + fis0)[mkfs(class1, ty, fieldvar) ', val], st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 9:
∀ class1, st, ty, fieldvar, val. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val]) = addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st), ty ≠ ty0 ∨ fieldvar ≠ fieldvar0 ⊦ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val][jvmref -- mkfs(class1, ty0, fieldvar0) ', val0]) = (addclass(class1, fis0[mkfs(class1, ty, fieldvar) ', val], st)[jvmref -- mkfs(class1, ty0, fieldvar0) ', val0])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : sk0 ≠ sk ⊦ ((sk0 × val0) ' + fis)[sk, val] = (sk0 × val0) ' + fis[sk, val]], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0])]]