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Proof step 7 from proof ac-lookup-03 (previous step)

fs = mkfs(class, ty, fieldvar), ∀ class1, st. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done) ∨ mkfs(class1, void_type, `initstate' .field) ' ∈ fis0 ⊦ mkfs(class, void_type, `initstate' .field) = fs, (addclass(class, (fs ' × val) ' + fis0, st)[jvmref -- mkfs(class, void_type, `initstate' .field) ']) = initval(done), mkfs(class, void_type, `initstate' .field) ' ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ addclass(class1, (mkfs(class1, ty, fieldvar) ' × val) ' + fis, st) = (addclass(class1, fis, st)[jvmref -- mkfs(class1, ty, fieldvar) ', val])
Proof step 6:
∀ class1, st. (addclass(class1, fis0, st)[jvmref -- mkfs(class1, void_type, `initstate' .field) ']) = initval(done) ∨ mkfs(class1, void_type, `initstate' .field) ' ∈ fis0, void_type ≠ ty ∨ `initstate' .field ≠ fieldvar ⊦ (((void_type = ty ∧ `initstate' .field = fieldvar) ⊃ val; addclass(class, fis0, st)[jvmref -- mkfs(class, void_type, `initstate' .field) '])) = initval(done), mkfs(class, void_type, `initstate' .field) ' ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ ¬ ¬ (r = r0 ∧ sk = sk0)], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)])]]