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Proof step 10 from proof ac-in (previous step)

sk = fs ', fs = mkfs(class, ty0, fieldvar0), is_fskey(sk), ∀ class1, ty, fieldvar, st. jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class1, fis0, st) ↔ ty = void_type ∧ fieldvar = `initstate' .field ∨ mkfs(class1, ty, fieldvar) ' ∈ fis0 ∨ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st ⊦ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class1, (sk × val) ' + fis0, st) ↔ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st ∨ mkfs(class1, ty, fieldvar) ' = sk ∨ mkfs(class1, ty, fieldvar) ' ∈ fis0 ∨ ty = void_type ∧ fieldvar = `initstate' .field, class ≠ class1 ∧ ¬ is_indexkey(sk)

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 9:
∀ class1, ty, fieldvar, st. jvmref -- mkfs(class1, ty, fieldvar) ' ∈ addclass(class1, fis0, st) ↔ ty = void_type ∧ fieldvar = `initstate' .field ∨ mkfs(class1, ty, fieldvar) ' ∈ fis0 ∨ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st ⊦ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ (addclass(class1, fis0, st)[jvmref -- mkfs(class1, ty0, fieldvar0) ', val]) ↔ jvmref -- mkfs(class1, ty, fieldvar) ' ∈ st ∨ ty = ty0 ∧ fieldvar = fieldvar0 ∨ mkfs(class1, ty, fieldvar) ' ∈ fis0 ∨ ty = void_type ∧ fieldvar = `initstate' .field

Rule argument

[emptyarg]

Additional information

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