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Proof step 12 from proof init-put-24 (conclusion)

⊦ ty ≠ void_type → (initdone(class1, st[jvmref -- mkfs(class, ty, fieldvar) ', val]) ↔ initdone(class1, st))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ initdone(class1, st) ↔ ¬ initerror(class1, st) ∧ ¬ initundone(class1, st)
Proof step 2:
sk ≠ mkfs(class1, void_type, `initstate' .field) ' ⊦ initerror(class1, st[jvmref -- sk, val]) ↔ initerror(class1, st)
Proof step 3:
⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st
Proof step 4:
⊦ initundone(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(undone) ∈ st ∨ ¬ jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ st
Proof step 5:
⊦ initdone(class1, st) ↔ ¬ ¬ (¬ initerror(class1, st) ∧ ¬ initundone(class1, st))
Proof step 6:
⊦ initundone(class1, st) ↔ ¬ ¬ ( (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(undone) ∈ st ∨ ¬ jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ st)
Proof step 7:
⊦ r -- sk ∈ st → r ∈ st
Proof step 11:
jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st, jvmref ∈ st ⊦ ty = void_type, (st[jvmref -- mkfs(class, ty, fieldvar) ', val][jvmref -- mkfs(class1, void_type, `initstate' .field) ']) ≠ initval(undone) ↔ st[jvmref -- mkfs(class1, void_type, `initstate' .field) '] ≠ initval(undone), st[jvmref -- mkfs(class1, void_type, `initstate' .field) '] = initval(error)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ jvmref -- sk = _uninit ↔ sk = mkfs (`java.lang.Object' .class, void_type, `uninit' .field) '], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : sk ≠ sk0 ⊦ r -- sk ∈ st[r -- sk0, val] ↔ r -- sk ∈ st], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0])]]