Proof step 13 from proof init-put-notnull (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 2:

  ⊦ r ≠ jvmref → (initdone(class1, st[r -- sk, val]) ↔ initdone(class1, st))

• Proof step 3:

  ⊦ initdone(class1, st) ↔ ¬ initerror(class1, st) ∧ ¬ initundone(class1, st)

• Proof step 4:

  ⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st

• Proof step 5:

  ⊦ 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 12:

  ⊦ r = jvmref, (∀ class. tdname∃(str, class) → (¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(error)) ∧ (¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(undone)) ∧ (jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ ¬ _uninit ∈ st)) ↔ init(str, st)

Rule argument

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)])]]