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Proof step 25 from proof init-put-rkvs-01 (previous step)

∀ class. ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs ⊦ (∀ class. tdname∃(str, class) → initdone(class, st[rkvs])) ↔ init(str, st), _uninit ∈ rkvs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ initdone(class1, st) ↔ ¬ initerror(class1, st) ∧ ¬ initundone(class1, st)
Proof step 3:
⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st
Proof step 4:
⊦ rk ∈ st[rkvs] ↔ rk ∈ st ∨ rk ∈ rkvs
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 24:
∀ class. ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs ⊦ (∀ class. tdname∃(str, class) → ( ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs ∨ (st[rkvs][jvmref -- mkfs(class, void_type, `initstate' .field) ']) ≠ initval(error)) ∧ ( ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ rkvs ∨ (st[rkvs][jvmref -- mkfs(class, void_type, `initstate' .field) ']) ≠ initval(undone)) ∧ (jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st[rkvs] ∨ ¬ _uninit ∈ st)) ↔ init(str, st), _uninit ∈ rkvs

Rule argument

[emptyarg]

Additional information

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