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Proof step 23 from proof init-put-rkvs-01 (previous step)

∀ 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)) ↔ (∀ class. tdname∃(str, class) → initdone(class, st)), _uninit ∈ rkvs

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ initdone(class1, st) ↔ ¬ ¬ (¬ initerror(class1, st) ∧ ¬ initundone(class1, st))
Proof step 8:
⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st
Proof step 9:
⊦ 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 22:
∀ 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)) ↔ (∀ 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)), _uninit ∈ rkvs

Rule argument

[emptyarg]

Additional information

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