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Proof step 9 from proof init-endfmode (conclusion)

⊦ initdone(class1, st[_endfinallymode, val]) ↔ initdone(class1, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∧ rk ≠ _uninit → (initdone(class, st[rk, val]) ↔ initdone(class, st))
Proof step 2:
⊦ initdone(class1, st) ↔ ¬ initerror(class1, st) ∧ ¬ initundone(class1, st)
Proof step 3:
⊦ initerror(class1, st[_endfinallymode, val]) ↔ initerror(class1, st)
Proof step 4:
⊦ initerror(class1, st) ↔ (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(error) ∈ st
Proof step 5:
⊦ initundone(class1, st[_endfinallymode, val]) ↔ 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:
⊦ initdone(class1, st) ↔ ¬ ¬ (¬ initerror(class1, st) ∧ ¬ initundone(class1, st))
Proof step 8:
⊦ initundone(class1, st) ↔ ¬ ¬ ( (jvmref -- mkfs(class1, void_type, `initstate' .field) ') × initval(undone) ∈ st ∨ ¬ jvmref -- mkfs(class1, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ st)

Rule argument

[crewrite-arg: init-put-04 , F , [val, rk, st, class] → [val, _endfinallymode, st, class1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val])], [EXTRATERMS : (val, _endfinallymode, st, class1)]]