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

⊦ r = jvmref, ¬ _uninit ∈ st ∧ (∀ rk. (rk = r -- sk ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- sk ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- sk ⊃ val; st[rk])) ≠ initval(error)) ↔ init(st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ init(st) ↔ ¬ _uninit ∈ st ∧ (∀ rk. rk ∈ st ∧ rk .ref = jvmref ∧ is_fskey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → st[rk] ≠ initval(undone) ∧ st[rk] ≠ initval(error))
Proof step 22:
⊦ r = jvmref, ¬ _uninit ∈ st ∧ (∀ rk. (rk = r -- sk ∨ rk ∈ st) ∧ rk .ref = jvmref ∧ ¬ is_indexkey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → ((rk = r -- sk ⊃ val; st[rk])) ≠ initval(undone) ∧ ((rk = r -- sk ⊃ val; st[rk])) ≠ initval(error)) ↔ ¬ _uninit ∈ st ∧ (∀ rk. rk ∈ st ∧ rk .ref = jvmref ∧ is_fskey(rk .key) ∧ rk .key .fs .type = void_type ∧ rk .key .fs .field = `initstate' .field → st[rk] ≠ initval(undone) ∧ st[rk] ≠ initval(error))

Rule argument

[crewrite-arg: init-def, F, [st] → [st]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st)]]