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Proof step 13 from proof union-init-01 (previous step)

⊦ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st0 ∧ _uninit ∈ st ∪ st0 ∨ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∪ st0 ∧ (st ∪ st0)[jvmref -- mkfs(class, void_type, `initstate' .field) '] = initval(undone) ↔ initundone(class, st0), jvmref ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ rk ∈ st → (st ∪ st0)[rk] = st0[rk]
Proof step 4:
⊦ rk ∈ st ∪ st0 ↔ rk ∈ st ∨ rk ∈ st0
Proof step 12:
¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ⊦ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st0 ∧ _uninit ∈ st ∪ st0 ∨ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∪ st0 ∧ st0[jvmref -- mkfs(class, void_type, `initstate' .field) '] = initval(undone) ↔ initundone(class, st0), jvmref ∈ st

Rule argument

[crewrite-arg: union-at-right-02 , F , [rk, st0, st] → [jvmref -- mkfs(class, void_type, `initstate' .field) ', st0, st] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ r -- sk ∈ st → r ∈ st])], [EXTRATERMS : (jvmref -- mkfs(class, void_type, `initstate' .field) ', st0, st)]]