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Proof step 4 from proof init-endfmode-01 (conclusion)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ rk ≠ _uninit ∧ rk ≠ jvmref -- mkfs(class, void_type, `initstate' .field) ' → (initundone(class, st[rk, val]) ↔ initundone(class, st))
Proof step 2:
⊦ 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 3:
⊦ 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-05 , F , [val, rk, st, class] → [val, _endfinallymode, st, class1] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk × val ∈ st ↔ rk ∈ st ∧ st[rk] = val], [CSIMPSEQ : ⊦ (st[rk0, val][rk]) = ((rk = rk0 ⊃ val; st[rk]))], [CSIMPSEQ : ⊦ _endfinallymode = r -- sk ↔ ¬ ¬ ( r = jvmref ∧ sk = mkfs (`java.lang.Object' .class, void_type, `endfinallymode' .field) ')], [CSIMPSEQ : ⊦ fs ' = fs0 ' ↔ fs = fs0], [CSIMPSEQ : ⊦ mkfs(class, ty, fieldvar) = mkfs(class0, ty0, fieldvar0) ↔ class = class0 ∧ ty = ty0 ∧ fieldvar = fieldvar0], [CSIMPSEQ : ⊦ stringvar .field = stringvar0 .field ↔ stringvar = stringvar0], [CSIMPSEQ : ⊦ rk ∈ st[rk0, val] ↔ rk = rk0 ∨ rk ∈ st], [CSIMPSEQ : ⊦ mkfs(class1, ty, fieldvar) = mkfs(class2, ty0, fieldvar0) ↔ ¬ ¬ ( class1 = class2 ∧ ty = ty0 ∧ fieldvar = fieldvar0)], [CSIMPSEQ : ⊦ rk × val ∈ st ↔ ¬ ¬ (rk ∈ st ∧ st[rk] = val)], [CSIMPSEQ : ⊦ _endfinallymode ≠ _uninit])], [EXTRATERMS : (val, _endfinallymode, st, class1)]]