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Proof step 12 from proof nouninit-addarrays (previous step)

newref_list(1 + # refs, st) = r ' + refs, 1 + # refs = i→n(countrefs(ints)), 0 ≤ i, posints(ints), class ∈ claset, 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 ∧ jvmref -- mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ' ∈ st, ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(undone) ⊦ claset = ∅, # claset = 0, jvmref = r, ints = [], jvmref ∈ refs, ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ jvmref -- mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ' ∈ addarrays(r ' + refs, ty, ints, i, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ ¬ r ∈ refs → (r -- sk ∈ addarrays(refs, ty, ints, i, st) ↔ r -- sk ∈ st)

Rule argument

[crewrite-arg: addarrays-refin , F , [st, i, ints, ty, refs, sk, r] → [st, i, ints, ty, r ' + refs, mkfs(`java.lang.Object' .class, void_type, `uninit' .field) ', jvmref] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ jvmref ∈ refs → newref_list(n, st) ≠ refs], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, i, ints, ty, r ' + refs, mkfs (`java.lang.Object' .class, void_type, `uninit' .field) ', jvmref)]]