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Proof step 8 from proof nouninit-addarrays (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

[speclemmaarg: ,# refs ≠ # refs0 → refs ≠ refs0 ,[refs0, refs] → [r ' + refs, newref_list(i→n(countrefs(ints)), st)] ,F ,list-data ,references ,length-neq ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # newref_list(n, st) = n], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (r ' + refs, newref_list(i→n(countrefs(ints)), st))]]