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Proof step 15 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, 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

Proof step 6:
⊦ ¬ r ∈ refs ∧ # refs = i→n(countrefs(ints)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) → (addarrays(refs, ty, ints, i, st)[r -- sk]) = st[r -- sk]
Proof step 9:
¬ (¬ jvmref ∈ r ' + refs ∧ # (r ' + refs) = i→n(countrefs(ints)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints)), 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, jvmref ∈ refs, ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ addarrays(r ' + refs, ty, ints, i, st)
Proof step 14:
¬ jvmref ∈ r ' + refs ∧ # (r ' + refs) = i→n(countrefs(ints)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints), 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 ∨ st[jvmref -- mkfs(class, void_type, `initstate' .field) '] ≠ initval(undone) ⊦ claset = ∅, ints = [], # claset = 0, jvmref = r, jvmref ∈ refs, ¬ jvmref -- mkfs(class, void_type, `initstate' .field) ' ∈ st ∧ _uninit ∈ addarrays(r ' + refs, ty, ints, i, st)

Rule argument

[crewrite-arg: addarrays-at-other , F , [sk, r, st, i, ints, ty, refs] → [mkfs(class, void_type, `initstate' .field) ', jvmref, st, i, ints, ty, r ' + refs] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (mkfs(class, void_type, `initstate' .field) ', jvmref, st, i, ints, ty, r ' + refs)]]