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Proof step 4 from proof multi-isarrayref-01 (previous step)

# refs = i→n(countrefs(i ' + ints0)), j < i0, 0 < i, 0 ≤ j, 0 ≤ i0, posints(ints0), 0 ≤ i, i ≤ i0, j < i, 0 < i0, r -- j ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st), r ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st), ∀ j. ¬ j < 0 ∧ ¬ i ≤ j → r -- j ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st) ⊦ 0 ∈ (i0 ' + ints0) .butlast, r ∈ refs, r -- j ' ∈ st

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ r ∈ refs ∧ # refs = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (r -- sk ∈ addmultiarrays(refs, i, acc, ty, ints, st) ↔ r -- sk ∈ st)

Rule argument

[crewrite-arg: multi-in-other , F , [st, ints, ty, acc, i, refs, sk, r] → [st, i0 ' + ints0, ty, acc, i, refs, j ', r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (i ' + ints) .rest = ints], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i < j → ¬ j < i], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)])], [EXTRATERMS : (st, i0 ' + ints0, ty, acc, i, refs, j ', r)]]