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

# refs = i→n(countrefs(i ' + ints0)), j0 < j, i ≤ i0, 0 ≤ i, posints(ints0), 0 ≤ i0, 0 ≤ j0, 0 < j, r -- j0 ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st), r ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st), ∀ j0. ¬ j0 < 0 ∧ ¬ j ≤ j0 → r -- j0 ' ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st) ⊦ r -- j0 ' ∈ st, r ∈ refs, 0 ∈ (i0 ' + ints0) .butlast

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, j0 ', 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 ↔ false)], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ (i ' + ints) .first = i])], [EXTRATERMS : (st, i0 ' + ints0, ty, acc, i, refs, j0 ', r)]]