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Proof step 70 from proof multi-isarrayref (previous step)

n→i(# acc) + i = ints .first, # refs = i→n(countrefs(i ' + ints .rest)), r ∈ refs, posints(ints), 0 ≤ i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ ints = [], is_arrayref(r, (addmultiarrays(refs, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, ints, st)), 0 ∈ ints .butlast

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 69:
ints = i0 + ints0, n→i(# acc) + i = i0, # refs = i→n(countrefs(i ' + ints0)), r ∈ refs, posints(ints), 0 ≤ i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ ints = [], is_arrayref(r, (addmultiarrays(refs, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, ints, st)), 0 ∈ ints .butlast

Rule argument

[speclemmaarg: ints ≠ [] ,i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0 ,[ints, i, ints0] → [ints, i0, ints0] ,T ,list-data ,intlista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ints ≠ [] ⊦ i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0])], [EXTRATERMS : (ints, i0, ints0)]]