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Proof step 55 from proof multi-lengthin (previous step)

# refs = i→n(countrefs(i ' + ints0)), r ∈ refs, posints(ints0), 0 < i0, i ≤ i0, 0 < i, ∀ st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ ints0 = [], 0 = i0, i = 0, 0 ∈ ints0 .butlast, r -- _length ∈ addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), ints0 .first, [], ty, ints0, st)) ∧ is_integervalue (addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), ints0 .first, [], ty, ints0, st)) [r -- _length ]) ∧ ¬ (addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), ints0 .first, [], ty, ints0, st)) [r -- _length ] ) .intval < 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 54:
ints0 = i1 + ints1, # refs = i→n(countrefs(i ' + ints0)), r ∈ refs, posints(ints0), 0 < i0, i ≤ i0, 0 < i, ∀ st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ ints0 = [], 0 = i0, i = 0, 0 ∈ ints0 .butlast, r -- _length ∈ addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), i1, [], ty, ints0, st)) ∧ is_integervalue (addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), i1, [], ty, ints0, st)) [r -- _length ]) ∧ ¬ (addmultiarrays (firstn(# refs - i→n(countrefs(ints0)), refs), i - 1, lastn(i→n(countrefs(ints0)), refs) .first ' + acc, ty, i0 ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), refs), i1, [], ty, ints0, st)) [r -- _length ] ) .intval < 0

Rule argument

[speclemmaarg: ints ≠ [] ,i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0 ,[ints, i, ints0] → [ints0, i1, ints1] ,T ,list-data ,intlista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ints ≠ [] ⊦ i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0])], [EXTRATERMS : (ints0, i1, ints1)]]