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Proof step 52 from proof multi-isarrayref (previous step)

# refs = i→n(countrefs(i ' + i0 ' + ints1)), 0 < n→i(# acc) + i, 0 < i, r ∈ refs, posints(ints1), 0 ≤ i0, ∀ 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)))) ⊦ 0 = n→i(# acc) + i, i = 0, 0 ∈ (i0 ' + ints1) .butlast, is_arrayref (r, (addmultiarrays (firstn(# refs - i→n(countrefs(i0 ' + ints1)), refs), i - 1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) .intval, addmultiarrays (firstn(# refs - i→n(countrefs(i0 ' + ints1)), refs), i - 1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 51:
i = i1 + 1, # refs = i→n(countrefs(i ' + i0 ' + ints1)), 0 < n→i(# acc) + i, 0 < i, r ∈ refs, posints(ints1), 0 ≤ i0, ∀ 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)))) ⊦ 0 = n→i(# acc) + i, i = 0, 0 ∈ (i0 ' + ints1) .butlast, is_arrayref (r, (addmultiarrays (firstn(# refs - i→n(countrefs(i0 ' + ints1)), refs), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) .intval, addmultiarrays (firstn(# refs - i→n(countrefs(i0 ' + ints1)), refs), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)))

Rule argument

[speclemmaarg: ,i0 = i - j ↔ i = i0 + j ,[i, j, i0] → [i, 1, i1] ,T ,int-abs , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ i0 = i - j ↔ i = i0 + j])], [EXTRATERMS : (i, 1, i1)]]