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Proof step 50 from proof multi-isarrayref (previous step)

# refs = 1 + i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), r ∈ refs, posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, ∀ 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)))) ⊦ (~1) = n→i(# acc) + i1, (~1) = i1, 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) + i1 + 1) ' + 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) + i1 + 1) ' + 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 6:
⊦ countrefs(ints) ≠ 0
Proof step 49:
# refs = n + i→n(countrefs(i0 ' + ints1)) ∧ i→n(countrefs(i0 ' + ints1)) ≤ # refs, # refs = 1 + i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), r ∈ refs, posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, ∀ 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)))) ⊦ (~1) = n→i(# acc) + i1, (~1) = i1, 0 ∈ (i0 ' + ints1) .butlast, is_arrayref (r, (addmultiarrays (firstn(n, refs), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) .intval, addmultiarrays (firstn(n, refs), i1, lastn(i→n(countrefs(i0 ' + ints1)), refs) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), refs), i0, [], ty, i0 ' + ints1, st)))

Rule argument

[speclemmaarg: n ≤ m ,n0 = m - n ↔ m = n0 + n ,[m, n, n0] → [# refs, i→n(countrefs(i0 ' + ints1)), n] ,T ,nat , ,elim-sub ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ m ≤ n ↔ n < m], [CSIMPFORWARD : ⊦ m < n ∧ m = n0 → n0 < n], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPSEQ : ⊦ i→n(i) = 0 ↔ i = 0], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPELIM : n ≤ m ⊦ n0 = m - n ↔ m = n0 + n])], [EXTRATERMS : (# refs, i→n(countrefs(i0 ' + ints1)), n)]]