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Proof step 17 from proof multi-length-first (previous step)

lastn(i→n(countrefs(i0 ' + ints1)), r ' + refs) = r0 ' + refs1, # refs = i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), 1 + # refs - i→n(countrefs(i0 ' + ints1)) = m + 1, 0 ≤ i1, 0 ≤ n→i(# acc) + i1, 0 ≤ i0, posints(ints1), ∀ st, ty, r, acc, ints, i, refs0. # refs0 < # refs → ( true → ( # refs0 + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs0, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first))) ⊦ (addmultiarrays (r ' + firstn(m, refs), i1, r0 ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(r0 ' + refs1, i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) = intval(n→i(# acc) + i1 + 1), (~1) = i1, (~1) = n→i(# acc) + i1, 0 ∈ (i0 ' + ints1) .butlast, m = i→n(countrefs(i0 ' + ints1)) * i→n(i1) ∧ 0 ≤ n→i(# acc) + i1 + 1 ∧ posints(i0 ' + ints1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
lastn(i→n(countrefs(i0 ' + ints1)), r ' + refs) = r0 ' + refs1, # refs = i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), 1 + # refs - i→n(countrefs(i0 ' + ints1)) = m + 1, 0 ≤ i1, 0 ≤ n→i(# acc) + i1, 0 ≤ i0, posints(ints1), ∀ st, ty, r, acc, ints, i, refs0. # refs0 < # refs → ( true → ( # refs0 + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs0, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first))) ⊦ (addmultiarrays (r ' + firstn(m, refs), i1, r0 ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(r0 ' + refs1, i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) = intval(n→i(# acc) + i1 + 1), (~1) = i1, (~1) = n→i(# acc) + i1, m = i→n(countrefs(i0 ' + ints1)) * i→n(i1), 0 ∈ (i0 ' + ints1) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : i0 ≠ 0, i0 ≤ i ⊦ ((* i)) ≤ j → ((* i0)) ≤ j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ((* j)) ≤ i0 + ((* j0)) ↔ j - j0 ≤ i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n])]]