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Proof step 27 from proof multi-length-first (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ i → countrefs((i + 1) ' + i0 ' + ints) = 1 + (i + 1) * countrefs(i0 ' + ints)
Proof step 5:
⊦ 0 ≤ i2 → i→n(1 + (i2 + 1) * countrefs(ints)) = 1 + i→n(i2 + 1) * i→n(countrefs(ints))
Proof step 26:
# refs = i→n(countrefs(i0 ' + ints1)) * i→n(i1) + i→n(countrefs(i0 ' + ints1)), posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, ∀ 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 (firstn(1 + # refs - i→n(countrefs(i0 ' + ints1)), r ' + refs), i1, lastn(i→n(countrefs(i0 ' + ints1)), r ' + refs) .first ' + acc, ty, (n→i(# acc) + i1 + 1) ' + i0 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i0 ' + ints1)), r ' + refs), i0, [], ty, i0 ' + ints1, st)) [r -- _length ] ) = intval(n→i(# acc) + i1 + 1), (~1) = n→i(# acc) + i1, (~1) = i1, 0 ∈ (i0 ' + ints1) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * (n + 1) = m * n + m], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ((* j)) = i0 + ((* j0)) ↔ j - j0 = i0], [CSIMPSEQ : ⊦ i + j = j + i])]]