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Proof step 29 from proof multi-length-first (previous step)

ints0 = i0 + ints1, # refs + 1 = i→n(countrefs(i ' + ints0)), posints(ints0), 0 < n→i(# acc) + i, 0 < i, ∀ 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))) ⊦ ints0 = [], 0 = n→i(# acc) + i, i = 0, (addmultiarrays (firstn(1 + # refs - i→n(countrefs(ints0)), r ' + refs), i - 1, lastn(i→n(countrefs(ints0)), r ' + refs) .first ' + acc, ty, (n→i(# acc) + i) ' + ints0, addmultiarrays(lastn(i→n(countrefs(ints0)), r ' + refs), i0, [], ty, ints0, st)) [r -- _length ] ) = intval(n→i(# acc) + i), 0 ∈ ints0 .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
# 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), i - 1, 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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' + ints ≠ []], [CSIMPSEQ : ⊦ i + ints = i ' + ints])]]