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Proof step 31 from proof multi-length-first (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# 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), ints0 .first, [], ty, ints0, st)) [r -- _length ] ) = intval(n→i(# acc) + i), 0 ∈ ints0 .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ r + refs = r ' + refs], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (i ' + ints) .rest = ints], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0])]]