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Proof step 36 from proof multi-length-first (previous step)

# ((n→i(# acc) + i) ' + ints0) ≠ 1, # refs + 1 = i→n(countrefs(i ' + ints0)), 0 ≤ i, posints(ints0), 0 ≤ n→i(# acc) + 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(r ' + refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) = intval(n→i(# acc) + i), 0 ∈ ((n→i(# acc) + i) ' + ints0) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
# refs + 1 = i→n(countrefs(i ' + ints0)), 0 ≤ i, posints(ints0), 0 < n→i(# acc) + 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(r ' + refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) = intval(n→i(# acc) + i), ints0 = [], 0 = n→i(# acc) + i, 0 ∈ ints0 .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ¬ i ∈ i0 ' + ints ↔ i ≠ i0 ∧ ¬ i ∈ ints], [CSIMPSEQ : ⊦ ints ≠ [] → (ints0 + ints) .butlast = ints0 + ints .butlast], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0])]]