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Proof step 24 from proof multi-mode (previous step)

i0 = i1 + 1, 2 ≤ i0, 0 ≤ i0, 0 < i0, ∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#(i0 + ints2) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ ints2 = [], (addarraymultlist (refs .first, ty, addarraymultlist (r, ty, st[r -- i1 ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, (1 + n→i(# ints2)) + i))][r -- _length, intval(ints0 .first)], refs .rest, i1 ' + ints2, ints0, i), restn(i→n(countrefs2(i1 ' + ints2)), refs .rest), ints2, ints0 .rest, i) [_mode ] ) = st[_mode]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
⊦ ints ≠ [] ∧ 0 < i → countrefs2(i ' + ints) = i + i * countrefs2(ints)
Proof step 23:
(~1) ≤ i1, 0 < i1, ∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#((i1 + 1) + ints2) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ ints2 = [], (addarraymultlist (refs .first, ty, addarraymultlist (r, ty, st[r -- i1 ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, (1 + n→i(# ints2)) + i))][r -- _length, intval(ints0 .first)], refs .rest, i1 ' + ints2, ints0, i), restn(i→n(i1 * (countrefs2(ints2) + 1)), refs .rest), ints2, ints0 .rest, i) [_mode ] ) = st[_mode]

Rule argument

[emptyarg]

Additional information

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