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Proof step 13 from proof multi-mode (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
∀ i, ints0, refs, st, ty, r, ints1. ints#(ints1) < ints#(1 + ints2) → (true → (addarraymultlist(r, ty, st, refs, ints1, ints0, i)[_mode]) = st[_mode]) ⊦ (addarraymultlist (refs .first, ty, st[r -- 0 ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, (1 + n→i(# ints2)) + i))][r -- _length, intval(ints0 .first)], refs .rest, ints2, ints0 .rest, i) [_mode ] ) = st[_mode], ints2 = []

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' + ints ≠ []], [CSIMPSEQ : ⊦ i + ints = i ' + ints])]]