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Proof step 15 from proof multi-mode (previous step)

# ints > 1 ∧ ints .first = 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 = 1, (addarraymultlist (refs .first, ty, st[r -- (ints .first - 1) ', refval(refs .first)][r -- _type, typeval(mktype_from_dims(ty, i + n→i(# ints)))][r -- _length, intval(ints0 .first)], refs .rest, ints .rest, ints0 .rest, i) [_mode ] ) = st[_mode], ints ≠ [] ∧ ¬ 0 < ints .first, ints ≠ [] ∧ ¬ ints .first < 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
ints .first = 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, ints .rest, ints0 .rest, i) [_mode ] ) = st[_mode], # ints = 1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ 0 < j → (j < 2 ↔ j = 1)], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ i = j → i - j = 0])]]