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Proof step 16 from proof multi-mode (previous step)

∀ 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(r, ty, st, refs, ints, ints0, i)[_mode]) = st[_mode], ints ≠ [] ∧ ¬ 0 < ints .first, ints ≠ [] ∧ ¬ ints .first < 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ # ints > 1 ∧ ints .first = 1 → addarraymultlist(r, ty, st, refs, ints, ints0, i) = 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)
Proof step 10:
¬ (# 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(r, ty, st, refs, ints, ints0, i)[_mode]) = st[_mode], ints ≠ [] ∧ ¬ 0 < ints .first, ints ≠ [] ∧ ¬ ints .first < 2
Proof step 15:
# 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

Rule argument

[crewrite-arg: addarraymultlist_more_1 , F , [i, ints0, ints, refs, st, ty, r] → [i, ints0, ints, refs, st, ty, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (i, ints0, ints, refs, st, ty, r)]]