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Proof step 29 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ # ints > 1 ∧ ints .first ≥ 1 + 1 → addarraymultlist(r, ty, st, refs, ints, ints0, i) = addarraymultlist (refs .first, ty, addarraymultlist (r, 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 .first - 1) + ints .rest, ints0, i), restn(i→n(countrefs2((ints .first - 1) + ints .rest)), refs .rest), ints .rest, ints0 .rest, i)
Proof step 17:
¬ (# ints > 1 ∧ ints .first ≥ 1 + 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
Proof step 28:
# ints > 1 ∧ ints .first ≥ 1 + 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, addarraymultlist (r, 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 .first - 1) + ints .rest, ints0, i), restn(i→n(countrefs2((ints .first - 1) + ints .rest)), refs .rest), ints .rest, ints0 .rest, i) [_mode ] ) = st[_mode], ints ≠ [] ∧ ¬ 0 < ints .first

Rule argument

[crewrite-arg: addarraymultlist_more_2 , 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)]]