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Proof step 58 from proof multi-at-other (previous step)

# refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ sk, st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( ¬ r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- sk]) = st[r -- sk])) ⊦ (addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- sk]) = st[r -- sk], ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ i = 0 ∧ # ints > 1 → addmultiarrays(refs, i, acc, ty, ints, st) = addarray(refs .first, mktype_from_dims(ty, n→i(# ints) - 1), mkjavavalues(acc), st)
Proof step 54:
¬ (i = 0 ∧ # (i0 ' + ints0) > 1), # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ sk, st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( ¬ r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- sk]) = st[r -- sk])) ⊦ (addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- sk]) = st[r -- sk], ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast
Proof step 57:
i = 0 ∧ # (i0 ' + ints0) > 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ sk, st, ty, acc, ints, i, r, refs0. # refs0 < # refs → ( true → ( ¬ r ∈ refs0 ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- sk]) = st[r -- sk])) ⊦ (addarray(refs .first, mktype_from_dims(ty, n→i(# (i0 ' + ints0)) - 1), mkjavavalues(acc), st)[r -- sk]) = st[r -- sk], ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast

Rule argument

[crewrite-arg: addmultiarrays-done , F , [st, ints, ty, acc, i, refs] → [st, i0 ' + ints0, ty, acc, i, refs] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0 ' + ints0, ty, acc, i, refs)]]