| # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ st, ty, acc, sk, 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 → (r -- sk ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- sk ∈ st))) ⊦ r -- sk ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st) ↔ r -- sk ∈ st, ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast |
⊦ 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)
¬ (i = 0 ∧ # (i0 ' + ints0) > 1), # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ st, ty, acc, sk, 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 → (r -- sk ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ↔ r -- sk ∈ st))) ⊦ r -- sk ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st) ↔ r -- sk ∈ st, ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast
i = 0 ∧ # (i0 ' + ints0) > 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, posints(ints0), 0 < i0, ∀ st, ty, acc, sk, 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 → (r -- sk ∈ 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, ints0 = [], 0 = i0, r ∈ refs, 0 ∈ ints0 .butlast
[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, i0 ' + ints0, ty, acc, i, refs)]]