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Proof step 62 from proof multi-isarrayref (previous step)

# refs = i→n(countrefs(i ' + ints0)), 0 ≤ i, r ∈ refs, posints(ints0), 0 < n→i(# acc) + i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, is_arrayref (r, (addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)), 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 57:
¬ (i = 0 ∧ # ((n→i(# acc) + i) ' + ints0) > 1), # refs = i→n(countrefs(i ' + ints0)), 0 ≤ i, r ∈ refs, posints(ints0), 0 < n→i(# acc) + i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, is_arrayref (r, (addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)), 0 ∈ ints0 .butlast
Proof step 61:
i = 0 ∧ # ((n→i(# acc) + i) ' + ints0) > 1, # refs = i→n(countrefs(i ' + ints0)), 0 ≤ i, r ∈ refs, posints(ints0), 0 < n→i(# acc) + i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, is_arrayref (r, (addarray(refs .first, mktype_from_dims(ty, n→i(# ((n→i(# acc) + i) ' + ints0)) - 1), mkjavavalues(acc), st)[r -- _length]) .intval, addarray(refs .first, mktype_from_dims(ty, n→i(# ((n→i(# acc) + i) ' + ints0)) - 1), mkjavavalues(acc), st)), 0 ∈ ints0 .butlast

Rule argument

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

Additional information

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