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Proof step 68 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)))) ⊦ 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 ∈ ((n→i(# acc) + i) ' + ints0) .butlast

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ # ints = 1 → addmultiarrays(refs, i, acc, ty, ints, st) = addarray(refs .first, ty, ints .first, st)
Proof step 63:
# ((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)))) ⊦ 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 ∈ ((n→i(# acc) + i) ' + ints0) .butlast
Proof step 67:
# ((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)))) ⊦ is_arrayref (r, (addarray(refs .first, ty, ((n→i(# acc) + i) ' + ints0) .first, st)[r -- _length]) .intval, addarray(refs .first, ty, ((n→i(# acc) + i) ' + ints0) .first, st)), 0 ∈ ((n→i(# acc) + i) ' + ints0) .butlast

Rule argument

[crewrite-arg: addmultiarrays-base , 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)]]