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Proof step 66 from proof multi-lengthin (previous step)

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

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 61:
# (i0 ' + ints0) ≠ 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, r ∈ refs, posints(ints0), 0 ≤ i0, ∀ 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 → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ 0 ∈ (i0 ' + ints0) .butlast, r -- _length ∈ addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st) ∧ is_integervalue(addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- _length]) ∧ ¬ (addmultiarrays(refs, i, acc, ty, i0 ' + ints0, st)[r -- _length]) .intval < 0
Proof step 65:
# (i0 ' + ints0) = 1, # refs = i→n(countrefs(i ' + ints0)), i ≤ i0, 0 ≤ i, r ∈ refs, posints(ints0), 0 ≤ i0, ∀ 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 → r -- _length ∈ addmultiarrays(refs0, i, acc, ty, ints, st) ∧ is_integervalue(addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) ∧ 0 ≤ (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval)) ⊦ 0 ∈ (i0 ' + ints0) .butlast, r -- _length ∈ addarray(refs .first, ty, (i0 ' + ints0) .first, st) ∧ is_integervalue(addarray(refs .first, ty, (i0 ' + ints0) .first, st)[r -- _length]) ∧ ¬ (addarray(refs .first, ty, (i0 ' + ints0) .first, st)[r -- _length]) .intval < 0

Rule argument

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