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Proof step 36 from proof multi-lengthin (previous step)

lastn(i→n(countrefs(i1 ' + ints1)), r1 ' + refs2) = r0 ' + refs1, # refs2 = i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- _length]) = intval(i3), 0 ≤ i3, r ∈ addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st), i→n(countrefs(i1 ' + ints1)) ≤ 1 + # refs2, 0 ≤ i2, i2 < i0, 0 < i0, 0 ≤ i1, posints(ints1), r -- _length ∈ addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st), ∀ st, ty, acc, ints, i, r, refs0. # refs0 < # (r1 + refs2) → ( 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)) ⊦ r = r1 ∨ r ∈ firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), (~1) = i2, 0 = i0, 0 ∈ (i1 ' + ints1) .butlast, r ≠ r1 ∧ ¬ r ∈ refs2, r -- _length ∈ addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) ∧ is_integervalue (addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- _length ]) ∧ ¬ (addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- _length ] ) .intval < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
lastn(i→n(countrefs(i1 ' + ints1)), r1 ' + refs2) = r0 ' + refs1, # refs2 = i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), (addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)[r -- _length]) = intval(i3), 0 ≤ i3, r ∈ addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st), i→n(countrefs(i1 ' + ints1)) ≤ 1 + # refs2, 0 ≤ i2, i2 < i0, 0 < i0, 0 ≤ i1, posints(ints1), r -- _length ∈ addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st), r ∈ refs2, ∀ st, ty, acc, ints, i, r, refs0. # refs0 < # (r1 + refs2) → ( 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)) ⊦ r = r1, (~1) = i2, 0 = i0, r ∈ firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), 0 ∈ (i1 ' + ints1) .butlast, r -- _length ∈ addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) ∧ is_integervalue (addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- _length ]) ∧ ¬ (addmultiarrays (r1 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r0 ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r0 ' + refs1, i1, [], ty, i1 ' + ints1, st)) [r -- _length ] ) .intval < 0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n])]]