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Proof step 35 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), 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ lastn(n, refs) = refs0 ∧ ¬ r ∈ refs0 ∧ r ∈ refs ∧ n ≤ # refs ∧ m = # refs - n → r ∈ firstn(m, refs)
Proof step 34:
¬ ( lastn(i→n(countrefs(i1 ' + ints1)), r1 ' + refs2) = r0 ' + refs1 ∧ ¬ r ∈ r0 ' + refs1 ∧ r ∈ r1 ' + refs2 ∧ i→n(countrefs(i1 ' + ints1)) ≤ # (r1 ' + refs2) ∧ i→n(countrefs(i1 ' + ints1)) * i→n(i2) = # (r1 ' + refs2) - i→n(countrefs(i1 ' + ints1))), 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

[speclemmaarg: , lastn(n, refs) = refs0 ∧ ¬ r ∈ refs0 ∧ r ∈ refs ∧ n ≤ # refs ∧ m = # refs - n → r ∈ firstn(m, refs) ,[n, refs, refs0, r, m] → [i→n(countrefs(i1 ' + ints1)), r1 ' + refs2, r0 ' + refs1, r, i→n(countrefs(i1 ' + ints1)) * i→n(i2)] ,F ,list-del ,references ,lastn-firstn-in-01 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ ¬ r ∈ r0 ' + refs ↔ r ≠ r0 ∧ ¬ r ∈ refs], [CSIMPSEQ : n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ m = m + n ↔ n = 0], [CSIMPSEQ : ⊦ m * n = n * m])], [EXTRATERMS : (i→n(countrefs(i1 ' + ints1)), r1 ' + refs2, r0 ' + refs1, r, i→n(countrefs(i1 ' + ints1)) * i→n(i2))]]