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Proof step 25 from proof multi-field (previous step)

i = i2 + 1, # refs = i→n(countrefs(i ' + i1 ' + ints1)), 0 < i0, i ≤ i0, 0 < i, posints(ints1), 0 ≤ i1, ∀ r, st, ty, acc, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs '])) ⊦ 0 = i0, i = 0, fs ' = _length, fs ' = _type, (addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, lastn(i→n(countrefs(i1 ' + ints1)), refs) .first ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i1 ' + ints1)), refs), i1, [], ty, i1 ' + ints1, st)) [r -- fs ' ] ) = st[r -- fs '], 0 ∈ (i1 ' + ints1) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ 0 ≤ i → countrefs((i + 1) ' + i0 ' + ints) = 1 + (i + 1) * countrefs(i0 ' + ints)
Proof step 5:
⊦ 0 ≤ i2 → i→n(1 + (i2 + 1) * countrefs(ints)) = 1 + i→n(i2 + 1) * i→n(countrefs(ints))
Proof step 24:
# refs = 1 + i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, ∀ r, st, ty, acc, ints, i, fs, refs0. # refs0 < # refs → ( true → ( fs ' ≠ _type ∧ fs ' ≠ _length ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- fs ']) = st[r -- fs '])) ⊦ fs ' = _length, fs ' = _type, (addmultiarrays (firstn(# refs - i→n(countrefs(i1 ' + ints1)), refs), i2, lastn(i→n(countrefs(i1 ' + ints1)), refs) .first ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(lastn(i→n(countrefs(i1 ' + ints1)), refs), i1, [], ty, i1 ' + ints1, st)) [r -- fs ' ] ) = st[r -- fs '], 0 = i0, (~1) = i2, 0 ∈ (i1 ' + ints1) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * (n + 1) = m * n + m], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + 1) = i→n(i) + 1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (~1) < i ↔ 0 ≤ i], [CSIMPSEQ : ⊦ ((* j)) < i0 + ((* j0)) ↔ j - j0 < i0], [CSIMPSEQ : ⊦ i + 1 ≤ j ↔ i < j], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ ((* j)) = i0 + ((* j0)) ↔ j - j0 = i0])]]