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Proof step 15 from proof multi-field (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ (i ' + ints) .rest = ints], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m * n = n * m], [CSIMPSEQ : ⊦ m0 * m * n = (m0 * m) * n])]]