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Proof step 18 from proof multi-refin (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
# refs2 = i→n(countrefs(i1 ' + ints1)) * i→n(i2) + i→n(countrefs(i1 ' + ints1)), lastn(i→n(countrefs(i1 ' + ints1)), r0 ' + refs2) = r ' + refs1, rk ∈ st, posints(ints1), 0 ≤ i1, 0 < i0, i2 < i0, 0 ≤ i2, i→n(countrefs(i1 ' + ints1)) ≤ 1 + # refs2, ∀ ty, acc, ints, i, st, rk, refs0. # refs0 < # (r0 + refs2) → ( true → ( rk ∈ st ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → rk ∈ addmultiarrays(refs0, i, acc, ty, ints, st))) ⊦ 0 = i0, (~1) = i2, rk ∈ addmultiarrays (r0 ' + firstn(i→n(countrefs(i1 ' + ints1)) * i→n(i2), refs2), i2, r ' + acc, ty, i0 ' + i1 ' + ints1, addmultiarrays(r ' + refs1, i1, [], ty, i1 ' + ints1, st)), 0 ∈ (i1 ' + ints1) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPSEQ : ⊦ r ' + refs ≠ []], [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 = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ r + refs = r ' + refs])]]