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Proof step 30 from proof multi-isarrayref (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 29:
# refs1 = 1 + # refs + i→n(i1) * # refs + i→n(i1), lastn(1 + # refs, refs1) = r1 ' + refs, 1 + # refs = i→n(countrefs(i0 ' + ints1)), r ∈ refs1, posints(ints1), 0 ≤ i0, 0 ≤ n→i(# acc) + i1, 0 ≤ i1, # refs < # refs1, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # (r0 + refs1) → ( true → ( r ∈ refs0 ∧ n→i(# acc) + i = ints .first ∧ # refs0 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first → is_arrayref(r, (addmultiarrays(refs0, i, acc, ty, ints, st)[r -- _length]) .intval, addmultiarrays(refs0, i, acc, ty, ints, st)))) ⊦ refs1 = [], r = r0, (~1) = n→i(# acc) + i1, (~1) = i1, r = r1, i→n(i1) * # refs + i→n(i1) = # refs1 - 1 + # refs, r ∈ firstn(i→n(i1) * # refs + i→n(i1), refs1), r ∈ refs, 0 ∈ (i0 ' + ints1) .butlast, is_arrayref (r, (addmultiarrays(r1 ' + refs, i0, [], ty, i0 ' + ints1, st)[r -- _length]) .intval, addmultiarrays(r1 ' + refs, i0, [], ty, i0 ' + ints1, st))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ∈ r0 ' ↔ r = r0], [CSIMPSEQ : ⊦ r ∈ refs + refs0 ↔ ¬ ¬ (r ∈ refs ∨ r ∈ refs0)], [CSIMPSEQ : ⊦ ¬ m + n < m], [CSIMPSEQ : ⊦ m < n + 1 ↔ ¬ n < m], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPFORWARD : ⊦ m < n → n ≠ 0], [CSIMPFORWARD : ⊦ m < n ∧ n = n0 → m < n0], [CSIMPFORWARD : ⊦ r ' + refs = refs0 → r ∈ refs0], [CSIMPFORWARD : ⊦ m = n + 1 ∧ n < n0 → m ≤ n0], [CSIMPSEQ : ⊦ m < n → (n ≤ m ↔ false)], [CSIMPSEQ : ⊦ ¬ m < n ↔ n ≤ m], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → (r ∈ r0 ' + refs ↔ r ∈ refs)], [CSIMPSEQ : ⊦ m < n → m ≤ n], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≤ n ↔ m < n])]]