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Proof step 57 from proof multi-isarrayref (previous step)

¬ (i = 0 ∧ # ((n→i(# acc) + i) ' + ints0) > 1), # refs = i→n(countrefs(i ' + ints0)), 0 ≤ i, r ∈ refs, posints(ints0), 0 < n→i(# acc) + i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( 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)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, is_arrayref (r, (addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)), 0 ∈ ints0 .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 56:
# refs = i→n(countrefs(i ' + ints0)), r ∈ refs, posints(ints0), 0 < n→i(# acc) + i, 0 < i, ∀ st, ty, ints, i, acc, r, refs0. # refs0 < # refs → ( 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)))) ⊦ ints0 = [], 0 = n→i(# acc) + i, i = 0, is_arrayref (r, (addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)[r -- _length]) .intval, addmultiarrays(refs, i, acc, ty, (n→i(# acc) + i) ' + ints0, st)), 0 ∈ ints0 .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ 1 = m + 1 ↔ m = 0], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0])]]