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Proof step 37 from proof addarrays-at-other (previous step)

# (i0 ' + getdims(ints0)) > 1 ∧ (i0 ' + getdims(ints0)) .first > 0, n→i(# refs) = countrefs(i0 ' + ints0), 0 ≤ i0, posints(ints0), 0 ≤ i, 0 < i0 ⊦ (addmultiarrays(refs, i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st)[r -- sk]) = st[r -- sk], r ∈ refs, # refs = i→n(1 + (i0 ' + getdims(ints0)) .first * countrefs((i0 ' + getdims(ints0)) .rest)) ∧ ¬ 0 ∈ (i0 ' + getdims(ints0)) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 21:
⊦ countrefs(getdims(ints)) = countrefs(ints)
Proof step 22:
⊦ 0 ≤ i → i→n(1 + countrefs(ints) * i) = 1 + i→n(countrefs(ints)) * i→n(i)
Proof step 36:
n→i(# refs) = countrefs(i0 ' + ints0), 0 ≤ i0, posints(ints0), 0 ≤ i, 0 < i0 ⊦ (addmultiarrays(refs, i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st)[r -- sk]) = st[r -- sk], ints0 = [], r ∈ refs, # refs = 1 + i→n(countrefs(ints0)) * i→n(i0) ∧ ¬ 0 ∈ (i0 ' + getdims(ints0)) .butlast

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i * j = j * i], [CSIMPSEQ : ⊦ i * j * j0 = (i * j) * j0], [CSIMPSEQ : ⊦ (i ' + ints) .rest = ints], [CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [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])]]