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Proof step 15 from proof addarrays-length (previous step)

1 + n→i(# refs) = countrefs(i0 ' + ints0), getdims(i0 ' + ints0) = i1 ' + ints, is_newref_list(r ' + refs, st), 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ (addmultiarrays(r ' + refs, i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), i1 ' + ints, st)[r -- _length]) = intval(i0), # refs + 1 = i→n(countrefs(i0 ' + ints)) ∧ ¬ 0 ∈ (i1 ' + ints) .butlast ∧ ¬ i1 < i0 ∧ ¬ i0 < i1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < j → getdims(j ' + ints) = j ' + getdims(ints)
Proof step 9:
⊦ j ≤ 0 → getdims(j ' + ints) = 0 '
Proof step 10:
⊦ countrefs(0 ' + ints) = 1
Proof step 11:
⊦ j ≤ 0 → countdims(j ' + ints, i) = i + n→i(# ints)
Proof step 12:
⊦ 0 < j → countdims(j ' + ints, i) = countdims(ints, i)
Proof step 13:
⊦ 0 < i → ¬ 0 ∈ (i ' + getdims(ints)) .butlast
Proof step 14:
⊦ countrefs(i ' + getdims(ints)) = countrefs(i ' + ints)

Rule argument

[crewrite-arg: getdims-rec, F, [ints, j] → [ints0, i0]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ 0 ≤ i → i→n(i + n→i(n)) = i→n(i) + n], [CSIMPSEQ : ⊦ i ≤ i], [CSIMPSEQ : ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 < i → 0 < j], [CSIMPFORWARD : ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j], [CSIMPFORWARD : ⊦ i < i0 ∧ i0 < i1 → i < i1], [CSIMPSEQ : ⊦ i ' + ints = i0 ' + ints0 ↔ i = i0 ∧ ints = ints0], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' = i0 ' + ints ↔ i = i0 ∧ ints = []], [CSIMPSEQ : ⊦ ((* j)) = i0 + ((* j0)) ↔ j - j0 = i0], [CSIMPSEQ : ⊦ n→i(n) = 0 ↔ n = 0], [CSIMPSEQ : ⊦ # refs = 0 ↔ refs = []], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPFORWARD : ⊦ i < i0 ∧ i = i1 → i1 < i0], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPFORWARD : ⊦ j < i ∧ i ≤ 0 → j < 0], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ ¬ i < i], [CSIMPSEQ : ⊦ ¬ i < j → (¬ j < i ↔ i = j)], [CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPSEQ : ⊦ ints + [] = ints], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPFORWARD : ints ≠ [] ⊦ i ∈ ints .butlast → i ∈ ints], [CSIMPSEQ : ⊦ refs + [] = refs], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ i ∈ i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i ' .butlast = []], [CSIMPSEQ : ⊦ ¬ i ∈ []])], [EXTRATERMS : (ints0, i0)]]