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Proof step 44 from proof addarrays-at-other-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ 0 < j → getdims(j ' + ints) = j ' + getdims(ints)
Proof step 18:
⊦ countrefs(0 ' + ints) = 1
Proof step 19:
⊦ j ≤ 0 → countdims(j ' + ints, i) = i + n→i(# ints)
Proof step 20:
⊦ j ≤ 0 → getdims(j ' + ints) = 0 '
Proof step 21:
⊦ countrefs(i ') = 1
Proof step 43:
0 < i0, 0 ≤ i0, posints(ints0), i < 0, r ∈ st ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), i0 ' + getdims(ints0), st) [r -- sk ] ) = st[r -- sk], countrefs(i0 ' + ints0) = countrefs(i0 ' + (i0 ' + getdims(ints0)) .rest) ∧ ¬ 0 ∈ (i0 ' + getdims(ints0)) .butlast ∧ ¬ (i0 ' + getdims(ints0)) .first < i0

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ newref_list(1, st) = newref(st) '], [CSIMPSEQ : ⊦ i ' .rest = []], [CSIMPSEQ : ⊦ ints + [] = ints], [CSIMPSEQ : ⊦ i ' .butlast = []], [CSIMPSEQ : ⊦ ¬ i ∈ []], [CSIMPSEQ : ⊦ i ' .first = i])], [EXTRATERMS : (ints0, i0)]]