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Proof step 42 from proof addarrays-at-other-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ # ints > 1 ∧ ints .first > 0 → countrefs(ints) = 1 + ints .first * countrefs(ints .rest)
Proof step 24:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 25:
⊦ countrefs(0 ' + ints) = 1
Proof step 26:
⊦ countrefs(i ') = 1
Proof step 27:
⊦ countdims([], i) = i
Proof step 28:
⊦ getdims([]) = []
Proof step 41:
# (i0 ' + getdims(ints0)) > 1 ∧ (i0 ' + getdims(ints0)) .first > 0, 0 ≤ i0, posints(ints0), i < 0, r ∈ st, 0 < i0 ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st) [r -- sk ] ) = st[r -- sk], countrefs(i0 ' + ints0) = 1 + (i0 ' + getdims(ints0)) .first * countrefs((i0 ' + getdims(ints0)) .rest) ∧ ¬ 0 ∈ (i0 ' + getdims(ints0)) .butlast

Rule argument

[crewrite-arg: countrefs-rec, F, [ints] → [i0 ' + getdims(ints0)]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # (ints + ints0) = # ints + # ints0], [CSIMPSEQ : ⊦ # i ' = 0 +1], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ m > n ↔ n < m], [CSIMPSEQ : ⊦ 1 < m ↔ ¬ (m = 0 ∨ m = 1)], [CSIMPSEQ : ⊦ m + 1 ≠ 0], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ 1 = m + 1 ↔ m = 0], [CSIMPSEQ : ⊦ # ints = 0 ↔ ints = []], [CSIMPSEQ : ⊦ (i ' + ints) .first = i], [CSIMPSEQ : ⊦ i > j ↔ j < i], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPSEQ : ⊦ newref_list(1, st) = newref(st) '], [CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ ints + [] = ints], [CSIMPSEQ : ⊦ posints([])], [CSIMPSEQ : ⊦ i ' .butlast = []], [CSIMPSEQ : ⊦ ¬ i ∈ []])], [EXTRATERMS : (i0 ' + getdims(ints0))]]