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Proof step 19 from proof addarrays-length (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ # refs + 1 = i→n(countrefs(i ' + ints .rest)) ∧ ints ≠ [] ∧ 0 ≤ i ∧ posints(ints) ∧ ¬ 0 ∈ ints .butlast ∧ i ≤ ints .first ∧ n→i(# acc) + i = ints .first → (addmultiarrays(r ' + refs, i, acc, ty, ints, st)[r -- _length]) = intval(ints .first)
Proof step 18:
¬ ( # refs + 1 = i→n(countrefs(i0 ' + getdims(i0 ' + ints0) .rest)) ∧ getdims(i0 ' + ints0) ≠ [] ∧ 0 ≤ i0 ∧ posints(getdims(i0 ' + ints0)) ∧ ¬ 0 ∈ getdims(i0 ' + ints0) .butlast ∧ i0 ≤ getdims(i0 ' + ints0) .first ∧ n→i(# []) + i0 = getdims(i0 ' + ints0) .first), 1 + n→i(# refs) = countrefs(i0 ' + ints0), is_newref_list(r ' + refs, st), 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ (addmultiarrays(r ' + refs, i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st)[r -- _length]) = intval(i0)

Rule argument

[crewrite-arg: multi-length-first , F , [st, ints, ty, acc, i, refs, r] → [st, getdims(i0 ' + ints0), mktype_from_dims(ty, countdims(i0 ' + ints0, i)), [], i0, refs, r] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ intval(i) = intval(i0) ↔ i = i0])], [EXTRATERMS : (st, getdims(i0 ' + ints0), mktype_from_dims(ty, countdims(i0 ' + ints0, i)), [], i0, refs, r)]]