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Proof step 21 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 ⊦ (addarrays(r ' + refs, ty, i0 ' + ints0, i, st)[r -- _length]) = intval(i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ints ≠ [] ∧ n→i(# refs) = countrefs(ints) ∧ posints(ints) → addarrays(refs, ty, ints, i, st) = addmultiarrays(refs, ints .first, [], mktype_from_dims(ty, countdims(ints, i)), getdims(ints), st)
Proof step 20:
i0 ' + ints0 ≠ [] ∧ n→i(# (r ' + refs)) = countrefs(i0 ' + ints0) ∧ posints(i0 ' + ints0), 1 + n→i(# refs) = countrefs(i0 ' + ints0), is_newref_list(r ' + refs, st), 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ (addmultiarrays(r ' + refs, (i0 ' + ints0) .first, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st)[r -- _length]) = intval(i0)

Rule argument

[crewrite-arg: addarrays-def , F , [st, i, ints, ty, refs] → [st, i, i0 ' + ints0, ty, r ' + refs] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ # (refs + refs0) = # refs + # refs0], [CSIMPSEQ : ⊦ # r ' = 0 +1], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ n→i(m + n) = n→i(m) + n→i(n)], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ posints(i ' + ints) ↔ 0 ≤ i ∧ posints(ints)])], [EXTRATERMS : (st, i, i0 ' + ints0, ty, r ' + refs)]]