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Proof step 17 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), # refs + 1 = i→n(countrefs(i0 ' + getdims(i0 ' + ints0) .rest)) ∧ ¬ 0 ∈ getdims(i0 ' + ints0) .butlast ∧ ¬ getdims(i0 ' + ints0) .first < i0 ∧ ¬ i0 < getdims(i0 ' + ints0) .first

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 6:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 16:
getdims(i0 ' + ints0) = i1 + ints ∧ getdims(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, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st)[r -- _length]) = intval(i0), # refs + 1 = i→n(countrefs(i0 ' + ints)) ∧ ¬ 0 ∈ getdims(i0 ' + ints0) .butlast ∧ ¬ i1 < i0 ∧ ¬ i0 < i1

Rule argument

[speclemmaarg: ints ≠ [] ,i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0 ,[ints, i, ints0] → [getdims(i0 ' + ints0), i1, ints] ,T ,list-data ,intlista ,elim-list-c ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPELIM : ints ≠ [] ⊦ i = ints .first ∧ ints0 = ints .rest ↔ ints = i + ints0])], [EXTRATERMS : (getdims(i0 ' + ints0), i1, ints)]]