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Proof step 18 from proof addarrays-fieldin (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 17:
getdims(i0 ' + ints0) = i1 + ints ∧ getdims(i0 ' + ints0) ≠ [], n→i(# refs) = countrefs(i0 ' + ints0), posints(ints0), 0 ≤ i0 ⊦ fs ' = _length, fs ' = _type, r -- fs ' ∈ addmultiarrays(refs, i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st) ↔ r -- fs ' ∈ st, # refs = i→n(countrefs(i0 ' + ints)) ∧ ¬ 0 ∈ getdims(i0 ' + ints0) .butlast ∧ ¬ i1 < i0

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)]]