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Proof step 16 from proof addarrays-length (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 15:
1 + n→i(# refs) = countrefs(i0 ' + ints0), getdims(i0 ' + ints0) = i1 ' + ints, is_newref_list(r ' + refs, st), 0 ≤ i, posints(ints0), 0 ≤ i0 ⊦ (addmultiarrays(r ' + refs, i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), i1 ' + ints, st)[r -- _length]) = intval(i0), # refs + 1 = i→n(countrefs(i0 ' + ints)) ∧ ¬ 0 ∈ (i1 ' + ints) .butlast ∧ ¬ i1 < i0 ∧ ¬ i0 < i1

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ∈ i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i ∈ ints + ints0 ↔ ¬ ¬ (i ∈ ints ∨ i ∈ ints0)], [CSIMPFORWARD : ⊦ i ' + ints = ints0 → i ∈ ints0], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' + ints ≠ []], [CSIMPSEQ : ⊦ i + ints = i ' + ints])]]