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

¬ ( # 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 5:
⊦ ¬ posints(getdims(ints)) ↔ false
Proof step 17:
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

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ i < j → (i ≠ j ↔ j < i)], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + 0 = i], [CSIMPSEQ : ⊦ # [] = 0], [CSIMPSEQ : ⊦ i ≤ j → (¬ ¬ j < i ↔ false)], [CSIMPSEQ : ⊦ ¬ i ≤ j ↔ j < i], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ' ≠ []], [CSIMPSEQ : ⊦ ¬ ints + ints0 ≠ [] ↔ ints = [] ∧ ints0 = []])]]