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Proof step 45 from proof addarrays-at-other-01 (previous step)

¬ ( ¬ r ∈ newref_list(i→n(countrefs(i0 ' + ints0)), st) ∧ # newref_list(i→n(countrefs(i0 ' + ints0)), st) = 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), 0 ≤ i0, posints(ints0), i < 0, r ∈ st ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st) [r -- sk ] ) = st[r -- sk]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 14:
⊦ abs(countrefs(ints)) = countrefs(ints)
Proof step 15:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 16:
⊦ ¬ posints(getdims(ints)) ↔ false
Proof step 44:
0 ≤ i0, posints(ints0), i < 0, r ∈ st ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(i0 ' + ints0, i)), getdims(i0 ' + ints0), st) [r -- sk ] ) = st[r -- sk], countrefs(i0 ' + ints0) = countrefs(i0 ' + getdims(i0 ' + ints0) .rest) ∧ ¬ 0 ∈ getdims(i0 ' + ints0) .butlast ∧ ¬ getdims(i0 ' + ints0) .first < i0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([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 = []], [CSIMPSEQ : ⊦ i→n(i) = i→n(j) ↔ abs(i) = abs(j)], [CSIMPSEQ : ⊦ # newref_list(n, st) = n], [CSIMPSEQ : ⊦ r ∈ st → ¬ r ∈ newref_list(n, st)])]]