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Proof step 39 from proof addarrays-at-other-01 (previous step)

getdims(ints0) ≠ [], 0 ≤ i0, posints(ints0), i < 0, r ∈ st, 0 < i0 ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st) [r -- sk ] ) = st[r -- sk], ints0 = [], countrefs(i0 ' + ints0) = 1 + countrefs(ints0) * i0 ∧ ¬ 0 ∈ i0 ' + getdims(ints0) .butlast

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 33:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 34:
⊦ ints ≠ [] → ¬ 0 ∈ getdims(ints) .butlast
Proof step 35:
⊦ countrefs(0 ' + ints) = 1
Proof step 38:
posints(ints0), i < 0, r ∈ st, 0 < i0 ⊦ (addmultiarrays(newref_list(i→n(countrefs(i0 ' + ints0)), st), i0, [], mktype_from_dims(ty, countdims(ints0, i)), i0 ' + getdims(ints0), st) [r -- sk ] ) = st[r -- sk], ints0 = [], countrefs(i0 ' + ints0) = 1 + countrefs(ints0) * i0, 0 = i0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i ≠ j → (i ≤ j ↔ i < j)], [CSIMPSEQ : ⊦ newref_list(1, st) = newref(st) '], [CSIMPSEQ : ⊦ (ints + ints0) + ints1 = ints + ints0 + ints1], [CSIMPSEQ : ⊦ i ∈ i0 ' ↔ i = i0], [CSIMPSEQ : ⊦ i ∈ ints + ints0 ↔ ¬ ¬ (i ∈ ints ∨ i ∈ ints0)])]]