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Proof step 40 from proof addarrays-at-other-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ ints ≠ [] → (i ' + ints) .butlast = i ' + ints .butlast
Proof step 32:
⊦ getdims(ints) = [] ↔ ints = []
Proof step 39:
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

Rule argument

[speclemmaarg: ,ints ≠ [] → (i ' + ints) .butlast = i ' + ints .butlast ,[ints, i] → [getdims(ints0), i0] ,F ,list-last ,intlista ,bc ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (getdims(ints0), i0)]]