Definition aspace_cap A B BeA := ASpace (@aspace_cap_subproof A B BeA).
Fact centraliser1_is_aspace u : is_aspace 'C[u].
Canonical centraliser1_aspace u := ASpace (centraliser1_is_aspace u).
Fact centraliser_is_aspace V : is_aspace 'C(V).
Canonical centraliser_aspace V := ASpace (centraliser_is_aspace V).

Lemma centv_algid A : algid A \in 'C(A)%VS.