Section SkewField.
Hypothesis fieldT : GRing.Field.mixin_of aT.

(* Specifications: *)
Lemma skew_field_algid1 A : algid A = 1.
Lemma skew_field_module_dimS A M : (A * M <= M)%VS -> \dim A %| \dim M.
Lemma skew_field_dimS A B : (A <= B)%VS -> \dim A %| \dim B.
Lemma agenvEr U : agenv U = (1 + agenv U * U)%VS.
Lemma agenv_modl U V : (U * V <= V -> agenv U * V <= V)%VS.
Lemma agenv_modr U V : (V * U <= V -> V * agenv U <= V)%VS.
Fact agenv_is_aspace U : is_aspace (agenv U).