Definition kHom U V f := ahom_in V f && (U <= fixedSpace f)%VS.

(* Specifications: *)
Lemma k1HomE V f : kHom 1 V f = ahom_in V f.
Lemma kHomSl U1 U2 V f : (U1 <= U2)%VS -> kHom U2 V f -> kHom U1 V f.
Lemma kHomSr K V1 V2 f : (V1 <= V2)%VS -> kHom K V2 f -> kHom K V1 f.
Lemma kHomS K1 K2 V1 V2 f : (K1 <= K2)%VS -> (V1 <= V2)%VS -> kHom K2 V2 f -> kHom K1 V1 f.