let R be Ring; :: thesis: for V being RightMod of R holds V is Submodule of V
let V be RightMod of R; :: thesis: V is Submodule of V
A1: ( the carrier of V c= the carrier of V & 0. V = 0. V ) ;
( the addF of V = the addF of V | [:the carrier of V,the carrier of V:] & the rmult of V = the rmult of V | [:the carrier of V,the carrier of R:] ) by FUNCT_2:40;
hence V is Submodule of V by A1, Def2; :: thesis: verum