let V be Z_Module; :: thesis: for W being Submodule of V
for x being object st x in W holds
x in V
let W be Submodule of V; :: thesis: for x being object st x in W holds
x in V
let x be object ; :: thesis: ( x in W implies x in V )
assume x in W ; :: thesis: x in V
then A1: x in the carrier of W ;
the carrier of W c= the carrier of V by Def9;
hence x in V by A1; :: thesis: verum