let R be Ring; :: thesis: for V being LeftMod of R
for A being Subset of V holds A is Subset of (Lin A)
let V be LeftMod of R; :: thesis: for A being Subset of V holds A is Subset of (Lin A)
let A be Subset of V; :: thesis: A is Subset of (Lin A)
for x being object st x in A holds
x in the carrier of (Lin A)

proof

let x be object ; :: thesis: ( x in A implies x in the carrier of (Lin A) )
assume A1: x in A ; :: thesis: x in the carrier of (Lin A)
x in Lin A by A1, MOD_3:5;
hence x in the carrier of (Lin A) ; :: thesis: verum

end;

then A c= the carrier of (Lin A) ;
hence A is Subset of (Lin A) ; :: thesis: verum