reserve GF for add-associative right_zeroed right_complementable Abelian
  associative well-unital distributive non empty doubleLoopStr;
reserve M for Abelian add-associative right_zeroed right_complementable
  vector-distributive scalar-distributive scalar-associative scalar-unital
   non empty ModuleStr over GF;
reserve W,W1,W2,W3 for Subspace of M;
reserve u,u1,u2,v,v1,v2 for Element of M;
reserve X,Y for set, x,y,y1,y2 for object;

theorem Th3:
  x in W1 /\ W2 iff x in W1 & x in W2
proof
  x in W1 /\ W2 iff x in the carrier of W1 /\ W2 by STRUCT_0:def 5;
  then x in W1 /\ W2 iff x in (the carrier of W1) /\ (the carrier of W2) by
Def2;
  then x in W1 /\ W2 iff x in the carrier of W1 & x in the carrier of W2 by
XBOOLE_0:def 4;
  hence thesis by STRUCT_0:def 5;
end;
