reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
 B c= A & A is trivial implies B is trivial
proof assume that
A1: B c= A and
A2: A is trivial;
  let x,y;
 assume x in B & y in B;
  then x in A & y in A by A1;
 hence thesis by A2;
end;
