reserve x,x1,x2,x3,x4,y,y1,y2,y3,y4,z,z1,z2,z2,z4 for object;
reserve X,X1,X2,X3,X4,Y for set;

theorem Th8:
 X c= Y implies proj1 X c= proj1 Y
proof assume
A1: X c= Y;
 let x be object;
 assume x in proj1 X;
  then consider y such that
A2: [x,y] in X by Def12;
  [x,y] in Y by A1,A2;
 hence thesis by Def12;
end;
