reserve a,b,c,d,x,y,z for object, X,Y,Z for set;
reserve R,S,T for Relation;
reserve F,G for Function;

theorem Th14:
  (R |_2 X)-Seg(a) c= R-Seg(a)
proof
  let x be object;
  assume
A1: x in (R |_2 X)-Seg(a);
  then [x,a] in R |_2 X by Th1;
  then
A2: [x,a] in R by XBOOLE_0:def 4;
  x <> a by A1,Th1;
  hence thesis by A2,Th1;
end;
