reserve A,X,X1,X2,Y,Y1,Y2 for set, a,b,c,d,x,y,z for object;
reserve P,P1,P2,Q,R,S for Relation;

theorem
  for f,g being Relation, A,B being set st f|A = g|A & f|B = g|B holds
  f|(A \/ B) = g|(A \/ B)
proof
  let f,g be Relation, A,B be set;
  assume f|A = g|A & f|B = g|B;
  hence f|(A \/ B) = g|A \/ g|B by Th72
    .= g|(A \/ B) by Th72;
end;
