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 Y being set, R being Relation holds Y|`R c= R|(R"Y)
proof
  let Y be set, R be Relation;
  let a,b be object;
  assume
A1: [a,b] in Y|`R;
  then
A2: b in Y by Def10;
A3: [a,b] in R by A1,Def10;
  then a in R"Y by A2,Def12;
  hence thesis by A3,Def9;
end;
