theorem
  for F being Function st X c= F"X1 holds F.:X c= X1
proof
  let F be Function;
  assume X c= F"X1;
  then
A1: F.:X c= F.:F"X1 by RELAT_1:123;
  F.:F"X1 c= X1 by FUNCT_1:75;
  hence thesis by A1;
end;
