theorem
  for a being Element of X st a is minimal holds f.a is minimal
proof
  let a be Element of X;
  assume a is minimal;
  then f.a=f.(a``)by BCIALG_2:29;
  then f.a=f.0.X\(f.(0.X\a)) by Def6;
  then f.a=f.0.X\(f.0.X\f.a) by Def6;
  then f.a=(f.0.X\f.a)` by Th35;
  then f.a=(f.a)`` by Th35;
  hence thesis by BCIALG_2:29;
end;
