reserve a,b,c,d,e for Real;

theorem Th08:
  for X being non empty set
  for f,g being Function of X,REAL holds
  min(f,g) <= f
  proof
    let X be non empty set;
    let f,g be Function of X,REAL;
    now
      let x be Element of X;
      (min(f,g)).x = min(f.x,g.x) by DEFM1;
      hence (min(f,g)).x <= f.x & (min(f,g)).x <= g.x by XXREAL_0:17;
    end;
    hence thesis;
  end;
