theorem Th45:
  F is having_a_unity implies F[:](f,the_unity_wrt F) = f
proof
  set e = the_unity_wrt F;
  assume
A1: F is having_a_unity;
  now
    let c;
    thus (F[:](f,e)).c = F.(f.c,e) by FUNCOP_1:48
      .= f.c by A1,SETWISEO:15;
  end;
  hence thesis by FUNCT_2:63;
end;
