reserve a,b,c,d for Real;

theorem
  L[01]((#)(0,1),(0,1)(#)) = id Closed-Interval-TSpace(0,1)
proof
  for x being Point of Closed-Interval-TSpace(0,1) holds L[01]((#)(0,1),(0
  ,1)(#)).x = x
  proof
    let x be Point of Closed-Interval-TSpace(0,1);
    reconsider y = x as Real;
    (#)(0,1) = 0 & (0,1)(#) = 1 by Def1,Def2;
    hence L[01]((#)(0,1),(0,1)(#)).x = (1-y)*0 + y*1 by Def3
      .= x;
  end;
  hence thesis by FUNCT_2:124;
end;
