
theorem
  N_CC = AffineMap (-1,1)|[.0,1.]
  proof
    set N = N_CC;
    set f = AffineMap (-1,1)|[.0,1.];
A2: dom AffineMap (-1,1) = REAL by FUNCT_2:def 1;
AA: dom N = dom f by A2,FUNCT_2:def 1;
    for x being object st x in dom N holds
      f.x = N.x
    proof
      let x be object;
      assume x in dom N; then
      reconsider xx = x as Element of [.0,1.] by FUNCT_2:def 1;
      f.x = AffineMap (-1,1).xx by FUNCT_1:49
         .= (-1) * xx + 1 by FCONT_1:def 4
         .= 1-xx
         .= N.x by FUZIMPL3:def 6;
      hence thesis;
    end;
    hence thesis by AA,FUNCT_1:2;
  end;
