reserve E,F,G for RealNormSpace;
reserve f for Function of E,F;
reserve g for Function of F,G;
reserve a,b,c for Point of E;
reserve t for Real;

theorem Th16:
  f is bijective Affine implies f/" is Affine
  proof
    assume that
A1: f is bijective and
A2: f is Affine;
    set g = f/";
    let a,b be Point of F;
    let t such that
A3: 0 <= t & t <= 1;
A4: g*f = id E by A1,Lm3;
    f.(g.a) = a & f.(g.b) = b by A1,Lm2;
    hence g.((1-t)*a+t*b) = g.(f.((1-t)*(g.a)+t*(g.b))) by A3,A2
    .= (g*f).((1-t)*(g.a)+t*(g.b)) by FUNCT_2:15
    .= (1-t)*g.a+t*g.b by A4;
  end;
