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 Th12:
  f is bijective isometric implies f/" is isometric
  proof
    assume that
A1: f is bijective and
A2: f is isometric;
    set g = f/";
    let a,b be Point of F;
    f.(g.a) = a & f.(g.b) = b by A1,Lm2;
    hence thesis by A2;
  end;
