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 Th11:
  f is isometric & g is isometric implies g*f is isometric
  proof
    assume that
A1: f is isometric and
A2: g is isometric;
    set h = g*f;
    let a,b;
    h.a = g.(f.a) & h.b = g.(f.b) by FUNCT_2:15;
    hence ||. h.a - h.b .|| = ||. f.a - f.b .|| by A2
    .= ||. a - b .|| by A1;
  end;
