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 Th20:
  ||. (a-reflection).b - a .|| = ||. b - a .||
  proof
    (a-reflection).b - a = a - b by Th19;
    hence thesis by NORMSP_1:7;
  end;
