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 Th22:
  ||. (a-reflection).b - b .|| = 2 * ||. b - a .||
  proof
A1: (a-reflection).b - b = 2 * (a - b) by Th21;
A2: |.2.| = 2 by COMPLEX1:43;
    ||. a - b .|| = ||. b - a .|| by NORMSP_1:7;
    hence thesis by A1,A2,NORMSP_1:def 1;
  end;
