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 Th19:
  (a-reflection).b - a = a - b
  proof
    set R = a-reflection;
A1: 1*a = a by RLVECT_1:def 8;
    R.b = 2*a - b by Def4;
    hence R.b - a = 2*a - a - b by VECTSP_1:34
    .= (2-1)*a - b by A1,RLVECT_1:35
    .= a - b by RLVECT_1:def 8;
  end;
