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 Th17:
  (a-reflection) * (a-reflection) = id E
  proof
    set R = a-reflection;
    let b;
    thus (R*R).b = R.(R.b) by FUNCT_2:15
    .= 2*a - R.b by Def4
    .= 2*a - (2*a - b) by Def4
    .= 2*a - 2*a + b by RLVECT_1:29
    .= (0.E) + b by RLVECT_1:5
    .= b
    .= (id E).b;
  end;
