reserve x,X for set,
        r,r1,r2,s for Real,
        i,j,k,m,n for Nat;
reserve p,q for Point of TOP-REAL n;

theorem Th19:
  1 <= i & i < j & j <= n implies
    Rotation(i,j,n,r) is Orthogonal &
    Rotation(i,j,n,r)~ = Rotation(i,j,n,-r)
proof
  assume 1<=i & i<j & j<=n;
  then Rotation(i,j,n,r)~  =Rotation(i,j,n,-r) &
       Rotation(i,j,n,r)@=Rotation(i,j,n,-r) by Lm4,Lm5;
  hence thesis by MATRIX_6:def 7;
end;
