 reserve i,n for Nat;
 reserve r for Real;
 reserve ra for Element of F_Real;
 reserve a,b,c for non zero Element of F_Real;
 reserve u,v for Element of TOP-REAL 3;
 reserve p1 for FinSequence of (1-tuples_on REAL);
 reserve pf,uf for FinSequence of F_Real;
 reserve N for Matrix of 3,F_Real;
 reserve K for Field;
 reserve k for Element of K;
 reserve N,N1,N2 for invertible Matrix of 3,F_Real;
 reserve P,P1,P2,P3 for Point of ProjectiveSpace TOP-REAL 3;

theorem
  (homography(N)).P1 = (homography(N)).P2 implies P1 = P2
  proof
    assume
A1: (homography(N)).P1 = (homography(N)).P2;
    P1 = (homography(N~)).((homography(N)).P1) by Th16
      .= P2 by A1,Th16;
    hence thesis;
  end;
