
theorem Th38:
  for P being Element of real_projective_plane st #P is non zero_proj1 holds
  ex P9 being non zero_proj1 Point of ProjectiveSpace TOP-REAL 3 st
  P = P9 & dual P = dual1 P9
  proof
    let P be Element of real_projective_plane;
    assume
A1: #P is non zero_proj1;
    reconsider P1 = #P as non zero_proj1 Point of ProjectiveSpace TOP-REAL 3
      by A1;
    per cases;
    suppose P1 is non zero_proj2 & P1 is zero_proj3;
      hence thesis by Def22;
    end;
    suppose P1 is zero_proj2 & P1 is non zero_proj3;
      hence thesis by Def22;
    end;
    suppose P1 is zero_proj2 & P1 is zero_proj3;
      hence thesis by Def22;
    end;
    suppose P1 is non zero_proj2 & P1 is non zero_proj3;
      hence thesis by Def22;
    end;
  end;
