theorem Th25:
  |{p3,p4,p8}| = 0 implies
  |{p3,p4,p6}| * |{p3,p5,p8}| = |{p3,p4,p5}| * |{p3,p6,p8}|
  proof
    assume
A1: |{p3,p4,p8}| = 0;
    |{p3,p4,p6}| * |{p3,p5,p8}| - |{p3,p4,p5}| * |{p3,p6,p8}| +
      |{p3,p4,p8}| * |{p3,p6,p5}| = 0 by ANPROJ_8:28;
    hence thesis by A1;
  end;
