reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem
  a<>d implies ex b,c st parallelogram a,b,c,d
proof
  assume a<>d;
  then consider b such that
A1: not a,d,b are_collinear by Th25;
  not b,a,d are_collinear by A1,Th22;
  then consider c such that
A2: parallelogram b,a,d,c by Th44;
  parallelogram a,b,c,d by A2,Th43;
  hence thesis;
end;
