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 Th47:
  parallelogram a,b,c,d implies not parallelogram a,b,d,c
proof
  assume
A1: parallelogram a,b,c,d;
  then not a,b,c are_collinear;
  then
A2: not a,b // a,c;
  assume not thesis;
  then
A3: a,d // b,c;
  a,b // c,d & a,c // b,d by A1;
  hence contradiction by A3,A2,Def1;
end;
