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 Th94:
  trap a,b,c,d,d implies d=b
proof
  assume
A1: trap a,b,c,d,d;
  then a,c // b,d;
  then
A2: d,b // a,c by Th6;
  d,a,b are_collinear by A1;
  then d,a // d,b;
  then
A3: d,b // a,d by Th6;
  assume not thesis;
  then a,d // a,c by A3,A2,Def1;
  then
A4: d,a // d,c by Th7;
  not d,a,c are_collinear by A1;
  hence contradiction by A4;
end;
