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<>b & a,b,c are_collinear & a,b,d are_collinear implies a,c,d are_collinear
by Def1;
