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 Th98:
  trap a,p,b,q,o & trap a,p,c,r,o implies b,c // q,r
proof
  assume that
A1: trap a,p,b,q,o and
A2: trap a,p,c,r,o;
  not o,a,b are_collinear by A1;
  then
A3: not o,a // o,b;
  o,c,r are_collinear by A2;
  then
A4: o,c //o,r;
  not o,a,c are_collinear by A2;
  then
A5: not o,a //o,c;
  o,b,q are_collinear by A1;
  then
A6: o,b //o,q;
  o,a,p are_collinear by A1;
  then
A7: o,a //o,p;
  a,b // p,q & a,c // p,r by A1,A2;
  hence thesis by A3,A7,A6,A5,A4,Def1;
end;
