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 Th49:
  parallelogram a,a9,b,b9 & parallelogram a,a9,c,c9 implies b,c // b9,c9
proof
  assume that
A1: parallelogram a,a9,b,b9 and
A2: parallelogram a,a9,c,c9;
A3: a,a9 // c,c9 & a,c // a9,c9 by A2;
  not a,a9,c are_collinear by A2;
  then
A4: not a,a9 // a,c;
  not a,a9,b are_collinear by A1;
  then
A5: not a,a9 // a,b;
  a,a9 // b,b9 & a,b // a9,b9 by A1;
  hence thesis by A5,A4,A3,Def1;
end;
