theorem Th41:
  a,b,c are_collinear & b<>c & parallelogram a,p,b,q &
  parallelogram a,p,c,r implies parallelogram b,q,c,r
proof
  assume that
A1: a,b,c are_collinear and
A2: b<>c and
A3: parallelogram a,p,b,q and
A4: parallelogram a,p,c,r;
A5: b<>q by A3,Th26;
  a,b '||'a,c by A1;
  then
A6: a,b '||' b,c by PARSP_1:24;
  thus thesis by A2,A3,A4,A5,A6,Th11,Th40;
end;
