theorem Th40:
  not b,q,c are_collinear & parallelogram a,p,b,q & parallelogram a
  ,p,c,r implies parallelogram b,q,c,r
proof
  assume that
A1: not b,q,c are_collinear and
A2: parallelogram a,p,b,q and
A3: parallelogram a,p,c,r;
A4: a,p '||' c,r by A3;
  a<>p & a,p '||' b,q by A2,Th26;
  then
A5: b,q '||' c,r by A4,PARSP_1:def 12;
  b,c '||' q,r by A2,A3,Th39;
  hence thesis by A1,A5;
end;
