reserve F for Field;
reserve a,b,c,d,p,q,r for Element of MPS(F);
reserve e,f,g,h,i,j,k,l,m,n,o,w for Element of [:the carrier of F,the carrier
  of F,the carrier of F:];
reserve K,L,M,N,R,S for Element of F;
reserve FdSp for FanodesSp;
reserve a,b,c,d,p,q,r,s,o,x,y for Element of FdSp;

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;
