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 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;
