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 Th29:
  parallelogram a,b,c,d implies not a,b,x are_collinear or not c,d,
  x are_collinear
proof
  assume
A1: parallelogram a,b,c,d;
  then
A2: c <>d by Th26;
  ( not a,b,c are_collinear)& a,b '||' c,d by A1;
  hence thesis by A2,Th17;
end;
