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 Th14:
  p<>q implies ex r st not p,q,r are_collinear
proof
  assume p<>q;
  then consider r such that
A1: not p,q '||' p,r by Th9;
  not p,q,r are_collinear by A1;
  hence thesis;
end;
