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 Th9:
  p<>q implies ex r st not p,q '||' p,r
proof
  consider a,b,c such that
A1: not a,b '||' a,c by Def1;
  assume p<>q;
  then not p,q '||' p,a or not p,q '||' p,b or not p,q '||' p,c by A1,
PARSP_1:38;
  hence thesis;
end;
