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 Th36:
  parallelogram a,b,c,d implies not a,d '||' b,c
proof
  assume
A1: parallelogram a,b,c,d;
  then not a,b,c are_collinear;
  then
A2: not a,b '||' a,c;
  a,b '||' c,d & a,c '||' b,d by A1;
  then not b,c '||' a,d by A2,Def1;
  hence thesis by PARSP_1:19;
end;
