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 Th34:
  not a,b,c are_collinear implies ex d st parallelogram a,b,c,d
proof
  consider d such that
A1: a,b '||' c,d & a,c '||' b,d by PARSP_1:def 12;
  assume not a,b,c are_collinear;
  then parallelogram a,b,c,d by A1;
  hence thesis;
end;
