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 Th43:
  a<>b implies ex c,d st parallelogram a,b,c,d
proof
  assume a<>b;
  then consider c such that
A1: not a,b,c are_collinear by Th14;
  ex d st parallelogram a,b,c,d by A1,Th34;
  hence thesis;
end;
