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 Th33:
  parallelogram a,b,c,d implies parallelogram a,c,b,d &
  parallelogram c,d,a,b & parallelogram b,a,d,c & parallelogram c,a,d,b &
  parallelogram d,b,c,a & parallelogram b,d,a,c & parallelogram d,c,b,a
proof
  assume
A1: parallelogram a,b,c,d;
  then parallelogram c,d,a,b by Th31;
  then
A2: parallelogram c,a,d,b by Th30;
  parallelogram b,a,d,c by A1,Th32;
  hence thesis by A1,A2,Th30,Th31;
end;
