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
  a,b congr c,d implies b,a congr d,c
proof
  assume
A1: a,b congr c,d;
A2: now
    assume a<>b;
    then consider p,q such that
A3: parallelogram p,q,a,b & parallelogram p,q,c,d by A1;
    parallelogram q,p,b,a & parallelogram q,p,d,c by A3,Th33;
    hence thesis;
  end;
  a=b implies thesis by A1,Th45;
  hence thesis by A2;
end;
