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 Th49:
  a,b congr c,d implies a,c '||' b,d
proof
  assume
A1: a,b congr c,d;
A2: now
    assume
A3: a=b;
    then c =d by A1,Th45;
    hence thesis by A3,PARSP_1:25;
  end;
  a<>b implies thesis by A1,Th39;
  hence thesis by A2;
end;
