theorem
  sum(a,x,o)=sum(a,y,o) implies x=y
proof
  assume
A1: sum(a,x,o)=sum(a,y,o);
  congr o,a,x,sum(a,x,o) by Def5;
  then
A2: congr a,o,sum(a,x,o),x by Th69;
  congr o,a,y,sum(a,y,o) by Def5;
  then congr a,o,sum(a,x,o),y by A1,Th69;
  hence thesis by A2,Th62;
end;
