reserve SAS for Semi_Affine_Space;
reserve a,a9,a1,a2,a3,a4,b,b9,c,c9,d,d9,d1,d2,o,p,p1,p2,q,r,r1,r2,s,x, y,t,z
  for Element of SAS;

theorem
  a,b // opposite(a,o),opposite(b,o)
proof
  sum(b,opposite(b,o),o)=o by Def6;
  then congr o,b,opposite(b,o),o by Def5;
  then
A1: congr b,o,o,opposite(b,o) by Th69;
  sum(a,opposite(a,o),o)=o by Def6;
  then congr o,a,opposite(a,o),o by Def5;
  then congr a,o,o,opposite(a,o) by Th69;
  hence thesis by A1,Th73;
end;
