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
  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;
