theorem
  sum(sum(a,b,o),c,o)=sum(a,sum(b,c,o),o)
proof
  congr o,a,b,sum(a,b,o) & congr o,a,sum(b,c,o),sum(a,sum(b,c,o),o) by Def5;
  then
A1: congr b,sum(a,b,o),sum(b,c,o),sum(a,sum(b,c,o),o) by Th65;
  congr o,b,c,sum(b,c,o) by Def5;
  then
A2: congr b,o,sum(b,c,o) ,c by Th69;
  congr o,sum(a,b,o),c,sum(sum(a,b,o),c,o) by Def5;
  then congr b,sum(a,b,o),sum(b,c,o),sum(sum(a,b,o),c,o) by A2,Th70;
  hence thesis by A1,Th62;
end;
