theorem Th68:
  <*A*>(+)G = <*A + G.1*>
proof
  dom (<*A*>(+) G)=dom <*A*> by Def10;
  then
A1: len (<*A*>(+) G) = len <*A*> by FINSEQ_3:29
    .= 1 by FINSEQ_1:39;
  then dom (<*A*>(+) G)={1} by FINSEQ_1:2,def 3;
  then 1 in dom (<*A*>(+) G) by TARSKI:def 1;
  then (<*A*>(+) G).1 = (<*A*>.1)+G.1 by Def10
    .= A+G.1;
  hence thesis by A1,FINSEQ_1:40;
end;
