theorem Th75:
  <*A*>(#)G = <*A * G.1*>
proof
  dom (<*A*>(#) G)=dom <*A*> by Def11;
  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 Def11
    .= A*G.1;
  hence thesis by A1,FINSEQ_1:40;
end;
