theorem Th70:
  <*A1,B1*>(+)<*A2,B2*> = <*A1+A2,B1+B2*>
proof
A1: len <*A2*>=1 by FINSEQ_1:39;
  len <*A1*>=1 by FINSEQ_1:39;
  hence (<*A1,B1*>)(+)(<*A2,B2*>) = (<*A1*>(+)<*A2*>)^(<*B1*>(+)<*B2*>) by A1
,Th67
    .= (<*A1*>(+)<*A2*>)^(<*B1+B2*>) by Th69
    .= <*A1+A2,B1+B2*> by Th69;
end;
