theorem Th15:
  Len <*M*> = <*len M*>
proof
  set F=<*M*>;
A1: len F=1 by FINSEQ_1:40;
A3: len F=len (Len F) by CARD_1:def 7;
A4: dom (Len F)=Seg len F by FINSEQ_2:124;
  1 in Seg 1;
  then (Len F).1 = len (F.1) by A1,A4,Def3;
  hence thesis by A1,A3,FINSEQ_1:40;
end;
