reserve i,j,m,n,k for Nat,
  x,y for set,
  K for Field,
  a,a1,a2 for Element of K,
  D for non empty set,
  d,d1,d2 for Element of D,
  M,M1,M2 for (Matrix of D),
  A,A1,A2,B1,B2 for (Matrix of K),
  f,g for FinSequence of NAT;
reserve F,F1,F2 for FinSequence_of_Matrix of D,
  G,G9,G1,G2 for FinSequence_of_Matrix of K;

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;
