reserve x,y for object,X,Y for set,
  D for non empty set,
  i,j,k,l,m,n,m9,n9 for Nat,
  i0,j0,n0,m0 for non zero Nat,
  K for Field,
  a,b for Element of K,
  p for FinSequence of K,
  M for Matrix of n,K;
reserve A for (Matrix of D),
  A9 for Matrix of n9,m9,D,
  M9 for Matrix of n9, m9,K,
  nt,nt1,nt2 for Element of n-tuples_on NAT,
  mt,mt1 for Element of m -tuples_on NAT,
  M for Matrix of K;

theorem Th44:
  Segm(A,{i0},{j0}) = <*<* A*(i0,j0) *>*>
proof
A1: card {j0}=1 by CARD_1:30;
A2: Sgm {i0}=<*i0*> by FINSEQ_3:44;
A3: <*j0*>.1=j0;
A4: <*i0*>.1=i0;
A5: Sgm {j0}=<*j0*> by FINSEQ_3:44;
  card {i0}= 1 by CARD_1:30;
  hence thesis by A1,A2,A5,A4,A3,Th21;
end;
