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 Th21:
  n = 1 & m = 1 implies Segm(A,nt,mt) = <*<* A*(nt.1,mt.1) *>*>
proof
A1: 1 in Seg 1;
  assume that
A2: n = 1 and
A3: m = 1;
  Indices Segm(A,nt,mt)=[:Seg 1,Seg 1:] by A2,A3,MATRIX_0:24;
  then [1,1] in Indices Segm(A,nt,mt) by A1,ZFMISC_1:87;
  then Segm(A,nt,mt)*(1,1)=A*(nt.1,mt.1) by Def1;
  hence thesis by A2,A3,Th20;
end;
