theorem Th20:
  for A be Matrix of 1,D holds A = <*<* A*(1,1) *>*>
proof
  let A be Matrix of 1,D;
  reconsider AA=<*<* A*(1,1) *>*> as Matrix of 1,D by MATRIX_0:15;
  now
A1: Indices A=[:Seg 1,Seg 1:] by MATRIX_0:24;
    let i,j such that
A2: [i,j] in Indices A;
    j in {1} by A2,A1,FINSEQ_1:2,ZFMISC_1:87;
    then
A3: j=1 by TARSKI:def 1;
    i in {1} by A2,A1,FINSEQ_1:2,ZFMISC_1:87;
    then i=1 by TARSKI:def 1;
    hence AA*(i,j)=A*(i,j) by A3,MATRIX_0:49;
  end;
  hence thesis by MATRIX_0:27;
end;
