theorem Th22:
  for A be Matrix of 2,D holds A = ( A*(1,1),A*(1,2) )][( A*(2,1), A*(2,2) )
proof
  let A be Matrix of 2,D;
  reconsider AA=(A*(1,1),A*(1,2))][(A*(2,1),A*(2,2)) as Matrix of 2,D;
  now
A1: Indices A=[:Seg 2,Seg 2:] by MATRIX_0:24;
    let i,j such that
A2: [i,j] in Indices A;
    j in {1,2} by A2,A1,FINSEQ_1:2,ZFMISC_1:87;
    then
A3: j=1 or j=2 by TARSKI:def 2;
    i in {1,2} by A2,A1,FINSEQ_1:2,ZFMISC_1:87;
    then i=1 or i=2 by TARSKI:def 2;
    hence AA*(i,j)=A*(i,j) by A3,MATRIX_0:50;
  end;
  hence thesis by MATRIX_0:27;
end;
