theorem
  (a,b)][(c,d)*(1,1)=a & (a,b)][(c,d)*(1,2)=b & (a,b)][(c,d)*(2,1)=c & (
  a,b)][(c,d)*(2,2)=d
proof
  set M=(a,b)][(c,d);
A1: M.1= <*a,b*> & M.2=<*c,d*>;
A2: <*a,b*>.1=a & <*a,b*>.2=b;
A3: [2,1] in Indices M & [2,2] in Indices M by Th48;
A4: <*c,d*>.1=c & <*c,d*>.2=d;
  [1,1] in Indices M & [1,2] in Indices M by Th48;
  hence thesis by A1,A2,A4,A3,Def5;
::   assume
:: A1: [i,j] in Indices M;
::   func M*(i,j) -> Element of D means
:: :Def5:
::   ex p being FinSequence of D st p = M.i & it = p.j;
end;
