theorem
  for M being Matrix of n,m,D st 1 <= i & i <= n & 1 <= j & j <= m holds
  [i,j] in Indices M
proof
  let M be Matrix of n,m,D such that
A1: 1 <= i & i <= n and
A2: 1 <= j & j <= m;
A3: len M = n by Def2;
  per cases;
  suppose
    n = 0;
    hence thesis by A1;
  end;
  suppose
    n > 0;
    then m = width M by Th23;
    hence thesis by A1,A2,A3,Th30;
  end;
end;
