theorem Th24:
  for M being Matrix of n,D holds len M = n & width M = n &
  Indices M = [:Seg n, Seg n:]
proof
  let M be Matrix of n,D;
A1: len M = n by Def2;
A2: now
    per cases;
    case
      n =0;
      hence width M = 0 by A1,Def3;
    end;
    case
      n > 0;
      hence width M= n by A1,Th20;
    end;
  end;
  Seg len M = dom M by FINSEQ_1:def 3;
  hence thesis by A2,Def2;
end;
