reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th53:
  for M being m-nonnegative Matrix of REAL for k st k in dom M
  holds Line(Infor_FinSeq_of M,k) = Infor_FinSeq_of Line(M,k)
proof
  let M be m-nonnegative Matrix of REAL;
  set M1 = Infor_FinSeq_of M;
  len M1 = len M by Def8;
  then
A1: dom M1 = dom M by FINSEQ_3:29;
  let k such that
A2: k in dom M;
  thus Line(M1,k) = M1.k by A2,A1,MATRIX_0:60
    .= Infor_FinSeq_of Line(M,k) by A2,A1,Def8;
end;
