reserve x,y,z for object,
  i,j,n,m for Nat,
  D for non empty set,
  s,t for FinSequence,
  a,a1,a2,b1,b2,d for Element of D,
  p, p1,p2,q,r for FinSequence of D;
reserve M,M1,M2 for Matrix of D;

theorem Th34:
  for M being FinSequence of D* holds M.i is FinSequence of D
proof
  let M be FinSequence of D*;
  per cases;
  suppose
    not i in dom M;
    then M.i = <*>D by FUNCT_1:def 2;
    hence thesis;
  end;
  suppose
A1: i in dom M;
A2: rng M c= D* by FINSEQ_1:def 4;
    M.i in rng M by A1,FUNCT_1:def 3;
    hence thesis by A2,FINSEQ_1:def 11;
  end;
end;
