reserve i,j,k,l for natural Number;
reserve A for set, a,b,x,x1,x2,x3 for object;
reserve D,D9,E for non empty set;
reserve d,d1,d2,d3 for Element of D;
reserve d9,d19,d29,d39 for Element of D9;
reserve p,q,r for FinSequence;

theorem Th9:
  for D being set for p being D-valued FinSequence st i in dom p holds p.i in D
proof
  let D be set;
  let p be D-valued FinSequence;
  assume i in dom p;
  then
A1: p.i in rng p by FUNCT_1:def 3;
  rng p c= D by RELAT_1:def 19;
  hence thesis by A1;
end;
