reserve D for non empty set;
reserve s for FinSequence of D;
reserve m,n for Element of NAT;

theorem Th26:
  for n be non zero Nat,
  f be NtoSEG Function of Segm n, Seg n,
  i be Nat st i < n holds f.i=i+1 & i in dom f
  proof
    let n be non zero Nat,
    f be NtoSEG Function of Segm n, Seg n,
    i be Nat;
    assume i < n;then
    A1:i in Segm n by NAT_1:44;then
    consider ii be Element of Segm n such that A2:ii=i;
    A3: ntoSeg ii = succ Segm ii
          .=Segm(ii+1) by NAT_1:38;
    thus f.i = i+1 by Def5,A2,A3;
    thus i in dom f by A1,FUNCT_2:def 1;
  end;
