 reserve x for Real,
    p,k,l,m,n,s,h,i,j,k1,t,t1 for Nat,
    X for Subset of REAL;
reserve x for object, X,Y,Z for set;
 reserve M,N for Cardinal;
reserve X for non empty set,
  s for sequence of X;

theorem
  x in Segm(n+1) implies x = 0 or ... or x = n
proof
  assume
A1:  x in Segm(n+1);
  then reconsider k = x as Nat;
  k < n+1 by A1,Th32;
  then k <= n by Th13;
  hence thesis;
end;
