reserve
  a for natural Number,
  k,l,m,n,k1,b,c,i for Nat,
  x,y,z,y1,y2 for object,
  X,Y for set,
  f,g for Function;

theorem Th1:
  for a,b being natural Number holds a in Seg b iff 1 <= a & a <= b
proof
  let a,b be natural Number;
A1: a is Nat & b is Nat by TARSKI:1;
  a in { m where m is Nat: 1 <= m & m <= b } iff
  ex m being Nat st a = m & 1 <= m & m <= b;
  hence thesis by A1;
end;
