
theorem Th10:
  for Gs being iterative eventually-constant ManySortedSet of NAT
  for n,m being Nat st Gs.Lifespan() <= n & n <= m holds Gs.m = Gs.n
proof
  let Gs be iterative eventually-constant ManySortedSet of NAT;
  let n,m be Nat such that
A1: Gs.Lifespan() <= n and
A2: n <= m;
  Gs.(Gs.Lifespan()) = Gs.m by A1,A2,Th9,XXREAL_0:2;
  hence thesis by A1,Th9;
end;
