Theorem limsupcli

Description: Closure of the superior limit. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	limsupcli.1	⊢ 𝐹 ∈ 𝑉
Assertion	limsupcli	⊢ ( lim sup ‘ 𝐹 ) ∈ ℝ*

Proof

Step	Hyp	Ref	Expression
1		limsupcli.1	⊢ 𝐹 ∈ 𝑉
2		limsupcl	⊢ ( 𝐹 ∈ 𝑉 → ( lim sup ‘ 𝐹 ) ∈ ℝ* )
3	1 2	ax-mp	⊢ ( lim sup ‘ 𝐹 ) ∈ ℝ*