Theorem refldivcl

Description: The floor function of a division of a real number by a positive real number is a real number. (Contributed by Alexander van der Vekens, 14-Apr-2018)

	Ref	Expression
Assertion	refldivcl	⊢ ( ( 𝐾 ∈ ℝ ∧ 𝐿 ∈ ℝ+ ) → ( ⌊ ‘ ( 𝐾 / 𝐿 ) ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		rerpdivcl	⊢ ( ( 𝐾 ∈ ℝ ∧ 𝐿 ∈ ℝ+ ) → ( 𝐾 / 𝐿 ) ∈ ℝ )
2		reflcl	⊢ ( ( 𝐾 / 𝐿 ) ∈ ℝ → ( ⌊ ‘ ( 𝐾 / 𝐿 ) ) ∈ ℝ )
3	1 2	syl	⊢ ( ( 𝐾 ∈ ℝ ∧ 𝐿 ∈ ℝ+ ) → ( ⌊ ‘ ( 𝐾 / 𝐿 ) ) ∈ ℝ )