Theorem erclwwlknrel

Description: .~ is a relation. (Contributed by Alexander van der Vekens, 25-Mar-2018) (Revised by AV, 30-Apr-2021)

	Ref	Expression
Hypotheses	erclwwlkn.w	⊢ 𝑊 = ( 𝑁 ClWWalksN 𝐺 )
	erclwwlkn.r	⊢ ∼ = { ⟨ 𝑡 , 𝑢 ⟩ ∣ ( 𝑡 ∈ 𝑊 ∧ 𝑢 ∈ 𝑊 ∧ ∃ 𝑛 ∈ ( 0 ... 𝑁 ) 𝑡 = ( 𝑢 cyclShift 𝑛 ) ) }
Assertion	erclwwlknrel	⊢ Rel ∼

Proof

Step	Hyp	Ref	Expression
1		erclwwlkn.w	⊢ 𝑊 = ( 𝑁 ClWWalksN 𝐺 )
2		erclwwlkn.r	⊢ ∼ = { ⟨ 𝑡 , 𝑢 ⟩ ∣ ( 𝑡 ∈ 𝑊 ∧ 𝑢 ∈ 𝑊 ∧ ∃ 𝑛 ∈ ( 0 ... 𝑁 ) 𝑡 = ( 𝑢 cyclShift 𝑛 ) ) }
3	2	relopabi	⊢ Rel ∼