This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: The length of a word representing a closed walk of a fixed length is this
fixed length. (Contributed by AV, 22-Mar-2022)
|
|
Ref |
Expression |
|
Assertion |
clwwlknlen |
⊢ ( 𝑊 ∈ ( 𝑁 ClWWalksN 𝐺 ) → ( ♯ ‘ 𝑊 ) = 𝑁 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
isclwwlkn |
⊢ ( 𝑊 ∈ ( 𝑁 ClWWalksN 𝐺 ) ↔ ( 𝑊 ∈ ( ClWWalks ‘ 𝐺 ) ∧ ( ♯ ‘ 𝑊 ) = 𝑁 ) ) |
| 2 |
1
|
simprbi |
⊢ ( 𝑊 ∈ ( 𝑁 ClWWalksN 𝐺 ) → ( ♯ ‘ 𝑊 ) = 𝑁 ) |