Description: A trail is a walk. (Contributed by Alexander van der Vekens, 20-Oct-2017) (Revised by AV, 7-Jan-2021) (Proof shortened by AV, 29-Oct-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | trliswlk | ⊢ ( 𝐹 ( Trails ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | istrl | ⊢ ( 𝐹 ( Trails ‘ 𝐺 ) 𝑃 ↔ ( 𝐹 ( Walks ‘ 𝐺 ) 𝑃 ∧ Fun ◡ 𝐹 ) ) | |
| 2 | 1 | simplbi | ⊢ ( 𝐹 ( Trails ‘ 𝐺 ) 𝑃 → 𝐹 ( Walks ‘ 𝐺 ) 𝑃 ) |