Proof of `Paths are trees`
groundedproofs/Lax68Proofs/Relationships.lean · lax-68
What this proof establishes
no assumptions
thm✓
Lax68.PathTreeAssuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The standard path is connected. In a cycle, its greatest vertex would have two distinct neighbours below it, but a path has only one such neighbour.