Proof of `Set-system representation of simple graphs`
groundedproofs/Lax683916Proofs/SetSystemRepresentation.lean · lax-683916
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Edges are sent to their two-element endpoint sets, and a 2-uniform family is read back as an adjacency relation.
Proof strategy
For the graph round trip, equality of two-element sets says that their endpoints agree either directly or after swapping. For the set-system round trip, 2-uniformity writes every member uniquely as a pair of distinct elements.
Attribution
Direct elementary correspondence between graph edges and two-element sets.