Theorems · Theorem · combinatorics

Graph.ext

∀ {α : Type u_1} {β : Type u_2} {G₁ G₂ : Graph α β},
  G₁.vertexSet = G₂.vertexSet → (∀ (e : β) (x y : α), G₁.IsLink e x y ↔ G₂.IsLink e x y) → G₁ = G₂

Two graphs with the same vertex set and binary incidences are equal. (We use this as the default extensionality lemma rather than adding @[ext] to the definition of Graph, so it doesn't require equality of the edge sets.)

Defined in

Mathlib.Combinatorics.Graph.Basic

Cited by

10 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Quot.sound