Relation_both_Symmetric_and_Asymmetric_is_Null
Provedproofwikisymmetric-relations
Let R be a relation on S which is both symmetric and asymmetric. Then R is the null relation.
Preamble
import Mathlib.Data.Set.Basic
Formal statement
theorem Relation_both_Symmetric_and_Asymmetric_is_Null {α : Type _} (R : α → α → Prop) (hSym : ∀ x y, R x y → R y x) (hAsym : ∀ x y, R x y → ¬ R y x) : ∀ x y, ¬ R x y := by sorrySource