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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".

Project: Xena
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/-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.category

/-!
The category of types with binary relations as morphisms.
-/

namespace category_theory

universe u

/-- A type synonym for `Type`, which carries the category instance for which
    morphisms are binary relations. -/
def Rel := Type u

instance Rel.inhabited : inhabited Rel := by unfold Rel; apply_instance

/-- The category of types with binary relations as morphisms. -/
-- We must work in `Type u` rather than `Sort u`, because
-- `X → Y → Prop` is in `Sort (max u 1)`.
instance rel : large_category Rel.{u} :=
{ hom  := λ X Y, X → Y → Prop,
  id   := λ X, λ x y, x = y,
  comp := λ X Y Z f g x z, ∃ y, f x y ∧ g y z }

end category_theory