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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
Views: 18536
License: APACHE
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/-
Copyright (c) 2019 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Simon Hudon
-/

import data.equiv.basic

universes u v

variables {α β : Type u} {f : Type u → Type v} [functor f] [is_lawful_functor f]
open functor equiv function is_lawful_functor

def functor.map_equiv (h : α ≃ β) : f α ≃ f β :=
{ to_fun    := map h,
  inv_fun   := map h.symm,
  left_inv  := λ x,
    by { rw map_map, convert is_lawful_functor.id_map x, ext a, apply symm_apply_apply },
  right_inv := λ x,
    by { rw map_map, convert is_lawful_functor.id_map x, ext a, apply apply_symm_apply } }