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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".

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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 } }