lean2/library/data/finset/comb.lean
2015-04-10 17:14:10 -07:00

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/-
Copyright (c) 2015 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Module: data.finset
Author: Leonardo de Moura
Combinators for finite sets
-/
import data.finset.basic
open list quot subtype decidable perm function
namespace finset
variables {A B : Type}
variable [h : decidable_eq B]
include h
definition map (f : A → B) (s : finset A) : finset B :=
quot.lift_on s
(λ l, to_finset (list.map f (elt_of l)))
(λ l₁ l₂ p, quot.sound (perm_erase_dup_of_perm (perm_map _ p)))
theorem map_empty (f : A → B) : map f ∅ = ∅ :=
rfl
end finset