swh:1:snp:04e159a4411e97cbe416dcf21d082639f654120b
Tip revision: b40d073921a3c81ad7091006d32daeb51725fc76 authored by Adrien Koutsos on 28 June 2021, 12:17:13 UTC
fixed PKE
fixed PKE
Tip revision: b40d073
FinType.eca
(* --------------------------------------------------------------------
* Copyright (c) - 2012--2016 - IMDEA Software Institute
* Copyright (c) - 2012--2018 - Inria
* Copyright (c) - 2012--2018 - Ecole Polytechnique
*
* Distributed under the terms of the CeCILL-B-V1 license
* -------------------------------------------------------------------- *)
(* -------------------------------------------------------------------- *)
require import AllCore List.
(* -------------------------------------------------------------------- *)
type t.
op enum : t list.
op card : int = size enum.
axiom enum_spec : forall x, count (pred1 x) enum = 1.
(* -------------------------------------------------------------------- *)
lemma enumP : forall x, mem enum x.
proof.
move=> x; have: 0 < count (pred1 x) enum by rewrite enum_spec.
by move/has_count/hasP; case=> y [h @/pred1 <-].
qed.
lemma enum_uniq : uniq enum.
proof. by apply/count_mem_uniq=> x; rewrite enumP enum_spec. qed.
lemma card_gt0 : 0 < card.
proof.
rewrite /card; have: mem enum witness by rewrite enumP.
by case: enum=> //= x s _; rewrite addzC ltzS size_ge0.
qed.
lemma count_mem xs :
uniq xs => count (mem xs) enum = size xs.
proof.
move=> eq_xs; rewrite count_swap // 1:&(enum_uniq).
by rewrite count_predT_eq // &(enumP).
qed.