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64 lines
1.5 KiB
Coq
64 lines
1.5 KiB
Coq
(********************************************************************)
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(* *)
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(* The Why3 Verification Platform / The Why3 Development Team *)
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(* Copyright 2010-2025 -- Inria - CNRS - Paris-Saclay University *)
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(* *)
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(* This software is distributed under the terms of the GNU Lesser *)
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(* General Public License version 2.1, with the special exception *)
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(* on linking described in file LICENSE. *)
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(********************************************************************)
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(* This file is generated by Why3's Coq-realize driver *)
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(* Beware! Only edit allowed sections below *)
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Require Import BuiltIn.
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Require BuiltIn.
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Require HighOrd.
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Require int.Int.
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Require set.Fset.
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(* Why3 goal *)
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Definition elt : Type.
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Proof.
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(* TODO find something more interesting *)
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exact Z.
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Defined.
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(* Why3 goal *)
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Definition set : Type.
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Proof.
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exact (set.Fset.fset elt).
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Defined.
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(* Why3 goal *)
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Definition to_fset : set -> set.Fset.fset elt.
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Proof.
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exact (fun x => x).
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Defined.
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(* Why3 goal *)
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Definition mk : set.Fset.fset elt -> set.
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Proof.
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exact (fun x => x).
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Defined.
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(* Why3 goal *)
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Lemma mk'spec : forall (s:set.Fset.fset elt), ((to_fset (mk s)) = s).
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Proof.
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trivial.
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Qed.
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(* Why3 goal *)
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Definition choose : set -> elt.
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Proof.
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exact Fset.pick.
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Defined.
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(* Why3 goal *)
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Lemma choose'spec :
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forall (s:set), ~ set.Fset.is_empty (to_fset s) ->
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set.Fset.mem (choose s) (to_fset s).
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Proof.
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apply Fset.pick_def.
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Qed.
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