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58 lines
1.7 KiB
Coq
58 lines
1.7 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 Import ClassicalEpsilon.
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(* Why3 assumption *)
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Definition map (a:Type) (b:Type) := a -> b.
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Global Instance map_WhyType : forall (a:Type) {a_WT:WhyType a} (b:Type) {b_WT:WhyType b}, WhyType (map a b).
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Proof.
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intros.
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repeat split.
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exact (fun _ => why_inhabitant).
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intros x y.
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apply excluded_middle_informative.
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Qed.
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(* Why3 goal *)
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Definition set {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b} :
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(a -> b) -> a -> b -> a -> b.
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Proof.
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intros m x y.
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intros x'.
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destruct (why_decidable_eq x x') as [H|H].
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exact y.
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exact (m x').
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Defined.
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(* Why3 goal *)
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Lemma set'def {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b} :
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forall (f:a -> b) (x:a) (v:b) (y:a),
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((y = x) -> ((set f x v y) = v)) /\ (~ (y = x) -> ((set f x v y) = (f y))).
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Proof.
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intros f x v y.
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unfold set.
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case (why_decidable_eq x y).
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intros <-.
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now split.
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intros H.
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split ; intros H'.
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now elim H.
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easy.
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Qed.
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