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42 lines
1.4 KiB
Coq
42 lines
1.4 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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Lemma function_extensionality:
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forall A B (f g : A -> B),
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(forall x, f x = g x) -> f = g.
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Admitted.
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(* Why3 assumption *)
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Definition infix_eqeq {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b}
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(m1:a -> b) (m2:a -> b) : Prop :=
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forall (x:a), ((m1 x) = (m2 x)).
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Notation "x == y" := (infix_eqeq x y) (at level 70, no associativity).
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(* Why3 goal *)
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Lemma extensionality {a:Type} {a_WT:WhyType a} {b:Type} {b_WT:WhyType b} :
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forall (m1:a -> b) (m2:a -> b), infix_eqeq m1 m2 -> (m1 = m2).
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Proof.
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intros m1 m2 h1.
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apply function_extensionality.
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intros x.
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generalize (h1 x).
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easy.
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Qed.
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