diff options
Diffstat (limited to 'theories/Arith/Between.v')
| -rw-r--r-- | theories/Arith/Between.v | 14 |
1 files changed, 10 insertions, 4 deletions
diff --git a/theories/Arith/Between.v b/theories/Arith/Between.v index 9b4071085..25d84a621 100644 --- a/theories/Arith/Between.v +++ b/theories/Arith/Between.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2017 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) Require Import Le. @@ -16,6 +18,8 @@ Implicit Types k l p q r : nat. Section Between. Variables P Q : nat -> Prop. + (** The [between] type expresses the concept + [forall i: nat, k <= i < l -> P i.]. *) Inductive between k : nat -> Prop := | bet_emp : between k k | bet_S : forall l, between k l -> P l -> between k (S l). @@ -47,6 +51,8 @@ Section Between. induction 1; auto with arith. Qed. + (** The [exists_between] type expresses the concept + [exists i: nat, k <= i < l /\ Q i]. *) Inductive exists_between k : nat -> Prop := | exists_S : forall l, exists_between k l -> exists_between k (S l) | exists_le : forall l, k <= l -> Q l -> exists_between k (S l). |