diff options
Diffstat (limited to 'theories/Init/Peano.v')
| -rw-r--r-- | theories/Init/Peano.v | 34 |
1 files changed, 19 insertions, 15 deletions
diff --git a/theories/Init/Peano.v b/theories/Init/Peano.v index 6c4a6350..d5322d09 100644 --- a/theories/Init/Peano.v +++ b/theories/Init/Peano.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* * 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) *) (************************************************************************) (** The type [nat] of Peano natural numbers (built from [O] and [S]) @@ -37,7 +39,7 @@ Hint Resolve f_equal_nat: core. (** The predecessor function *) -Notation pred := Nat.pred (compat "8.4"). +Notation pred := Nat.pred (only parsing). Definition f_equal_pred := f_equal pred. @@ -79,7 +81,7 @@ Hint Resolve n_Sn: core. (** Addition *) -Notation plus := Nat.add (compat "8.4"). +Notation plus := Nat.add (only parsing). Infix "+" := Nat.add : nat_scope. Definition f_equal2_plus := f_equal2 plus. @@ -90,7 +92,9 @@ Lemma plus_n_O : forall n:nat, n = n + 0. Proof. induction n; simpl; auto. Qed. -Hint Resolve plus_n_O: core. + +Remove Hints eq_refl : core. +Hint Resolve plus_n_O eq_refl: core. (* We want eq_refl to have higher priority than plus_n_O *) Lemma plus_O_n : forall n:nat, 0 + n = n. Proof. @@ -110,12 +114,12 @@ Qed. (** Standard associated names *) -Notation plus_0_r_reverse := plus_n_O (compat "8.2"). -Notation plus_succ_r_reverse := plus_n_Sm (compat "8.2"). +Notation plus_0_r_reverse := plus_n_O (only parsing). +Notation plus_succ_r_reverse := plus_n_Sm (only parsing). (** Multiplication *) -Notation mult := Nat.mul (compat "8.4"). +Notation mult := Nat.mul (only parsing). Infix "*" := Nat.mul : nat_scope. Definition f_equal2_mult := f_equal2 mult. @@ -137,12 +141,12 @@ Hint Resolve mult_n_Sm: core. (** Standard associated names *) -Notation mult_0_r_reverse := mult_n_O (compat "8.2"). -Notation mult_succ_r_reverse := mult_n_Sm (compat "8.2"). +Notation mult_0_r_reverse := mult_n_O (only parsing). +Notation mult_succ_r_reverse := mult_n_Sm (only parsing). (** Truncated subtraction: [m-n] is [0] if [n>=m] *) -Notation minus := Nat.sub (compat "8.4"). +Notation minus := Nat.sub (only parsing). Infix "-" := Nat.sub : nat_scope. (** Definition of the usual orders, the basic properties of [le] and [lt] @@ -219,8 +223,8 @@ Qed. (** Maximum and minimum : definitions and specifications *) -Notation max := Nat.max (compat "8.4"). -Notation min := Nat.min (compat "8.4"). +Notation max := Nat.max (only parsing). +Notation min := Nat.min (only parsing). Lemma max_l n m : m <= n -> Nat.max n m = n. Proof. |