diff options
Diffstat (limited to 'theories/ZArith/Znat.v')
| -rw-r--r-- | theories/ZArith/Znat.v | 126 |
1 files changed, 64 insertions, 62 deletions
diff --git a/theories/ZArith/Znat.v b/theories/ZArith/Znat.v index 06428a7c..5c960da1 100644 --- a/theories/ZArith/Znat.v +++ b/theories/ZArith/Znat.v @@ -1,10 +1,12 @@ (* -*- coding: utf-8 -*- *) (************************************************************************) -(* 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) *) (************************************************************************) (** Binary Integers (Pierre Crégut, CNET, Lannion, France) *) @@ -951,65 +953,65 @@ Definition inj_gt n m := proj1 (Nat2Z.inj_gt n m). (** For the others, a Notation is fine *) -Notation inj_0 := Nat2Z.inj_0 (compat "8.3"). -Notation inj_S := Nat2Z.inj_succ (compat "8.3"). -Notation inj_compare := Nat2Z.inj_compare (compat "8.3"). -Notation inj_eq_rev := Nat2Z.inj (compat "8.3"). -Notation inj_eq_iff := (fun n m => iff_sym (Nat2Z.inj_iff n m)) (compat "8.3"). -Notation inj_le_iff := Nat2Z.inj_le (compat "8.3"). -Notation inj_lt_iff := Nat2Z.inj_lt (compat "8.3"). -Notation inj_ge_iff := Nat2Z.inj_ge (compat "8.3"). -Notation inj_gt_iff := Nat2Z.inj_gt (compat "8.3"). -Notation inj_le_rev := (fun n m => proj2 (Nat2Z.inj_le n m)) (compat "8.3"). -Notation inj_lt_rev := (fun n m => proj2 (Nat2Z.inj_lt n m)) (compat "8.3"). -Notation inj_ge_rev := (fun n m => proj2 (Nat2Z.inj_ge n m)) (compat "8.3"). -Notation inj_gt_rev := (fun n m => proj2 (Nat2Z.inj_gt n m)) (compat "8.3"). -Notation inj_plus := Nat2Z.inj_add (compat "8.3"). -Notation inj_mult := Nat2Z.inj_mul (compat "8.3"). -Notation inj_minus1 := Nat2Z.inj_sub (compat "8.3"). -Notation inj_minus := Nat2Z.inj_sub_max (compat "8.3"). -Notation inj_min := Nat2Z.inj_min (compat "8.3"). -Notation inj_max := Nat2Z.inj_max (compat "8.3"). - -Notation Z_of_nat_of_P := positive_nat_Z (compat "8.3"). +Notation inj_0 := Nat2Z.inj_0 (only parsing). +Notation inj_S := Nat2Z.inj_succ (only parsing). +Notation inj_compare := Nat2Z.inj_compare (only parsing). +Notation inj_eq_rev := Nat2Z.inj (only parsing). +Notation inj_eq_iff := (fun n m => iff_sym (Nat2Z.inj_iff n m)) (only parsing). +Notation inj_le_iff := Nat2Z.inj_le (only parsing). +Notation inj_lt_iff := Nat2Z.inj_lt (only parsing). +Notation inj_ge_iff := Nat2Z.inj_ge (only parsing). +Notation inj_gt_iff := Nat2Z.inj_gt (only parsing). +Notation inj_le_rev := (fun n m => proj2 (Nat2Z.inj_le n m)) (only parsing). +Notation inj_lt_rev := (fun n m => proj2 (Nat2Z.inj_lt n m)) (only parsing). +Notation inj_ge_rev := (fun n m => proj2 (Nat2Z.inj_ge n m)) (only parsing). +Notation inj_gt_rev := (fun n m => proj2 (Nat2Z.inj_gt n m)) (only parsing). +Notation inj_plus := Nat2Z.inj_add (only parsing). +Notation inj_mult := Nat2Z.inj_mul (only parsing). +Notation inj_minus1 := Nat2Z.inj_sub (only parsing). +Notation inj_minus := Nat2Z.inj_sub_max (only parsing). +Notation inj_min := Nat2Z.inj_min (only parsing). +Notation inj_max := Nat2Z.inj_max (only parsing). + +Notation Z_of_nat_of_P := positive_nat_Z (only parsing). Notation Zpos_eq_Z_of_nat_o_nat_of_P := - (fun p => eq_sym (positive_nat_Z p)) (compat "8.3"). - -Notation Z_of_nat_of_N := N_nat_Z (compat "8.3"). -Notation Z_of_N_of_nat := nat_N_Z (compat "8.3"). - -Notation Z_of_N_eq := (f_equal Z.of_N) (compat "8.3"). -Notation Z_of_N_eq_rev := N2Z.inj (compat "8.3"). -Notation Z_of_N_eq_iff := (fun n m => iff_sym (N2Z.inj_iff n m)) (compat "8.3"). -Notation Z_of_N_compare := N2Z.inj_compare (compat "8.3"). -Notation Z_of_N_le_iff := N2Z.inj_le (compat "8.3"). -Notation Z_of_N_lt_iff := N2Z.inj_lt (compat "8.3"). -Notation Z_of_N_ge_iff := N2Z.inj_ge (compat "8.3"). -Notation Z_of_N_gt_iff := N2Z.inj_gt (compat "8.3"). -Notation Z_of_N_le := (fun n m => proj1 (N2Z.inj_le n m)) (compat "8.3"). -Notation Z_of_N_lt := (fun n m => proj1 (N2Z.inj_lt n m)) (compat "8.3"). -Notation Z_of_N_ge := (fun n m => proj1 (N2Z.inj_ge n m)) (compat "8.3"). -Notation Z_of_N_gt := (fun n m => proj1 (N2Z.inj_gt n m)) (compat "8.3"). -Notation Z_of_N_le_rev := (fun n m => proj2 (N2Z.inj_le n m)) (compat "8.3"). -Notation Z_of_N_lt_rev := (fun n m => proj2 (N2Z.inj_lt n m)) (compat "8.3"). -Notation Z_of_N_ge_rev := (fun n m => proj2 (N2Z.inj_ge n m)) (compat "8.3"). -Notation Z_of_N_gt_rev := (fun n m => proj2 (N2Z.inj_gt n m)) (compat "8.3"). -Notation Z_of_N_pos := N2Z.inj_pos (compat "8.3"). -Notation Z_of_N_abs := N2Z.inj_abs_N (compat "8.3"). -Notation Z_of_N_le_0 := N2Z.is_nonneg (compat "8.3"). -Notation Z_of_N_plus := N2Z.inj_add (compat "8.3"). -Notation Z_of_N_mult := N2Z.inj_mul (compat "8.3"). -Notation Z_of_N_minus := N2Z.inj_sub_max (compat "8.3"). -Notation Z_of_N_succ := N2Z.inj_succ (compat "8.3"). -Notation Z_of_N_min := N2Z.inj_min (compat "8.3"). -Notation Z_of_N_max := N2Z.inj_max (compat "8.3"). -Notation Zabs_of_N := Zabs2N.id (compat "8.3"). -Notation Zabs_N_succ_abs := Zabs2N.inj_succ_abs (compat "8.3"). -Notation Zabs_N_succ := Zabs2N.inj_succ (compat "8.3"). -Notation Zabs_N_plus_abs := Zabs2N.inj_add_abs (compat "8.3"). -Notation Zabs_N_plus := Zabs2N.inj_add (compat "8.3"). -Notation Zabs_N_mult_abs := Zabs2N.inj_mul_abs (compat "8.3"). -Notation Zabs_N_mult := Zabs2N.inj_mul (compat "8.3"). + (fun p => eq_sym (positive_nat_Z p)) (only parsing). + +Notation Z_of_nat_of_N := N_nat_Z (only parsing). +Notation Z_of_N_of_nat := nat_N_Z (only parsing). + +Notation Z_of_N_eq := (f_equal Z.of_N) (only parsing). +Notation Z_of_N_eq_rev := N2Z.inj (only parsing). +Notation Z_of_N_eq_iff := (fun n m => iff_sym (N2Z.inj_iff n m)) (only parsing). +Notation Z_of_N_compare := N2Z.inj_compare (only parsing). +Notation Z_of_N_le_iff := N2Z.inj_le (only parsing). +Notation Z_of_N_lt_iff := N2Z.inj_lt (only parsing). +Notation Z_of_N_ge_iff := N2Z.inj_ge (only parsing). +Notation Z_of_N_gt_iff := N2Z.inj_gt (only parsing). +Notation Z_of_N_le := (fun n m => proj1 (N2Z.inj_le n m)) (only parsing). +Notation Z_of_N_lt := (fun n m => proj1 (N2Z.inj_lt n m)) (only parsing). +Notation Z_of_N_ge := (fun n m => proj1 (N2Z.inj_ge n m)) (only parsing). +Notation Z_of_N_gt := (fun n m => proj1 (N2Z.inj_gt n m)) (only parsing). +Notation Z_of_N_le_rev := (fun n m => proj2 (N2Z.inj_le n m)) (only parsing). +Notation Z_of_N_lt_rev := (fun n m => proj2 (N2Z.inj_lt n m)) (only parsing). +Notation Z_of_N_ge_rev := (fun n m => proj2 (N2Z.inj_ge n m)) (only parsing). +Notation Z_of_N_gt_rev := (fun n m => proj2 (N2Z.inj_gt n m)) (only parsing). +Notation Z_of_N_pos := N2Z.inj_pos (only parsing). +Notation Z_of_N_abs := N2Z.inj_abs_N (only parsing). +Notation Z_of_N_le_0 := N2Z.is_nonneg (only parsing). +Notation Z_of_N_plus := N2Z.inj_add (only parsing). +Notation Z_of_N_mult := N2Z.inj_mul (only parsing). +Notation Z_of_N_minus := N2Z.inj_sub_max (only parsing). +Notation Z_of_N_succ := N2Z.inj_succ (only parsing). +Notation Z_of_N_min := N2Z.inj_min (only parsing). +Notation Z_of_N_max := N2Z.inj_max (only parsing). +Notation Zabs_of_N := Zabs2N.id (only parsing). +Notation Zabs_N_succ_abs := Zabs2N.inj_succ_abs (only parsing). +Notation Zabs_N_succ := Zabs2N.inj_succ (only parsing). +Notation Zabs_N_plus_abs := Zabs2N.inj_add_abs (only parsing). +Notation Zabs_N_plus := Zabs2N.inj_add (only parsing). +Notation Zabs_N_mult_abs := Zabs2N.inj_mul_abs (only parsing). +Notation Zabs_N_mult := Zabs2N.inj_mul (only parsing). Theorem inj_minus2 : forall n m:nat, (m > n)%nat -> Z.of_nat (n - m) = 0. Proof. |