diff options
Diffstat (limited to 'theories/Numbers/Cyclic/Abstract/CyclicAxioms.v')
| -rw-r--r-- | theories/Numbers/Cyclic/Abstract/CyclicAxioms.v | 21 |
1 files changed, 14 insertions, 7 deletions
diff --git a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v index 622ef225..8b84a484 100644 --- a/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v +++ b/theories/Numbers/Cyclic/Abstract/CyclicAxioms.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -88,8 +88,12 @@ Module ZnZ. is_even : t -> bool; (* square root *) sqrt2 : t -> t -> t * carry t; - sqrt : t -> t }. - + sqrt : t -> t; + (* bitwise operations *) + lor : t -> t -> t; + land : t -> t -> t; + lxor : t -> t -> t }. + Section Specs. Context {t : Type}{ops : Ops t}. @@ -98,10 +102,10 @@ Module ZnZ. Let wB := base digits. Notation "[+| c |]" := - (interp_carry 1 wB to_Z c) (at level 0, x at level 99). + (interp_carry 1 wB to_Z c) (at level 0, c at level 99). Notation "[-| c |]" := - (interp_carry (-1) wB to_Z c) (at level 0, x at level 99). + (interp_carry (-1) wB to_Z c) (at level 0, c at level 99). Notation "[|| x ||]" := (zn2z_to_Z wB to_Z x) (at level 0, x at level 99). @@ -199,7 +203,10 @@ Module ZnZ. [||WW x y||] = [|s|] ^ 2 + [+|r|] /\ [+|r|] <= 2 * [|s|]; spec_sqrt : forall x, - [|sqrt x|] ^ 2 <= [|x|] < ([|sqrt x|] + 1) ^ 2 + [|sqrt x|] ^ 2 <= [|x|] < ([|sqrt x|] + 1) ^ 2; + spec_lor : forall x y, [|lor x y|] = Z.lor [|x|] [|y|]; + spec_land : forall x y, [|land x y|] = Z.land [|x|] [|y|]; + spec_lxor : forall x y, [|lxor x y|] = Z.lxor [|x|] [|y|] }. End Specs. @@ -283,7 +290,7 @@ Module ZnZ. intros p Hp. generalize (spec_of_pos p). case (of_pos p); intros n w1; simpl. - case n; simpl Npos; auto with zarith. + case n; auto with zarith. intros p1 Hp1; contradict Hp; apply Z.le_ngt. replace (base digits) with (1 * base digits + 0) by ring. rewrite Hp1. |