diff options
Diffstat (limited to 'theories/Numbers/Rational/BigQ/QMake.v')
| -rw-r--r-- | theories/Numbers/Rational/BigQ/QMake.v | 28 |
1 files changed, 13 insertions, 15 deletions
diff --git a/theories/Numbers/Rational/BigQ/QMake.v b/theories/Numbers/Rational/BigQ/QMake.v index e2f53e12..c11e07fa 100644 --- a/theories/Numbers/Rational/BigQ/QMake.v +++ b/theories/Numbers/Rational/BigQ/QMake.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 *) @@ -39,8 +39,6 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. Definition t := t_. - Bind Scope abstract_scope with t t_. - (** Specification with respect to [QArith] *) Local Open Scope Q_scope. @@ -629,7 +627,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. assert (Hz := spec_irred_zero nx dy). assert (Hz':= spec_irred_zero ny dx). destruct irred as (n1,d1); destruct irred as (n2,d2). - simpl snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2']. + simpl @snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2']. rewrite spec_norm_denum. qsimpl. @@ -667,7 +665,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. assert (Hgc := strong_spec_irred nx dy). assert (Hgc' := strong_spec_irred ny dx). destruct irred as (n1,d1); destruct irred as (n2,d2). - simpl snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2']. + simpl @snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2']. unfold norm_denum; qsimpl. @@ -1033,7 +1031,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. Definition of_Qc q := of_Q (this q). - Definition to_Qc q := !! [q]. + Definition to_Qc q := Q2Qc [q]. Notation "[[ x ]]" := (to_Qc x). @@ -1085,7 +1083,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[add x y]] = [[x]] + [[y]]. Proof. unfold to_Qc. - transitivity (!! ([x] + [y])). + transitivity (Q2Qc ([x] + [y])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_add; auto. @@ -1099,7 +1097,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[add_norm x y]] = [[x]] + [[y]]. Proof. unfold to_Qc. - transitivity (!! ([x] + [y])). + transitivity (Q2Qc ([x] + [y])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_add_norm; auto. @@ -1147,7 +1145,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[mul x y]] = [[x]] * [[y]]. Proof. unfold to_Qc. - transitivity (!! ([x] * [y])). + transitivity (Q2Qc ([x] * [y])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_mul; auto. @@ -1161,7 +1159,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[mul_norm x y]] = [[x]] * [[y]]. Proof. unfold to_Qc. - transitivity (!! ([x] * [y])). + transitivity (Q2Qc ([x] * [y])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_mul_norm; auto. @@ -1185,7 +1183,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[inv x]] = /[[x]]. Proof. unfold to_Qc. - transitivity (!! (/[x])). + transitivity (Q2Qc (/[x])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_inv; auto. @@ -1199,7 +1197,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[inv_norm x]] = /[[x]]. Proof. unfold to_Qc. - transitivity (!! (/[x])). + transitivity (Q2Qc (/[x])). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_inv_norm; auto. @@ -1247,12 +1245,12 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. Theorem spec_squarec x: [[square x]] = [[x]]^2. Proof. unfold to_Qc. - transitivity (!! ([x]^2)). + transitivity (Q2Qc ([x]^2)). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_square; auto. simpl Qcpower. - replace (!! [x] * 1) with (!![x]); try ring. + replace (Q2Qc [x] * 1) with (Q2Qc [x]); try ring. simpl. unfold Qcmult, Q2Qc. apply Qc_decomp; intros _ _; unfold this. @@ -1264,7 +1262,7 @@ Module Make (NN:NType)(ZZ:ZType)(Import NZ:NType_ZType NN ZZ) <: QType. [[power_pos x p]] = [[x]] ^ Pos.to_nat p. Proof. unfold to_Qc. - transitivity (!! ([x]^Zpos p)). + transitivity (Q2Qc ([x]^Zpos p)). unfold Q2Qc. apply Qc_decomp; intros _ _; unfold this. apply Qred_complete; apply spec_power_pos; auto. |