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-rw-r--r--theories/Numbers/Rational/BigQ/BigQ.v11
-rw-r--r--theories/Numbers/Rational/BigQ/QMake.v28
-rw-r--r--theories/Numbers/Rational/SpecViaQ/QSig.v4
3 files changed, 21 insertions, 22 deletions
diff --git a/theories/Numbers/Rational/BigQ/BigQ.v b/theories/Numbers/Rational/BigQ/BigQ.v
index 8a90cacd..b64cfb64 100644
--- a/theories/Numbers/Rational/BigQ/BigQ.v
+++ b/theories/Numbers/Rational/BigQ/BigQ.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 *)
@@ -33,14 +33,13 @@ Module BigN_BigZ <: NType_ZType BigN.BigN BigZ.
Qed.
End BigN_BigZ.
-(** This allows to build [BigQ] out of [BigN] and [BigQ] via [QMake] *)
+(** This allows building [BigQ] out of [BigN] and [BigQ] via [QMake] *)
Delimit Scope bigQ_scope with bigQ.
Module BigQ <: QType <: OrderedTypeFull <: TotalOrder.
- Include QMake.Make BigN BigZ BigN_BigZ [scope abstract_scope to bigQ_scope].
- Bind Scope bigQ_scope with t t_.
- Include !QProperties <+ HasEqBool2Dec
+ Include QMake.Make BigN BigZ BigN_BigZ
+ <+ !QProperties <+ HasEqBool2Dec
<+ !MinMaxLogicalProperties <+ !MinMaxDecProperties.
Ltac order := Private_Tac.order.
End BigQ.
@@ -89,6 +88,8 @@ exact BigQ.add_opp_diag_r. exact BigQ.neq_1_0.
exact BigQ.div_mul_inv. exact BigQ.mul_inv_diag_l.
Qed.
+Declare Equivalent Keys pow_N pow_pos.
+
Lemma BigQpowerth :
power_theory 1 BigQ.mul BigQ.eq Z.of_N BigQ.power.
Proof.
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.
diff --git a/theories/Numbers/Rational/SpecViaQ/QSig.v b/theories/Numbers/Rational/SpecViaQ/QSig.v
index 67a5f673..5f831bfc 100644
--- a/theories/Numbers/Rational/SpecViaQ/QSig.v
+++ b/theories/Numbers/Rational/SpecViaQ/QSig.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 *)
@@ -104,7 +104,7 @@ Ltac qify := unfold eq, lt, le in *; autorewrite with qsimpl;
try rewrite spec_0 in *; try rewrite spec_1 in *; try rewrite spec_m1 in *.
(** NB: do not add [spec_0] in the autorewrite database. Otherwise,
- after instanciation in BigQ, this lemma become convertible to 0=0,
+ after instantiation in BigQ, this lemma become convertible to 0=0,
and autorewrite loops. Idem for [spec_1] and [spec_m1] *)
(** Morphisms *)
generated by cgit v1.2.3 (git 2.39.1) at 2024-06-06 16:51:43 +0000