diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Logic/ClassicalDescription.v | 2 | ||||
| -rw-r--r-- | theories/Logic/ClassicalFacts.v | 4 | ||||
| -rw-r--r-- | theories/Logic/ConstructiveEpsilon.v | 4 | ||||
| -rw-r--r-- | theories/Logic/Diaconescu.v | 2 | ||||
| -rw-r--r-- | theories/Numbers/Cyclic/Abstract/NZCyclic.v | 4 | ||||
| -rw-r--r-- | theories/Program/Utils.v | 6 | ||||
| -rw-r--r-- | theories/QArith/QArith_base.v | 2 |
7 files changed, 11 insertions, 13 deletions
diff --git a/theories/Logic/ClassicalDescription.v b/theories/Logic/ClassicalDescription.v index aa65eb44c8..8555886023 100644 --- a/theories/Logic/ClassicalDescription.v +++ b/theories/Logic/ClassicalDescription.v @@ -21,7 +21,7 @@ Set Implicit Arguments. Require Export Classical. Require Import ChoiceFacts. -Notation Local "'inhabited' A" := A (at level 200, only parsing). +Notation Local inhabited A := A. Axiom constructive_definite_description : forall (A : Type) (P : A->Prop), (exists! x : A, P x) -> { x : A | P x }. diff --git a/theories/Logic/ClassicalFacts.v b/theories/Logic/ClassicalFacts.v index f3f177a734..6673fa8c96 100644 --- a/theories/Logic/ClassicalFacts.v +++ b/theories/Logic/ClassicalFacts.v @@ -119,7 +119,7 @@ Qed. *) -Definition inhabited (A:Prop) := A. +Notation Local inhabited A := A. Lemma prop_ext_A_eq_A_imp_A : prop_extensionality -> forall A:Prop, inhabited A -> (A -> A) = A. @@ -514,8 +514,6 @@ Qed. 344 of Lecture Notes in Mathematics, Springer-Verlag, 1973. *) -Notation Local "'inhabited' A" := A (at level 10, only parsing). - Definition IndependenceOfGeneralPremises := forall (A:Type) (P:A -> Prop) (Q:Prop), inhabited A -> (Q -> exists x, P x) -> exists x, Q -> P x. diff --git a/theories/Logic/ConstructiveEpsilon.v b/theories/Logic/ConstructiveEpsilon.v index fe571779ca..83d5e002aa 100644 --- a/theories/Logic/ConstructiveEpsilon.v +++ b/theories/Logic/ConstructiveEpsilon.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id:$ i*) +(*i $Id$ i*) (** This module proves the constructive description schema, which infers the sigma-existence (i.e., [Set]-existence) of a witness to a @@ -53,7 +53,7 @@ of our searching algorithm. *) Let R (x y : nat) : Prop := x = S y /\ ~ P y. -Notation Local "'acc' x" := (Acc R x) (at level 10). +Notation Local acc x := (Acc R x). Lemma P_implies_acc : forall x : nat, P x -> acc x. Proof. diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v index a954cbef7d..b96ae30e4e 100644 --- a/theories/Logic/Diaconescu.v +++ b/theories/Logic/Diaconescu.v @@ -267,7 +267,7 @@ End ProofIrrel_RelChoice_imp_EqEM. (** Proof sketch from Bell [Bell93] (with thanks to P. Castéran) *) -Notation Local "'inhabited' A" := A (at level 10, only parsing). +Notation Local inhabited A := A. Section ExtensionalEpsilon_imp_EM. diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v index 92ada3d748..125fd3f127 100644 --- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v +++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v @@ -89,8 +89,8 @@ Open Local Scope IntScope. Notation "x == y" := (NZeq x y) (at level 70) : IntScope. Notation "x ~= y" := (~ NZeq x y) (at level 70) : IntScope. Notation "0" := NZ0 : IntScope. -Notation "'S'" := NZsucc : IntScope. -Notation "'P'" := NZpred : IntScope. +Notation S x := (NZsucc x). +Notation P x := (NZpred x). (*Notation "1" := (S 0) : IntScope.*) Notation "x + y" := (NZadd x y) : IntScope. Notation "x - y" := (NZsub x y) : IntScope. diff --git a/theories/Program/Utils.v b/theories/Program/Utils.v index c4a20506c7..149901c7bb 100644 --- a/theories/Program/Utils.v +++ b/theories/Program/Utils.v @@ -42,8 +42,8 @@ Notation dec := sumbool_of_bool. (** Hide proofs and generates obligations when put in a term. *) -Notation "'in_left'" := (@left _ _ _) : program_scope. -Notation "'in_right'" := (@right _ _ _) : program_scope. +Notation in_left := (@left _ _ _). +Notation in_right := (@right _ _ _). (** Extraction directives *) (* @@ -53,4 +53,4 @@ Extract Inductive bool => "bool" [ "true" "false" ]. Extract Inductive sumbool => "bool" [ "true" "false" ]. (* Extract Inductive prod "'a" "'b" => " 'a * 'b " [ "(,)" ]. *) (* Extract Inductive sigT => "prod" [ "" ]. *) -*)
\ No newline at end of file +*) diff --git a/theories/QArith/QArith_base.v b/theories/QArith/QArith_base.v index 9ebfa19cb4..f4b57d5bed 100644 --- a/theories/QArith/QArith_base.v +++ b/theories/QArith/QArith_base.v @@ -31,7 +31,7 @@ Notation "a # b" := (Qmake a b) (at level 55, no associativity) : Q_scope. Definition inject_Z (x : Z) := Qmake x 1. Arguments Scope inject_Z [Z_scope]. -Notation " 'QDen' p " := (Zpos (Qden p)) (at level 20, no associativity) : Q_scope. +Notation QDen p := (Zpos (Qden p)). Notation " 0 " := (0#1) : Q_scope. Notation " 1 " := (1#1) : Q_scope. |
