diff options
| -rw-r--r-- | CHANGES | 3 | ||||
| -rw-r--r-- | theories/Init/Logic.v | 14 | ||||
| -rw-r--r-- | theories/Logic/EqdepFacts.v | 10 | ||||
| -rw-r--r-- | theories/Vectors/VectorDef.v | 5 |
4 files changed, 19 insertions, 13 deletions
@@ -89,7 +89,8 @@ Libraries Vcons become Vector.cons. You can use notations by importing Vector.VectorNotations. - Removal of TheoryList. Requiring List instead should work most of the time. -- New syntax "rew Heq in H" and "rew <- Heq in H" for eq_rect and eq_rect_r. +- New syntax "rew Heq in H" and "rew <- Heq in H" for eq_rect and + eq_rect_r (available by importing module EqNotations). Internal infrastructure diff --git a/theories/Init/Logic.v b/theories/Init/Logic.v index 00a93efa0c..fe3f947da0 100644 --- a/theories/Init/Logic.v +++ b/theories/Init/Logic.v @@ -334,12 +334,14 @@ Section Logic_lemmas. Defined. End Logic_lemmas. -Notation "'rewrite' H 'in' H'" := (eq_rect _ _ H' _ H) - (at level 10, H' at level 9). -Notation "'rewrite' <- H 'in' H'" := (eq_rect_r _ H' H) - (at level 10, H' at level 9). -Notation "'rewrite' -> H 'in' H'" := (eq_rect _ _ H' _ H) - (at level 10, H' at level 9, only parsing). +Module EqNotations. + Notation "'rew' H 'in' H'" := (eq_rect _ _ H' _ H) + (at level 10, H' at level 10). + Notation "'rew' <- H 'in' H'" := (eq_rect_r _ H' H) + (at level 10, H' at level 10). + Notation "'rew' -> H 'in' H'" := (eq_rect _ _ H' _ H) + (at level 10, H' at level 10, only parsing). +End EqNotations. Theorem f_equal2 : forall (A1 A2 B:Type) (f:A1 -> A2 -> B) (x1 y1:A1) diff --git a/theories/Logic/EqdepFacts.v b/theories/Logic/EqdepFacts.v index 8fbd79fa49..a341a7a5a9 100644 --- a/theories/Logic/EqdepFacts.v +++ b/theories/Logic/EqdepFacts.v @@ -50,6 +50,8 @@ Table of contents: (************************************************************************) (** * Definition of dependent equality and equivalence with equality of dependent pairs *) +Import EqNotations. + Section Dependent_Equality. Variable U : Type. @@ -84,7 +86,7 @@ Section Dependent_Equality. equalities *) Inductive eq_dep1 (p:U) (x:P p) (q:U) (y:P q) : Prop := - eq_dep1_intro : forall h:q = p, x = rewrite h in y -> eq_dep1 p x q y. + eq_dep1_intro : forall h:q = p, x = rew h in y -> eq_dep1 p x q y. Lemma eq_dep1_dep : forall (p:U) (x:P p) (q:U) (y:P q), eq_dep1 p x q y -> eq_dep p x q y. @@ -164,7 +166,7 @@ Qed. Set Implicit Arguments. -Lemma eq_sigT_sig_eq : forall X P (x1 x2:X) H1 H2, existT P x1 H1 = existT P x2 H2 <-> {H:x1=x2 | rewrite H in H1 = H2}. +Lemma eq_sigT_sig_eq : forall X P (x1 x2:X) H1 H2, existT P x1 H1 = existT P x2 H2 <-> {H:x1=x2 | rew H in H1 = H2}. Proof. intros; split; intro H. - change x2 with (projT1 (existT P x2 H2)). @@ -186,7 +188,7 @@ Proof. Defined. Lemma eq_sigT_snd : - forall X P (x1 x2:X) H1 H2 (H:existT P x1 H1 = existT P x2 H2), rewrite (eq_sigT_fst H) in H1 = H2. + forall X P (x1 x2:X) H1 H2 (H:existT P x1 H1 = existT P x2 H2), rew (eq_sigT_fst H) in H1 = H2. Proof. intros. unfold eq_sigT_fst. @@ -206,7 +208,7 @@ Proof. Defined. Lemma eq_sig_snd : - forall X P (x1 x2:X) H1 H2 (H:exist P x1 H1 = exist P x2 H2), rewrite (eq_sig_fst H) in H1 = H2. + forall X P (x1 x2:X) H1 H2 (H:exist P x1 H1 = exist P x2 H2), rew (eq_sig_fst H) in H1 = H2. Proof. intros. unfold eq_sig_fst, eq_ind. diff --git a/theories/Vectors/VectorDef.v b/theories/Vectors/VectorDef.v index 9129b94de1..ad241462eb 100644 --- a/theories/Vectors/VectorDef.v +++ b/theories/Vectors/VectorDef.v @@ -18,6 +18,7 @@ have to be the same. complain if you see mistakes ... *) Require Import Arith_base. Require Vectors.Fin. +Import EqNotations. Open Local Scope nat_scope. (** @@ -202,13 +203,13 @@ Import EqdepFacts. (** This one has a better type *) Definition rev_append {A n p} (v: t A n) (w: t A p) :t A (n + p) := - rewrite <- (plus_tail_plus n p) in (rev_append_tail v w). + rew <- (plus_tail_plus n p) in (rev_append_tail v w). (** rev [a₁ ; a₂ ; .. ; an] is [an ; a{n-1} ; .. ; a₁] Caution : There is a lot of rewrite garbage in this definition *) Definition rev {A n} (v : t A n) : t A n := - rewrite <- (plus_n_O _) in (rev_append v []). + rew <- (plus_n_O _) in (rev_append v []). End BASES. Local Notation "v [@ p ]" := (nth v p) (at level 1). |