renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / tdeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq.ma
index 52784b53fa8dca6d6a61718bc8681dc2e51f8017..d431b7677a55bd28dc55f1e47578c4c7d06cbcd9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq.ma
@@ -12,9 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeq_4.ma".
+include "basic_2/notation/relations/stareq_4.ma".
 include "basic_2/syntax/item_sd.ma".
-include "basic_2/syntax/lenv.ma".
+include "basic_2/syntax/term.ma".
 
 (* DEGREE-BASED EQUIVALENCE ON TERMS ****************************************)
 
@@ -26,15 +26,12 @@ inductive tdeq (h) (o): relation term ≝
 .
 
 interpretation
-   "degree-based equivalence (terms)"
-   'LazyEq h o T1 T2 = (tdeq h o T1 T2).
-
-definition cdeq: ∀h. sd h → relation3 lenv term term ≝
-                 λh,o,L. tdeq h o.
+   "context-free degree-based equivalence (term)"
+   'StarEq h o T1 T2 = (tdeq h o T1 T2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact tdeq_inv_sort1_aux: â\88\80h,o,X,Y. X â\89¡[h, o] Y → ∀s1. X = ⋆s1 →
+fact tdeq_inv_sort1_aux: â\88\80h,o,X,Y. X â\89\9b[h, o] Y → ∀s1. X = ⋆s1 →
                          ∃∃s2,d. deg h o s1 d & deg h o s2 d & Y = ⋆s2.
 #h #o #X #Y * -X -Y
 [ #s1 #s2 #d #Hs1 #Hs2 #s #H destruct /2 width=5 by ex3_2_intro/
@@ -44,32 +41,32 @@ fact tdeq_inv_sort1_aux: ∀h,o,X,Y. X ≡[h, o] Y → ∀s1. X = ⋆s1 →
 ]
 qed-.
 
-lemma tdeq_inv_sort1: â\88\80h,o,Y,s1. â\8b\86s1 â\89¡[h, o] Y →
+lemma tdeq_inv_sort1: â\88\80h,o,Y,s1. â\8b\86s1 â\89\9b[h, o] Y →
                       ∃∃s2,d. deg h o s1 d & deg h o s2 d & Y = ⋆s2.
 /2 width=3 by tdeq_inv_sort1_aux/ qed-.
 
-fact tdeq_inv_lref1_aux: â\88\80h,o,X,Y. X â\89¡[h, o] Y → ∀i. X = #i → Y = #i.
+fact tdeq_inv_lref1_aux: â\88\80h,o,X,Y. X â\89\9b[h, o] Y → ∀i. X = #i → Y = #i.
 #h #o #X #Y * -X -Y //
 [ #s1 #s2 #d #_ #_ #j #H destruct
 | #I #V1 #V2 #T1 #T2 #_ #_ #j #H destruct
 ]
 qed-.
 
-lemma tdeq_inv_lref1: â\88\80h,o,Y,i. #i â\89¡[h, o] Y → Y = #i.
+lemma tdeq_inv_lref1: â\88\80h,o,Y,i. #i â\89\9b[h, o] Y → Y = #i.
 /2 width=5 by tdeq_inv_lref1_aux/ qed-.
 
-fact tdeq_inv_gref1_aux: â\88\80h,o,X,Y. X â\89¡[h, o] Y → ∀l. X = §l → Y = §l.
+fact tdeq_inv_gref1_aux: â\88\80h,o,X,Y. X â\89\9b[h, o] Y → ∀l. X = §l → Y = §l.
 #h #o #X #Y * -X -Y //
 [ #s1 #s2 #d #_ #_ #k #H destruct
 | #I #V1 #V2 #T1 #T2 #_ #_ #k #H destruct
 ]
 qed-.
 
-lemma tdeq_inv_gref1: â\88\80h,o,Y,l. §l â\89¡[h, o] Y → Y = §l.
+lemma tdeq_inv_gref1: â\88\80h,o,Y,l. §l â\89\9b[h, o] Y → Y = §l.
 /2 width=5 by tdeq_inv_gref1_aux/ qed-.
 
-fact tdeq_inv_pair1_aux: â\88\80h,o,X,Y. X â\89¡[h, o] Y → ∀I,V1,T1. X = ②{I}V1.T1 →
-                         â\88\83â\88\83V2,T2. V1 â\89¡[h, o] V2 & T1 â\89¡[h, o] T2 & Y = ②{I}V2.T2.
+fact tdeq_inv_pair1_aux: â\88\80h,o,X,Y. X â\89\9b[h, o] Y → ∀I,V1,T1. X = ②{I}V1.T1 →
+                         â\88\83â\88\83V2,T2. V1 â\89\9b[h, o] V2 & T1 â\89\9b[h, o] T2 & Y = ②{I}V2.T2.
 #h #o #X #Y * -X -Y
 [ #s1 #s2 #d #_ #_ #J #W1 #U1 #H destruct
 | #i #J #W1 #U1 #H destruct
@@ -78,19 +75,19 @@ fact tdeq_inv_pair1_aux: ∀h,o,X,Y. X ≡[h, o] Y → ∀I,V1,T1. X = ②{I}V1.
 ]
 qed-.
 
-lemma tdeq_inv_pair1: â\88\80h,o,I,V1,T1,Y. â\91¡{I}V1.T1 â\89¡[h, o] Y →
-                      â\88\83â\88\83V2,T2. V1 â\89¡[h, o] V2 & T1 â\89¡[h, o] T2 & Y = ②{I}V2.T2.
+lemma tdeq_inv_pair1: â\88\80h,o,I,V1,T1,Y. â\91¡{I}V1.T1 â\89\9b[h, o] Y →
+                      â\88\83â\88\83V2,T2. V1 â\89\9b[h, o] V2 & T1 â\89\9b[h, o] T2 & Y = ②{I}V2.T2.
 /2 width=3 by tdeq_inv_pair1_aux/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma tdeq_inv_sort1_deg: â\88\80h,o,Y,s1. â\8b\86s1 â\89¡[h, o] Y → ∀d. deg h o s1 d →
+lemma tdeq_inv_sort1_deg: â\88\80h,o,Y,s1. â\8b\86s1 â\89\9b[h, o] Y → ∀d. deg h o s1 d →
                           ∃∃s2. deg h o s2 d & Y = ⋆s2.
 #h #o #Y #s1 #H #d #Hs1 elim (tdeq_inv_sort1 … H) -H
 #s2 #x #Hx <(deg_mono h o … Hx … Hs1) -s1 -d /2 width=3 by ex2_intro/
 qed-.
 
-lemma tdeq_inv_sort_deg: â\88\80h,o,s1,s2. â\8b\86s1 â\89¡[h, o] ⋆s2 →
+lemma tdeq_inv_sort_deg: â\88\80h,o,s1,s2. â\8b\86s1 â\89\9b[h, o] ⋆s2 →
                          ∀d1,d2. deg h o s1 d1 → deg h o s2 d2 →
                          d1 = d2.
 #h #o #s1 #y #H #d1 #d2 #Hs1 #Hy
@@ -98,13 +95,20 @@ elim (tdeq_inv_sort1_deg … H … Hs1) -s1 #s2 #Hs2 #H destruct
 <(deg_mono h o … Hy … Hs2) -s2 -d1 //
 qed-.
 
-lemma tdeq_inv_pair: â\88\80h,o,I1,I2,V1,V2,T1,T2. â\91¡{I1}V1.T1 â\89¡[h, o] ②{I2}V2.T2 →
-                     â\88§â\88§ I1 = I2 & V1 â\89¡[h, o] V2 & T1 â\89¡[h, o] T2.
+lemma tdeq_inv_pair: â\88\80h,o,I1,I2,V1,V2,T1,T2. â\91¡{I1}V1.T1 â\89\9b[h, o] ②{I2}V2.T2 →
+                     â\88§â\88§ I1 = I2 & V1 â\89\9b[h, o] V2 & T1 â\89\9b[h, o] T2.
 #h #o #I1 #I2 #V1 #V2 #T1 #T2 #H elim (tdeq_inv_pair1 … H) -H
 #V0 #T0 #HV #HT #H destruct /2 width=1 by and3_intro/
 qed-.
 
-lemma tdeq_inv_pair_xy_y: ∀h,o,I,T,V. ②{I}V.T ≡[h, o] T → ⊥.
+lemma tdeq_inv_pair_xy_x: ∀h,o,I,V,T. ②{I}V.T ≛[h, o] V → ⊥.
+#h #o #I #V elim V -V
+[ #J #T #H elim (tdeq_inv_pair1 … H) -H #X #Y #_ #_ #H destruct
+| #J #X #Y #IHX #_ #T #H elim (tdeq_inv_pair … H) -H #H #HY #_ destruct /2 width=2 by/
+]
+qed-.
+
+lemma tdeq_inv_pair_xy_y: ∀h,o,I,T,V. ②{I}V.T ≛[h, o] T → ⊥.
 #h #o #I #T elim T -T
 [ #J #V #H elim (tdeq_inv_pair1 … H) -H #X #Y #_ #_ #H destruct
 | #J #X #Y #_ #IHY #V #H elim (tdeq_inv_pair … H) -H #H #_ #HY destruct /2 width=2 by/
@@ -113,7 +117,7 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma tdeq_fwd_atom1: â\88\80h,o,I,Y. â\93ª{I} â\89¡[h, o] Y → ∃J. Y = ⓪{J}.
+lemma tdeq_fwd_atom1: â\88\80h,o,I,Y. â\93ª{I} â\89\9b[h, o] Y → ∃J. Y = ⓪{J}.
 #h #o * #x #Y #H [ elim (tdeq_inv_sort1 … H) -H ]
 /3 width=4 by tdeq_inv_gref1, tdeq_inv_lref1, ex_intro/
 qed-.
@@ -131,7 +135,7 @@ lemma tdeq_sym: ∀h,o. symmetric … (tdeq h o).
 /2 width=3 by tdeq_sort, tdeq_lref, tdeq_gref, tdeq_pair/
 qed-.
 
-lemma tdeq_dec: â\88\80h,o,T1,T2. Decidable (T1 â\89¡[h, o] T2).
+lemma tdeq_dec: â\88\80h,o,T1,T2. Decidable (T1 â\89\9b[h, o] T2).
 #h #o #T1 elim T1 -T1 [ * #s1 | #I1 #V1 #T1 #IHV #IHT ] * [1,3,5,7: * #s2 |*: #I2 #V2 #T2 ]
 [ elim (deg_total h o s1) #d1 #H1
   elim (deg_total h o s2) #d2 #H2
@@ -172,10 +176,10 @@ qed-.
 (* Negated inversion lemmas *************************************************)
 
 lemma tdneq_inv_pair: ∀h,o,I1,I2,V1,V2,T1,T2.
-                      (â\91¡{I1}V1.T1 â\89¡[h, o] ②{I2}V2.T2 → ⊥) → 
+                      (â\91¡{I1}V1.T1 â\89\9b[h, o] ②{I2}V2.T2 → ⊥) → 
                       ∨∨ I1 = I2 → ⊥
-                      |  V1 ≡[h, o] V2 → ⊥
-                      |  (T1 â\89¡[h, o] T2 → ⊥).
+                      |  (V1 ≛[h, o] V2 → ⊥)
+                      |  (T1 â\89\9b[h, o] T2 → ⊥).
 #h #o #I1 #I2 #V1 #V2 #T1 #T2 #H12
 elim (eq_item2_dec I1 I2) /3 width=1 by or3_intro0/ #H destruct
 elim (tdeq_dec h o V1 V2) /3 width=1 by or3_intro1/