- exclusion binder in local environments

  updating of component rt_transition started
  cpg completed

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
index b682e561dff764cb8fc8feeabe755c352cab2425..260cd45a49c60dc3e56cf5f4fa9c7e8503cd3ff6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
@@ -30,8 +30,8 @@ inductive cpg (Rt:relation rtc) (h): rtc → relation4 genv lenv term term ≝
              ⬆*[1] V2 ≡ W2 → cpg Rt h c G (L.ⓓV1) (#0) W2
 | cpg_ell  : ∀c,G,L,V1,V2,W2. cpg Rt h c G L V1 V2 →
              ⬆*[1] V2 ≡ W2 → cpg Rt h (c+𝟘𝟙) G (L.ⓛV1) (#0) W2
-| cpg_lref : ∀c,I,G,L,V,T,U,i. cpg Rt h c G L (#i) T → 
-             â¬\86*[1] T â\89¡ U â\86\92 cpg Rt h c G (L.â\93\91{I}V) (#⫯i) U
+| cpg_lref : ∀c,I,G,L,T,U,i. cpg Rt h c G L (#i) T → 
+             â¬\86*[1] T â\89¡ U â\86\92 cpg Rt h c G (L.â\93\98{I}) (#⫯i) U
 | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2.
              cpg Rt h cV G L V1 V2 → cpg Rt h cT G (L.ⓑ{I}V1) T1 T2 →
              cpg Rt h ((↓cV)∨cT) G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2)
@@ -75,14 +75,14 @@ fact cpg_inv_atom1_aux: ∀Rt,c,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[Rt, c, h] T2
                                          L = K.ⓓV1 & J = LRef 0 & c = cV
                          | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                          L = K.ⓛV1 & J = LRef 0 & c = cV+𝟘𝟙
-                         | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 &
-                                        L = K.ⓑ{I}V & J = LRef (⫯i).
+                         | ∃∃I,K,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 &
+                                      L = K.ⓘ{I} & J = LRef (⫯i).
 #Rt #c #h #G #L #T1 #T2 * -c -G -L -T1 -T2
 [ #I #G #L #J #H destruct /3 width=1 by or5_intro0, conj/
 | #G #L #s #J #H destruct /3 width=3 by or5_intro1, ex3_intro/
 | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro2, ex5_4_intro/
 | #c #G #L #V1 #V2 #W2 #HV12 #VW2 #J #H destruct /3 width=8 by or5_intro3, ex5_4_intro/
-| #c #I #G #L #V #T #U #i #HT #HTU #J #H destruct /3 width=9 by or5_intro4, ex4_5_intro/
+| #c #I #G #L #T #U #i #HT #HTU #J #H destruct /3 width=8 by or5_intro4, ex4_4_intro/
 | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #J #H destruct
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #J #H destruct
 | #cU #cT #G #L #U1 #U2 #T1 #T2 #_ #_ #_ #J #H destruct
@@ -101,8 +101,8 @@ lemma cpg_inv_atom1: ∀Rt,c,h,J,G,L,T2. ⦃G, L⦄ ⊢ ⓪{J} ⬈[Rt, c, h] T2
                                       L = K.ⓓV1 & J = LRef 0 & c = cV
                       | ∃∃cV,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈[Rt, cV, h] V2 & ⬆*[1] V2 ≡ T2 &
                                       L = K.ⓛV1 & J = LRef 0 & c = cV+𝟘𝟙
-                      | ∃∃I,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 &
-                                     L = K.ⓑ{I}V & J = LRef (⫯i).
+                      | ∃∃I,K,T,i. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 &
+                                   L = K.ⓘ{I} & J = LRef (⫯i).
 /2 width=3 by cpg_inv_atom1_aux/ qed-.
 
 lemma cpg_inv_sort1: ∀Rt,c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ⬈[Rt, c, h] T2 →
@@ -111,7 +111,7 @@ lemma cpg_inv_sort1: ∀Rt,c,h,G,L,T2,s. ⦃G, L⦄ ⊢ ⋆s ⬈[Rt, c, h] T2 
 elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/
 [ #s0 #H destruct /3 width=1 by or_intror, conj/
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
-| #I #K #V1 #V2 #i #_ #_ #_ #H destruct
+| #I #K #T #i #_ #_ #_ #H destruct
 ]
 qed-.
 
@@ -125,18 +125,18 @@ lemma cpg_inv_zero1: ∀Rt,c,h,G,L,T2. ⦃G, L⦄ ⊢ #0 ⬈[Rt, c, h] T2 →
 elim (cpg_inv_atom1 … H) -H * /3 width=1 by or3_intro0, conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #HV12 #HVT2 #H1 #_ #H2 destruct /3 width=8 by or3_intro1, or3_intro2, ex4_4_intro/
-| #I #K #V1 #V2 #i #_ #_ #_ #H destruct
+| #I #K #T #i #_ #_ #_ #H destruct
 ]
 qed-.
 
 lemma cpg_inv_lref1: ∀Rt,c,h,G,L,T2,i. ⦃G, L⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 →
                      (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨
-                     ∃∃I,K,V,T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓑ{I}V.
+                     ∃∃I,K,T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2 & L = K.ⓘ{I}.
 #Rt #c #h #G #L #T2 #i #H
 elim (cpg_inv_atom1 … H) -H * /3 width=1 by or_introl, conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
-| #I #K #V1 #V2 #j #HV2 #HVT2 #H1 #H2 destruct /3 width=7 by ex3_4_intro, or_intror/
+| #I #K #T #j #HT #HT2 #H1 #H2 destruct /3 width=6 by ex3_3_intro, or_intror/
 ]
 qed-.
 
@@ -145,7 +145,7 @@ lemma cpg_inv_gref1: ∀Rt,c,h,G,L,T2,l. ⦃G, L⦄ ⊢ §l ⬈[Rt, c, h] T2 →
 elim (cpg_inv_atom1 … H) -H * /2 width=1 by conj/
 [ #s #H destruct
 |2,3: #cV #K #V1 #V2 #_ #_ #_ #H destruct
-| #I #K #V1 #V2 #i #_ #_ #_ #H destruct
+| #I #K #T #i #_ #_ #_ #H destruct
 ]
 qed-.
 
@@ -161,7 +161,7 @@ fact cpg_inv_bind1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 
 | #G #L #s #q #J #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #q #J #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #q #J #W #U1 #H destruct
-| #c #I #G #L #V #T #U #i #_ #_ #q #J #W #U1 #H destruct
+| #c #I #G #L #T #U #i #_ #_ #q #J #W #U1 #H destruct
 | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #q #J #W #U1 #H destruct /3 width=8 by ex4_4_intro, or_introl/
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #q #J #W #U1 #H destruct
 | #cU #cT #G #L #U1 #U2 #T1 #T2 #_ #_ #_ #q #J #W #U1 #H destruct
@@ -213,7 +213,7 @@ fact cpg_inv_appl1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 
 | #G #L #s #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct
-| #c #I #G #L #V #T #U #i #_ #_ #W #U1 #H destruct
+| #c #I #G #L #T #U #i #_ #_ #W #U1 #H destruct
 | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #W #U1 #H destruct /3 width=8 by or3_intro0, ex4_4_intro/
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #_ #W #U1 #H destruct
@@ -245,7 +245,7 @@ fact cpg_inv_cast1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G, L⦄ ⊢ U ⬈[Rt, c, h] U2 
 | #G #L #s #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct
 | #c #G #L #V1 #V2 #W2 #_ #_ #W #U1 #H destruct
-| #c #I #G #L #V #T #U #i #_ #_ #W #U1 #H destruct
+| #c #I #G #L #T #U #i #_ #_ #W #U1 #H destruct
 | #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #_ #_ #W #U1 #H destruct
 | #cV #cT #G #L #V1 #V2 #T1 #T2 #HRt #HV12 #HT12 #W #U1 #H destruct /3 width=9 by or3_intro0, ex5_4_intro/
@@ -276,11 +276,11 @@ lemma cpg_inv_zero1_pair: ∀Rt,c,h,I,G,K,V1,T2. ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈[
 * #z #Y #X1 #X2 #HX12 #HXT2 #H1 #H2 destruct /3 width=5 by or3_intro1, or3_intro2, ex4_2_intro/
 qed-.
 
-lemma cpg_inv_lref1_pair: ∀Rt,c,h,I,G,K,V,T2,i. ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 →
+lemma cpg_inv_lref1_bind: ∀Rt,c,h,I,G,K,T2,i. ⦃G, K.ⓘ{I}⦄ ⊢ #⫯i ⬈[Rt, c, h] T2 →
                           (T2 = #(⫯i) ∧ c = 𝟘𝟘) ∨
                           ∃∃T. ⦃G, K⦄ ⊢ #i ⬈[Rt, c, h] T & ⬆*[1] T ≡ T2.
-#Rt #c #h #I #G #L #V #T2 #i #H elim (cpg_inv_lref1 … H) -H /2 width=1 by or_introl/
-* #Z #Y #X #T #HT #HT2 #H destruct /3 width=3 by ex2_intro, or_intror/
+#Rt #c #h #I #G #L #T2 #i #H elim (cpg_inv_lref1 … H) -H /2 width=1 by or_introl/
+* #Z #Y #T #HT #HT2 #H destruct /3 width=3 by ex2_intro, or_intror/
 qed-.
 
 (* Basic forward lemmas *****************************************************)

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
index 758a278b7a15645529c1997f15f239e8104c1155..295cc229125f35c25126ff498229fc7e1458abb4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_drops.ma
@@ -26,7 +26,7 @@ lemma cpg_delta_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓓV → ⦃G,
 #Rt #c #h #G #K #V #V2 #i elim i -i
 [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_delta/
 | #i #IH #L0 #T0 #H0 #HV2 #HVT2
-  elim (drops_inv_succ … H0) -H0 #I #L #V0 #HLK #H destruct
+  elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct
   elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/
 ]
 qed.
@@ -36,7 +36,7 @@ lemma cpg_ell_drops: ∀Rt,c,h,G,K,V,V2,i,L,T2. ⬇*[i] L ≡ K.ⓛV → ⦃G, K
 #Rt #c #h #G #K #V #V2 #i elim i -i
 [ #L #T2 #HLK lapply (drops_fwd_isid … HLK ?) // #H destruct /3 width=3 by cpg_ell/
 | #i #IH #L0 #T0 #H0 #HV2 #HVT2
-  elim (drops_inv_succ … H0) -H0 #I #L #V0 #HLK #H destruct
+  elim (drops_inv_succ … H0) -H0 #I #L #HLK #H destruct
   elim (lifts_split_trans … HVT2 (𝐔❴⫯i❵) (𝐔❴1❵) ?) -HVT2 /3 width=3 by cpg_lref/
 ]
 qed.
@@ -53,7 +53,7 @@ lemma cpg_inv_lref1_drops: ∀Rt,c,h,G,i,L,T2. ⦃G, L⦄ ⊢ #i ⬈[Rt,c, h] T2
 [ #L #T2 #H elim (cpg_inv_zero1 … H) -H * /3 width=1 by or3_intro0, conj/
   /4 width=8 by drops_refl, ex4_4_intro, or3_intro2, or3_intro1/
 | #i #IH #L #T2 #H elim (cpg_inv_lref1 … H) -H * /3 width=1 by or3_intro0, conj/
-  #I #K #V #V2 #H #HVT2 #H0 destruct elim (IH … H) -IH -H
+  #I #K #V2 #H #HVT2 #H0 destruct elim (IH … H) -IH -H
   [ * #H1 #H2 destruct lapply (lifts_inv_lref1_uni … HVT2) -HVT2 #H destruct /3 width=1 by or3_intro0, conj/ ] *
   #cV #L #W #W2 #HKL #HW2 #HWV2 #H destruct
   lapply (lifts_trans … HWV2 … HVT2 ??) -V2
@@ -81,9 +81,10 @@ qed-.
 (* Properties with generic slicing for local environments *******************)
 
 (* Note: it should use drops_split_trans_pair2 *)
-lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt h c G).
+lemma cpg_lifts_sn: ∀Rt. reflexive … Rt →
+                    ∀c,h,G. d_liftable2_sn … lifts (cpg Rt h c G).
 #Rt #HRt #c #h #G #K #T generalize in match c; -c
-@(fqup_wf_ind_eq … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * *
+@(fqup_wf_ind_eq (Ⓣ) … G K T) -G -K -T #G0 #K0 #T0 #IH #G #K * *
 [ #s #HG #HK #HT #c #X2 #H2 #b #f #L #HLK #X1 #H1 destruct -IH
   lapply (lifts_inv_sort1 … H1) -H1 #H destruct
   elim (cpg_inv_sort1 … H2) -H2 * #H1 #H2 destruct
@@ -96,7 +97,8 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt
   lapply (drops_trans … HLK … HK0 ??) -HLK [3,6: |*: // ] #H
   elim (drops_split_trans … H) -H [1,6: |*: /2 width=6 by after_uni_dx/ ] #Y #HL0 #HY
   lapply (drops_tls_at … Hf … HY) -HY #HY
-  elim (drops_inv_skip2 … HY) -HY #L0 #W #HLK0 #HVW #H destruct
+  elim (drops_inv_skip2 … HY) -HY #Z #L0 #HLK0 #HZ #H destruct
+  elim (liftsb_inv_pair_sn … HZ) -HZ #W #HVW #H destruct
   elim (IH … HV2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -K -K0 -V #W2 #HVW2 #HW2
   elim (lifts_total W2 (𝐔❴⫯i2❵)) #U2 #HWU2
   lapply (lifts_trans … HVW2 … HWU2 ??) -HVW2 [3,6: |*: // ] #HVU2
@@ -111,10 +113,10 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt
   elim (cpg_inv_bind1 … H2) -H2 *
   [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
     elim (IH … HV12 … HLK … HVW1) -HV12 //
-    elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+    elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
     /3 width=5 by cpg_bind, lifts_bind, ex2_intro/
   | #cT #T2 #HT12 #HXT2 #H1 #H2 #H3 destruct
-    elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] #U2 #HTU2 #HU12
+    elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #U2 #HTU2 #HU12
     lapply (lifts_trans … HXT2 … HTU2 ??) -T2 [3: |*: // ] #HXU2
     elim (lifts_split_trans … HXU2 f (𝐔❴⫯O❵)) [2: /2 width=1 by after_uni_one_dx/ ]
     /3 width=5 by cpg_zeta, ex2_intro/
@@ -130,13 +132,13 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt
       elim (lifts_inv_bind1 … HTU1) -HTU1 #Z1 #U0 #HYZ1 #HTU1 #H destruct
       elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 //
       elim (IH … HY12 … HLK … HYZ1) -HY12 //
-      elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+      elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
       /4 width=7 by cpg_beta, lifts_bind, lifts_flat, ex2_intro/
     | #cV #cY #cT #a #V2 #V20 #Y1 #Y2 #T0 #T2 #HV12 #HV20 #HY12 #HT12 #H1 #H2 #H3 destruct
       elim (lifts_inv_bind1 … HTU1) -HTU1 #Z1 #U0 #HYZ1 #HTU1 #H destruct
       elim (IH … HV12 … HLK … HVW1) -HV12 -HVW1 // #W2 #HVW2 #HW12
       elim (IH … HY12 … HLK … HYZ1) -HY12 //
-      elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+      elim (IH … HT12 … HTU1) -IH -HT12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
       elim (lifts_total W2 (𝐔❴1❵)) #W20 #HW20
       lapply (lifts_trans … HVW2 … HW20 ??) -HVW2 [3: |*: // ] #H
       lapply (lifts_conf … HV20 … H (↑f) ?) -V2 /2 width=3 by after_uni_one_sn/
@@ -158,14 +160,16 @@ lemma cpg_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_sn (cpg Rt
 ]
 qed-.
 
-lemma cpg_lifts_bi: ∀Rt. reflexive … Rt → ∀c,h,G. d_liftable2_bi (cpg Rt h c G).
-/3 width=9 by cpg_lifts_sn, d_liftable2_sn_bi/ qed-.
+lemma cpg_lifts_bi: ∀Rt. reflexive … Rt →
+                    ∀c,h,G. d_liftable2_bi … lifts (cpg Rt h c G).
+/3 width=12 by cpg_lifts_sn, d_liftable2_sn_bi, lifts_mono/ qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
-lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (cpg Rt h c G).
+lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt →
+                        ∀c,h,G. d_deliftable2_sn … lifts (cpg Rt h c G).
 #Rt #HRt #c #h #G #L #U generalize in match c; -c
-@(fqup_wf_ind_eq … G L U) -G -L -U #G0 #L0 #U0 #IH #G #L * *
+@(fqup_wf_ind_eq (Ⓣ) … G L U) -G -L -U #G0 #L0 #U0 #IH #G #L * *
 [ #s #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct -IH
   lapply (lifts_inv_sort2 … H1) -H1 #H destruct
   elim (cpg_inv_sort1 … H2) -H2 * #H1 #H2 destruct
@@ -178,7 +182,8 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (
   lapply (drops_split_div … HLK (𝐔❴i1❵) ???) -HLK [4,8: * |*: // ] #Y0 #HK0 #HLY0
   lapply (drops_conf … HL0 … HLY0 ??) -HLY0 [3,6: |*: /2 width=6 by after_uni_dx/ ] #HLY0
   lapply (drops_tls_at … Hf … HLY0) -HLY0 #HLY0
-  elim (drops_inv_skip1 … HLY0) -HLY0 #K0 #V #HLK0 #HVW #H destruct
+  elim (drops_inv_skip1 … HLY0) -HLY0 #Z #K0 #HLK0 #HZ #H destruct
+  elim (liftsb_inv_pair_dx … HZ) -HZ #V #HVW #H destruct
   elim (IH … HW2 … HLK0 … HVW) -IH /2 width=2 by fqup_lref/ -L -L0 -W #V2 #HVW2 #HV2
   lapply (lifts_trans … HVW2 … HWU2 ??) -W2 [3,6: |*: // ] #HVU2
   elim (lifts_split_trans … HVU2 ? f) -HVU2 [1,4: |*: /2 width=4 by after_uni_succ_sn/ ]
@@ -192,10 +197,10 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (
   elim (cpg_inv_bind1 … H2) -H2 *
   [ #cW #cU #W2 #U2 #HW12 #HU12 #H1 #H2 destruct
     elim (IH … HW12 … HLK … HVW1) -HW12 //
-    elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+    elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
     /3 width=5 by cpg_bind, lifts_bind, ex2_intro/
   | #cU #U2 #HU12 #HXU2 #H1 #H2 #H3 destruct
-    elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ] #T2 #HTU2 #HT12
+    elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ] #T2 #HTU2 #HT12
     elim (lifts_div4_one … HTU2 … HXU2) -U2 /3 width=5 by cpg_zeta, ex2_intro/
   ]
 | * #W1 #U1 #HG #HL #HU #c #X2 #H2 #b #f #K #HLK #X1 #H1 destruct
@@ -209,13 +214,13 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (
       elim (lifts_inv_bind2 … HTU1) -HTU1 #Y1 #T0 #HYZ1 #HTU1 #H destruct
       elim (IH … HW12 … HLK … HVW1) -HW12 -HVW1 //
       elim (IH … HZ12 … HLK … HYZ1) -HZ12 //
-      elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+      elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
       /4 width=7 by cpg_beta, lifts_bind, lifts_flat, ex2_intro/
     | #cW #cZ #cU #a #W2 #W20 #Z1 #Z2 #U0 #U2 #HW12 #HW20 #HZ12 #HU12 #H1 #H2 #H3 destruct
       elim (lifts_inv_bind2 … HTU1) -HTU1 #Y1 #T0 #HYZ1 #HTU1 #H destruct
       elim (IH … HW12 … HLK … HVW1) -HW12 -HVW1 // #V2 #HVW2 #HV12
       elim (IH … HZ12 … HLK … HYZ1) -HZ12 //
-      elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip/ ]
+      elim (IH … HU12 … HTU1) -IH -HU12 -HTU1 [ |*: /3 width=3 by drops_skip, ext2_pair/ ]
       lapply (lifts_trans … HVW2 … HW20 ??) -W2 [3: |*: // ] #H
       elim (lifts_split_trans … H ? (↑f)) -H [ |*: /2 width=3 by after_uni_one_sn/ ]
       /4 width=9 by cpg_theta, lifts_bind, lifts_flat, ex2_intro/
@@ -236,5 +241,6 @@ lemma cpg_inv_lifts_sn: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_sn (
 ]
 qed-.
 
-lemma cpg_inv_lifts_bi: ∀Rt. reflexive … Rt → ∀c,h,G. d_deliftable2_bi (cpg Rt h c G).
-/3 width=9 by cpg_inv_lifts_sn, d_deliftable2_sn_bi/ qed-.
+lemma cpg_inv_lifts_bi: ∀Rt. reflexive … Rt →
+                        ∀c,h,G. d_deliftable2_bi … lifts (cpg Rt h c G).
+/3 width=12 by cpg_inv_lifts_sn, d_deliftable2_sn_bi, lifts_inj/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma
index 8dcc523e400af3d027ae22b5662bb5c1b21d6f4b..77425cce736fa54c30cfb5f68988061d53f4fa77 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg_lsubr.ma
@@ -29,11 +29,11 @@ lemma lsubr_cpg_trans: ∀Rt,c,h,G. lsub_trans … (cpg Rt h c G) lsubr.
 | #c #G #L1 #V1 #V2 #W2 #_ #HVW2 #IH #X #H
   elim (lsubr_inv_abst2 … H) -H * #L2 [2: #V ] #HL21 #H destruct
   /4 width=3 by cpg_delta, cpg_ell, cpg_ee/
-| #c #I1 #G #L1 #V1 #T1 #U1 #i #_ #HTU1 #IH #X #H
-  elim (lsubr_fwd_pair2 … H) -H #I2 #L2 #V2 #HL21 #H destruct
+| #c #I1 #G #L1 #T1 #U1 #i #_ #HTU1 #IH #X #H
+  elim (lsubr_fwd_bind2 … H) -H #I2 #L2 #HL21 #H destruct
   /3 width=3 by cpg_lref/
-|6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_pair/
+|6,12: /4 width=1 by cpg_bind, cpg_beta, lsubr_bind/
 |7,8,10,11: /3 width=1 by cpg_appl, cpg_cast, cpg_eps, cpg_ee/
-|9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_pair/
+|9,13: /4 width=3 by cpg_zeta, cpg_theta, lsubr_bind/
 ]
 qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma
index 4783017ee8c28fc10c7e2eaafeab6a6ea266ba24..c4ed53ed073eab1357c5f7a9bf1dbd302080095b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/tdeq_ext.ma
@@ -20,9 +20,12 @@ include "basic_2/syntax/lenv_ext2.ma".
 definition cdeq: ∀h. sd h → relation3 lenv term term ≝
                  λh,o,L. tdeq h o.
 
+definition tdeq_ext: ∀h. sd h → relation bind ≝
+                     λh,o. ext2 (tdeq h o).
+
 definition cdeq_ext: ∀h. sd h → relation3 lenv bind bind ≝
                      λh,o. cext2 (cdeq h o).
 
 interpretation
-   "degree-based equivalence (binders)"
-   'LazyEq h o I1 I2 = (ext2 (tdeq h o) I1 I2).
+   "degree-based equivalence (binder)"
+   'LazyEq h o I1 I2 = (tdeq_ext h o I1 I2).

diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index df82586f07817f633b8ba76385197dd3da82ac3b..80e174651c0672a289dc6fda55c91d4e666cde57 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -125,6 +125,7 @@ table {
    ]
    class "cyan"
    [ { "rt-transition" * } {
+(*
         [ { "uncounted rst-transition" * } {
              [ "fpbq ( ⦃?,?,?⦄ ≽[?] ⦃?,?,?⦄ )" "fpbq_aaa" * ]
              [ "fpb ( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" * ]
@@ -142,13 +143,13 @@ table {
              [ "cpx ( ⦃?,?⦄ ⊢ ? ⬈[?] ? )" "cpx_simple" + "cpx_drops" + "cpx_fqus" + "cpx_lsubr" + "cpx_lfxs" * ]
           }
         ]
+*)
         [ { "counted context-sensitive rt-transition" * } {
              [ "cpg ( ⦃?,?⦄ ⊢ ? ⬈[?,?] ? )" "cpg_simple" + "cpg_drops" + "cpg_lsubr" * ]
           }
         ]
      }
    ]
-*)
    class "water"
    [ { "iterated static typing" * } {
         [ { "iterated extension on referred entries" * } {
@@ -241,8 +242,9 @@ table {
              [ "theq ( ? ⩳[?,?] ? )" "theq_simple" + "theq_tdeq" + "theq_theq" + "theq_simple_vector" * ]
           }
         ]
-        [ { "degree-based equivalence for terms" * } {
-             [ "tdeq ( ? ≡[?,?] ? ) " "tdeq_ext" + "tdeq_tdeq" * ]
+        [ { "degree-based equivalence" * } {
+             [ "tdeq_ext ( ? ≡[?,?] ? )" * ]
+             [ "tdeq ( ? ≡[?,?] ? )" "tdeq_tdeq" * ]
           }
         ]
         [ { "closures" * } {