- support for candidates of reducibility continues ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / tps_lift.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma
index aaecbbf3b4acfe2084ccd75cef48c0ad8b0eac1a..3b1453c37e951c657990f90e38d260ff9df131f2 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/tps_lift.ma
@@ -20,7 +20,7 @@ include "Basic_2/substitution/tps.ma".
 (* Advanced inversion lemmas ************************************************)
 
 fact tps_inv_refl_SO2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → e = 1 →
-                           â\88\80K,V. â\86\93[0, d] L â\89¡ K. ð\9d\95\93{Abst} V â\86\92 T1 = T2.
+                           â\88\80K,V. â\87\93[0, d] L â\89¡ K. ð\9d\95\93{Abst} V â\86\92 T1 = T2.
 #L #T1 #T2 #d #e #H elim H -L -T1 -T2 -d -e
 [ //
 | #L #K0 #V0 #W #i #d #e #Hdi #Hide #HLK0 #_ #H destruct
@@ -34,15 +34,15 @@ fact tps_inv_refl_SO2_aux: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → e = 1 →
 qed.
 
 lemma tps_inv_refl_SO2: ∀L,T1,T2,d. L ⊢ T1 [d, 1] ≫ T2 →
-                        â\88\80K,V. â\86\93[0, d] L â\89¡ K. ð\9d\95\93{Abst} V â\86\92 T1 = T2.
+                        â\88\80K,V. â\87\93[0, d] L â\89¡ K. ð\9d\95\93{Abst} V â\86\92 T1 = T2.
 /2 width=8/ qed-.
 
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: subst1_lift_lt *)
 lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
-                   â\88\80L,U1,U2,d,e. â\86\93[d, e] L â\89¡ K â\86\92
-                   â\86\91[d, e] T1 â\89¡ U1 â\86\92 â\86\91[d, e] T2 â\89¡ U2 â\86\92
+                   â\88\80L,U1,U2,d,e. â\87\93[d, e] L â\89¡ K â\86\92
+                   â\87\91[d, e] T1 â\89¡ U1 â\86\92 â\87\91[d, e] T2 â\89¡ U2 â\86\92
                    dt + et ≤ d →
                    L ⊢ U1 [dt, et] ≫ U2.
 #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et
@@ -66,8 +66,8 @@ lemma tps_lift_le: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
 qed.
 
 lemma tps_lift_be: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
-                   â\88\80L,U1,U2,d,e. â\86\93[d, e] L â\89¡ K â\86\92
-                   â\86\91[d, e] T1 â\89¡ U1 â\86\92 â\86\91[d, e] T2 â\89¡ U2 â\86\92
+                   â\88\80L,U1,U2,d,e. â\87\93[d, e] L â\89¡ K â\86\92
+                   â\87\91[d, e] T1 â\89¡ U1 â\86\92 â\87\91[d, e] T2 â\89¡ U2 â\86\92
                    dt ≤ d → d ≤ dt + et →
                    L ⊢ U1 [dt, et + e] ≫ U2.
 #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et
@@ -99,8 +99,8 @@ qed.
 
 (* Basic_1: was: subst1_lift_ge *)
 lemma tps_lift_ge: ∀K,T1,T2,dt,et. K ⊢ T1 [dt, et] ≫ T2 →
-                   â\88\80L,U1,U2,d,e. â\86\93[d, e] L â\89¡ K â\86\92
-                   â\86\91[d, e] T1 â\89¡ U1 â\86\92 â\86\91[d, e] T2 â\89¡ U2 â\86\92
+                   â\88\80L,U1,U2,d,e. â\87\93[d, e] L â\89¡ K â\86\92
+                   â\87\91[d, e] T1 â\89¡ U1 â\86\92 â\87\91[d, e] T2 â\89¡ U2 â\86\92
                    d ≤ dt →
                    L ⊢ U1 [dt + e, et] ≫ U2.
 #K #T1 #T2 #dt #et #H elim H -K -T1 -T2 -dt -et
@@ -123,9 +123,9 @@ qed.
 
 (* Basic_1: was: subst1_gen_lift_lt *)
 lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
-                        â\88\80K,d,e. â\86\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92
+                        â\88\80K,d,e. â\87\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92
                         dt + et ≤ d →
-                        â\88\83â\88\83T2. K â\8a¢ T1 [dt, et] â\89« T2 & â\86\91[d, e] T2 â\89¡ U2.
+                        â\88\83â\88\83T2. K â\8a¢ T1 [dt, et] â\89« T2 & â\87\91[d, e] T2 â\89¡ U2.
 #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et
 [ #L * #i #dt #et #K #d #e #_ #T1 #H #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
@@ -150,9 +150,9 @@ lemma tps_inv_lift1_le: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
 qed.
 
 lemma tps_inv_lift1_be: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
-                        â\88\80K,d,e. â\86\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92
+                        â\88\80K,d,e. â\87\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92
                         dt ≤ d → d + e ≤ dt + et →
-                        â\88\83â\88\83T2. K â\8a¢ T1 [dt, et - e] â\89« T2 & â\86\91[d, e] T2 â\89¡ U2.
+                        â\88\83â\88\83T2. K â\8a¢ T1 [dt, et - e] â\89« T2 & â\87\91[d, e] T2 â\89¡ U2.
 #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et
 [ #L * #i #dt #et #K #d #e #_ #T1 #H #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
@@ -188,9 +188,9 @@ qed.
 
 (* Basic_1: was: subst1_gen_lift_ge *)
 lemma tps_inv_lift1_ge: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
-                        â\88\80K,d,e. â\86\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92
+                        â\88\80K,d,e. â\87\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92
                         d + e ≤ dt →
-                        â\88\83â\88\83T2. K â\8a¢ T1 [dt - e, et] â\89« T2 & â\86\91[d, e] T2 â\89¡ U2.
+                        â\88\83â\88\83T2. K â\8a¢ T1 [dt - e, et] â\89« T2 & â\87\91[d, e] T2 â\89¡ U2.
 #L #U1 #U2 #dt #et #H elim H -L -U1 -U2 -dt -et
 [ #L * #i #dt #et #K #d #e #_ #T1 #H #_
   [ lapply (lift_inv_sort2 … H) -H #H destruct /2 width=3/
@@ -221,7 +221,7 @@ qed.
 
 (* Basic_1: was: subst1_gen_lift_eq *)
 lemma tps_inv_lift1_eq: ∀L,U1,U2,d,e.
-                        L â\8a¢ U1 [d, e] â\89« U2 â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92 U1 = U2.
+                        L â\8a¢ U1 [d, e] â\89« U2 â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92 U1 = U2.
 #L #U1 #U2 #d #e #H elim H -L -U1 -U2 -d -e
 [ //
 | #L #K #V #W #i #d #e #Hdi #Hide #_ #_ #T1 #H
@@ -254,9 +254,9 @@ qed.
                                        (EX u1 | t1 = (lift (minus (plus d h) (S i)) (S i) u1)).
 *)
 lemma tps_inv_lift1_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
-                        â\88\80K,d,e. â\86\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92
+                        â\88\80K,d,e. â\87\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92
                         d ≤ dt → dt ≤ d + e → d + e ≤ dt + et →
-                        â\88\83â\88\83T2. K â\8a¢ T1 [d, dt + et - (d + e)] â\89« T2 & â\86\91[d, e] T2 â\89¡ U2.
+                        â\88\83â\88\83T2. K â\8a¢ T1 [d, dt + et - (d + e)] â\89« T2 & â\87\91[d, e] T2 â\89¡ U2.
 #L #U1 #U2 #dt #et #HU12 #K #d #e #HLK #T1 #HTU1 #Hddt #Hdtde #Hdedet
 elim (tps_split_up … HU12 (d + e) ? ?) -HU12 // -Hdedet #U #HU1 #HU2
 lapply (tps_weak … HU1 d e ? ?) -HU1 // [ >commutative_plus /2 width=1/ ] -Hddt -Hdtde #HU1
@@ -265,9 +265,9 @@ elim (tps_inv_lift1_ge … HU2 … HLK … HTU1 ?) -U -L // <minus_plus_m_m /2 w
 qed.
 
 lemma tps_inv_lift1_be_up: ∀L,U1,U2,dt,et. L ⊢ U1 [dt, et] ≫ U2 →
-                           â\88\80K,d,e. â\86\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\86\91[d, e] T1 â\89¡ U1 â\86\92
+                           â\88\80K,d,e. â\87\93[d, e] L â\89¡ K â\86\92 â\88\80T1. â\87\91[d, e] T1 â\89¡ U1 â\86\92
                            dt ≤ d → dt + et ≤ d + e →
-                           â\88\83â\88\83T2. K â\8a¢ T1 [dt, d - dt] â\89« T2 & â\86\91[d, e] T2 â\89¡ U2.
+                           â\88\83â\88\83T2. K â\8a¢ T1 [dt, d - dt] â\89« T2 & â\87\91[d, e] T2 â\89¡ U2.
 #L #U1 #U2 #dt #et #HU12 #K #d #e #HLK #T1 #HTU1 #Hdtd #Hdetde
 lapply (tps_weak … HU12 dt (d + e - dt) ? ?) -HU12 // /2 width=3/ -Hdetde #HU12
 elim (tps_inv_lift1_be … HU12 … HLK … HTU1 ? ?) -U1 -L // /2 width=3/