X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Freducibility%2Fcpr_lift.ma;h=fcdcdcdd8a08ca3038070884cabc1f4189ee23e1;hb=13a37618a5cebc5e0088a7da213f1de033d281db;hp=4c2101504a9a3eab9bc4c7e1d62a6035861747ac;hpb=f75be90562ddd964ef7ed43b956eb908f3133e3a;p=helm.git

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_lift.ma b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_lift.ma
index 4c2101504..fcdcdcdd8 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_lift.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr_lift.ma
@@ -21,58 +21,59 @@ include "Basic_2/reducibility/cpr.ma".
 (* Advanced properties ******************************************************)
 
 lemma cpr_cdelta: ∀L,K,V1,W1,W2,i.
-                  ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫* W1 →
-                  ↑[0, i + 1] W1 ≡ W2 → L ⊢ #i ⇒ W2.
+                  ⇩[0, i] L ≡ K. ⓓV1 → K ⊢ V1 [0, |L| - i - 1] ▶* W1 →
+                  ⇧[0, i + 1] W1 ≡ W2 → L ⊢ #i ➡ W2.
 #L #K #V1 #W1 #W2 #i #HLK #HVW1 #HW12
-@ex2_1_intro [2: // | skip | @tpss_subst /2 width=6/ ] (**) (* /4 width=6/ is too slow *)
+lapply (ldrop_fwd_ldrop2_length … HLK) #Hi
+@ex2_1_intro [2: // | skip | @tpss_subst /width=6/ ] (**) (* /3 width=6/ is too slow *)
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was: pr2_gen_lref *)
-lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ⇒ T2 →
+lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ➡ T2 →
                      T2 = #i ∨
-                     ∃∃K,V1,T1. ↓[0, i] L ≡ K. 𝕓{Abbr} V1 &
-                                K ⊢ V1 [0, |L| - i - 1] ≫* T1 &
-                                ↑[0, i + 1] T1 ≡ T2 &
+                     ∃∃K,V1,T1. ⇩[0, i] L ≡ K. ⓓV1 &
+                                K ⊢ V1 [0, |L| - i - 1] ▶* T1 &
+                                ⇧[0, i + 1] T1 ≡ T2 &
                                 i < |L|.
 #L #T2 #i * #X #H
 >(tpr_inv_atom1 … H) -H #H
-elim (tpss_inv_lref1 … H) -H /2/
+elim (tpss_inv_lref1 … H) -H /2 width=1/
 * /3 width=6/
-qed.
+qed-.
 
 (* Basic_1: was: pr2_gen_abst *)
-lemma cpr_inv_abst1: ∀V1,T1,U2. 𝕔{Abst} V1. T1 ⇒ U2 →
-                     ∃∃V2,T2. V1 ⇒ V2 & T1 ⇒ T2 & U2 = 𝕔{Abst} V2. T2.
-/2/ qed.
+lemma cpr_inv_abst1: ∀V1,T1,U2. ⓛV1. T1 ➡ U2 →
+                     ∃∃V2,T2. V1 ➡ V2 & T1 ➡ T2 & U2 = ⓛV2. T2.
+/2 width=3/ qed-.
 
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was: pr2_lift *)
-lemma cpr_lift: ∀L,K,d,e. ↓[d, e] L ≡ K →
-                ∀T1,U1. ↑[d, e] T1 ≡ U1 → ∀T2,U2. ↑[d, e] T2 ≡ U2 →
-                K ⊢ T1 ⇒ T2 → L ⊢ U1 ⇒ U2.
+lemma cpr_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+                ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
+                K ⊢ T1 ➡ T2 → L ⊢ U1 ➡ U2.
 #L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 * #T #HT1 #HT2
 elim (lift_total T d e) #U #HTU 
 lapply (tpr_lift … HT1 … HTU1 … HTU) -T1 #HU1
 elim (lt_or_ge (|K|) d) #HKd
-[ lapply (tpss_lift_le … HT2 … HLK HTU … HTU2) -T2 T HLK [ /2/ | /3/ ]
-| lapply (tpss_lift_be … HT2 … HLK HTU … HTU2) -T2 T HLK // /3/
+[ lapply (tpss_lift_le … HT2 … HLK HTU … HTU2) -T2 -T -HLK [ /2 width=2/ | /3 width=4/ ]
+| lapply (tpss_lift_be … HT2 … HLK HTU … HTU2) -T2 -T -HLK // /3 width=4/
 ]
 qed.
 
 (* Basic_1: was: pr2_gen_lift *)
-lemma cpr_inv_lift: ∀L,K,d,e. ↓[d, e] L ≡ K →
-                    ∀T1,U1. ↑[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ⇒ U2 →
-                    ∃∃T2. ↑[d, e] T2 ≡ U2 & K ⊢ T1 ⇒ T2.
+lemma cpr_inv_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
+                    ∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀U2. L ⊢ U1 ➡ U2 →
+                    ∃∃T2. ⇧[d, e] T2 ≡ U2 & K ⊢ T1 ➡ T2.
 #L #K #d #e #HLK #T1 #U1 #HTU1 #U2 * #U #HU1 #HU2
 elim (tpr_inv_lift … HU1 … HTU1) -U1 #T #HTU #T1
 elim (lt_or_ge (|L|) d) #HLd
-[ elim (tpss_inv_lift1_le … HU2 … HLK … HTU ?) -U HLK [ /5/ | /2/ ]
+[ elim (tpss_inv_lift1_le … HU2 … HLK … HTU ?) -U -HLK [ /5 width=4/ | /2 width=2/ ]
 | elim (lt_or_ge (|L|) (d + e)) #HLde
-  [ elim (tpss_inv_lift1_be_up … HU2 … HLK … HTU ? ?) -U HLK // [ /5/ | /2/ ] 
-  | elim (tpss_inv_lift1_be … HU2 … HLK … HTU ? ?) -U HLK // /5/
+  [ elim (tpss_inv_lift1_be_up … HU2 … HLK … HTU ? ?) -U -HLK // [ /5 width=4/ | /2 width=2/ ] 
+  | elim (tpss_inv_lift1_be … HU2 … HLK … HTU ? ?) -U -HLK // /5 width=4/
   ]
 ]
 qed.