renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / drops_lreq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
index 56f2fbf85e084afaa116f26c532710f8e083dcad..d07ea22109df3a83609ae5542309a35fc67aa164 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_lreq.ma
@@ -12,46 +12,50 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/relocation/drops_ceq.ma".
 include "basic_2/relocation/drops_lexs.ma".
 
 (* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
 
 (* Properties with ranged equivalence for local environments ****************)
 
-lemma lreq_dedropable: dedropable_sn lreq.
-@lexs_liftable_dedropable
-/2 width=6 by cfull_lift, ceq_lift, cfull_refl, ceq_refl/
-qed-.
+lemma lreq_co_dedropable_sn: co_dedropable_sn lreq.
+@lexs_liftable_co_dedropable_sn
+/2 width=6 by cfull_lift_sn, ceq_lift_sn/ qed-.
+
+lemma lreq_co_dropable_sn: co_dropable_sn lreq.
+@lexs_co_dropable_sn qed-.
 
-lemma lreq_dropable: ∀RN,RP. dropable_dx (lexs RN RP).
-@lexs_dropable qed-.
+lemma lreq_co_dropable_dx: co_dropable_dx lreq.
+@lexs_co_dropable_dx qed-.
 
 (* Basic_2A1: includes: lreq_drop_trans_be *)
-lemma lreq_drops_trans_next: ∀L1,L2,f2. L1 ≡[f2] L2 →
-                             ∀I,K2,V,c,f. ⬇*[c,f] L2 ≡ K2.ⓑ{I}V → 𝐔⦃f⦄ →
-                             ∀f1. f ⊚ ⫯f1 ≡ f2 →
-                             ∃∃K1. ⬇*[c,f] L1 ≡ K1.ⓑ{I}V & K1 ≡[f1] K2.
-#L1 #L2 #f2 #HL12 #I #K1 #V #c #f #HLK1 #Hf #f1 #Hf2
-elim (lexs_drops_trans_next … HL12 … HLK1 Hf … Hf2) -L2 -f2 -Hf
+lemma lreq_drops_trans_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
+                             ∀b,f,I,K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} → 𝐔⦃f⦄ →
+                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
+                             ∃∃K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} & K1 ≡[f1] K2.
+#f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
+elim (lexs_drops_trans_next … HL12 … HLK2 Hf … Hf2) -f2 -L2 -Hf
+#I1 #K1 #HLK1 #HK12 #H <(ceq_ext_inv_eq … H) -I2
 /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_drop_conf_be *)
-lemma lreq_drops_conf_next: ∀L1,L2,f2. L1 ≡[f2] L2 →
-                            ∀I,K1,V,c,f. ⬇*[c,f] L1 ≡ K1.ⓑ{I}V → 𝐔⦃f⦄ →
-                            ∀f1. f ⊚ ⫯f1 ≡ f2 →
-                            ∃∃K2. ⬇*[c,f] L2 ≡ K2.ⓑ{I}V & K1 ≡[f1] K2.
-#L1 #L2 #f2 #HL12 #I #K1 #V #c #f #HLK1 #Hf #f1 #Hf2
-elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -L1 -f2 -Hf
+lemma lreq_drops_conf_next: ∀f2,L1,L2. L1 ≡[f2] L2 →
+                            ∀b,f,I,K1. ⬇*[b, f] L1 ≘ K1.ⓘ{I} → 𝐔⦃f⦄ →
+                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
+                            ∃∃K2. ⬇*[b, f] L2 ≘ K2.ⓘ{I} & K1 ≡[f1] K2.
+#f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
+elim (lreq_drops_trans_next … (lreq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
 /3 width=3 by lreq_sym, ex2_intro/
 qed-.
 
-lemma drops_lreq_trans_next: ∀K1,K2,f1. K1 ≡[f1] K2 →
-                             ∀I,L1,V,c,f. ⬇*[c,f] L1.ⓑ{I}V ≡ K1 →
-                             ∀f2. f ⊚ f1 ≡ ⫯f2 →
-                             ∃∃L2. ⬇*[c,f] L2.ⓑ{I}V ≡ K2 & L1 ≡[f2] L2 & L1.ⓑ{I}V≡[f]L2.ⓑ{I}V.
-#K1 #K2 #f1 #HK12 #I #L1 #V #c #f #HLK1 #f2 #Hf2
-elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -K1 -f1
-/2 width=6 by cfull_lift, ceq_lift, cfull_refl, ceq_refl, ex3_intro/
+lemma drops_lreq_trans_next: ∀f1,K1,K2. K1 ≡[f1] K2 →
+                             ∀b,f,I,L1. ⬇*[b, f] L1.ⓘ{I} ≘ K1 →
+                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
+                             ∃∃L2. ⬇*[b, f] L2.ⓘ{I} ≘ K2 & L1 ≡[f2] L2 & L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
+#f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
+elim (drops_lexs_trans_next … HK12 … HLK1 … Hf2) -f1 -K1
+/2 width=6 by cfull_lift_sn, ceq_lift_sn/
+#I2 #L2 #HLK2 #HL12 #H >(ceq_ext_inv_eq … H) -I1
+/2 width=4 by ex3_intro/
 qed-.