syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / drops_seq.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_seq.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_seq.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_seq.ma
@@ -0,0 +1,61 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "static_2/relocation/drops_sex.ma".
+
+(* GENERIC SLICING FOR LOCAL ENVIRONMENTS ***********************************)
+
+(* Properties with syntactic equivalence for selected local environments ****)
+
+lemma seq_co_dedropable_sn: co_dedropable_sn seq.
+@sex_liftable_co_dedropable_sn
+/2 width=6 by cfull_lift_sn, ceq_lift_sn/ qed-.
+
+lemma seq_co_dropable_sn: co_dropable_sn seq.
+@sex_co_dropable_sn qed-.
+
+lemma seq_co_dropable_dx: co_dropable_dx seq.
+@sex_co_dropable_dx qed-.
+
+(* Basic_2A1: includes: lreq_drop_trans_be *)
+lemma seq_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 (sex_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 seq_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 (seq_drops_trans_next … (seq_sym … HL12) … HLK1 … Hf2) // -f2 -L1 -Hf
+/3 width=3 by seq_sym, ex2_intro/
+qed-.
+
+lemma drops_seq_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_sex_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-.