milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rdeq_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_drops.ma
index 6b9537f61add366ff1fdb87a4044a1b1c1d95bb6..f2ea3b8945a7f2564d979e7101da42295daa72b6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rdeq_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rdeq_drops.ma
@@ -16,32 +16,37 @@ include "static_2/relocation/lifts_tdeq.ma".
 include "static_2/static/rex_drops.ma".
 include "static_2/static/rdeq.ma".
 
-(* DEGREE-BASED EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ******)
+(* SORT-IRRELEVANT EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES ***)
 
 (* Properties with generic slicing for local environments *******************)
 
-lemma rdeq_lifts_sn: ∀h,o. f_dedropable_sn (cdeq h o).
+lemma rdeq_lifts_sn: f_dedropable_sn cdeq.
 /3 width=5 by rex_liftable_dedropable_sn, tdeq_lifts_sn/ qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
-lemma rdeq_inv_lifts_sn: ∀h,o. f_dropable_sn (cdeq h o).
+lemma rdeq_inv_lifts_sn: f_dropable_sn cdeq.
 /2 width=5 by rex_dropable_sn/ qed-.
 
-(* Note: missing in basic_2A1 *)
-lemma rdeq_inv_lifts_dx: ∀h,o. f_dropable_dx (cdeq h o).
+lemma rdeq_inv_lifts_dx: f_dropable_dx cdeq.
 /2 width=5 by rex_dropable_dx/ qed-.
 
-(* Basic_2A1: uses: lleq_inv_lift_le lleq_inv_lift_be lleq_inv_lift_ge *)
-lemma rdeq_inv_lifts_bi: ∀h,o,L1,L2,U. L1 ≛[h, o, U] L2 → ∀b,f. 𝐔⦃f⦄ →
+lemma rdeq_inv_lifts_bi: ∀L1,L2,U. L1 ≛[U] L2 → ∀b,f. 𝐔⦃f⦄ →
                          ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
-                         ∀T. ⬆*[f] T ≘ U → K1 ≛[h, o, T] K2.
+                         ∀T. ⬆*[f] T ≘ U → K1 ≛[T] K2.
 /2 width=10 by rex_inv_lifts_bi/ qed-.
 
-lemma rdeq_inv_lref_pair_sn: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
-                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+lemma rdeq_inv_lref_pair_sn: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                             ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ≛[V1] K2 & V1 ≛ V2.
 /2 width=3 by rex_inv_lref_pair_sn/ qed-.
 
-lemma rdeq_inv_lref_pair_dx: ∀h,o,L1,L2,i. L1 ≛[h, o, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
-                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[h, o, V1] K2 & V1 ≛[h, o] V2.
+lemma rdeq_inv_lref_pair_dx: ∀L1,L2,i. L1 ≛[#i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                             ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ≛[V1] K2 & V1 ≛ V2.
 /2 width=3 by rex_inv_lref_pair_dx/ qed-.
+
+lemma rdeq_inv_lref_pair_bi (L1) (L2) (i):
+                            L1 ≛[#i] L2 →
+                            ∀I1,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I1}V1 →
+                            ∀I2,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I2}V2 →
+                            ∧∧ K1 ≛[V1] K2 & V1 ≛ V2 & I1 = I2.
+/2 width=6 by rex_inv_lref_pair_bi/ qed-.