renaming in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lsuba_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_drops.ma
index f2440c801c8200131b64e22e8a035ce16d1a8ea7..e55602e4f25b6ac2bdd6dd07499744748c85fe84 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba_drops.ma
@@ -12,54 +12,57 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lrsubeqa_3.ma".
-include "basic_2/static/lsubr.ma".
-include "basic_2/static/aaa.ma".
+include "basic_2/relocation/drops.ma".
+include "basic_2/static/lsuba.ma".
 
 (* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
 
-(* Basic properties *********************************************************)
+(* Properties with generic slicing for local environments *******************)
 
-(* Note: the constant 0 cannot be generalized *)
-lemma lsuba_drop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀K1,c,k. ⬇[c, 0, k] L1 ≡ K1 →
-                          ∃∃K2. G ⊢ K1 ⫃⁝ K2 & ⬇[c, 0, k] L2 ≡ K2.
+(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
+(* Basic_2A1: includes: lsuba_drop_O1_conf *)
+lemma lsuba_drops_conf_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → 
+                              ∀b,f,K1. 𝐔⦃f⦄ → ⬇*[b, f] L1 ≘ K1 →
+                              ∃∃K2. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L2 ≘ K2.
 #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #V #_ #IHL12 #K1 #c #k #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
-  [ destruct
-    elim (IHL12 L1 c 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, drop_pair, ex2_intro/
-  | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
+| #I #L1 #L2 #HL12 #IH #b #f #K1 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsuba_bind, drops_refl, ex2_intro/
+  | #g #Hg #HLK1 #H destruct -HL12
+    elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
   ]
-| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #c #k #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK1
-  [ destruct
-    elim (IHL12 L1 c 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_beta, drop_pair, ex2_intro/
-  | elim (IHL12 … HLK1) -L1 /3 width=3 by drop_drop_lt, ex2_intro/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #IH #b #f #K1 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by drops_refl, lsuba_beta, ex2_intro/
+  | #g #Hg #HLK1 #H destruct -HL12
+    elim (IH … Hg HLK1) -L1 -Hg /3 width=3 by drops_drop, ex2_intro/
   ]
 ]
 qed-.
 
-(* Note: the constant 0 cannot be generalized *)
-lemma lsuba_drop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀K2,c,k. ⬇[c, 0, k] L2 ≡ K2 →
-                           ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇[c, 0, k] L1 ≡ K1.
+(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
+(* Basic_2A1: includes: lsuba_drop_O1_trans *)
+lemma lsuba_drops_trans_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
+                               ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2 →
+                               ∃∃K1. G ⊢ K1 ⫃⁝ K2 & ⬇*[b, f] L1 ≘ K1.
 #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
-| #I #L1 #L2 #V #_ #IHL12 #K2 #c #k #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
-  [ destruct
-    elim (IHL12 L2 c 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, drop_pair, ex2_intro/
-  | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
+| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsuba_bind, drops_refl, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
   ]
-| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #c #k #H
-  elim (drop_inv_O1_pair1 … H) -H * #Hm #HLK2
-  [ destruct
-    elim (IHL12 L2 c 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_beta, drop_pair, ex2_intro/
-  | elim (IHL12 … HLK2) -L2 /3 width=3 by drop_drop_lt, ex2_intro/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by drops_refl, lsuba_beta, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
   ]
 ]
 qed-.