X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flsuba.ma;h=91b50e3fce4e9a83f9518378c660b93a0601b813;hb=b4b5f03ffca4f250a1dc02f277b70e4f33ac8a9b;hp=49441a887da6be0dc9793192991855772bc72661;hpb=3e9d72c26091f0e157a024ea9bd6f95a95729860;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
index 49441a887..91b50e3fc 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
@@ -13,25 +13,24 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqa_3.ma".
-include "basic_2/relocation/lsubr.ma".
 include "basic_2/static/aaa.ma".
 
-(* LOCAL ENVIRONMENT REFINEMENT FOR ATOMIC ARITY ASSIGNMENT *****************)
+(* RESTRICTED REFINEMENT FOR ATOMIC ARITY ASSIGNMENT ************************)
 
 inductive lsuba (G:genv): relation lenv ≝
 | lsuba_atom: lsuba G (⋆) (⋆)
 | lsuba_pair: ∀I,L1,L2,V. lsuba G L1 L2 → lsuba G (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsuba_abbr: ∀L1,L2,W,V,A. ⦃G, L1⦄ ⊢ ⓝW.V ⁝ A → ⦃G, L2⦄ ⊢ W ⁝ A →
+| lsuba_beta: ∀L1,L2,W,V,A. ⦃G, L1⦄ ⊢ ⓝW.V ⁝ A → ⦃G, L2⦄ ⊢ W ⁝ A →
               lsuba G L1 L2 → lsuba G (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
 interpretation
-  "local environment refinement (atomic arity assigment)"
+  "local environment refinement (atomic arity assignment)"
   'LRSubEqA G L1 L2 = (lsuba G L1 L2).
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L1 = ⋆ → L2 = ⋆.
+fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L1 = ⋆ → L2 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -39,27 +38,27 @@ fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L1 = ⋆ → L2 = 
 ]
 qed-.
 
-lemma lsuba_inv_atom1: ∀G,L2. G ⊢ ⋆ ⁝⊑ L2 → L2 = ⋆.
+lemma lsuba_inv_atom1: ∀G,L2. G ⊢ ⋆ ⫃⁝ L2 → L2 = ⋆.
 /2 width=4 by lsuba_inv_atom1_aux/ qed-.
 
-fact lsuba_inv_pair1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (∃∃K2. G ⊢ K1 ⁝⊑ K2 & L2 = K2.ⓑ{I}X) ∨
+fact lsuba_inv_pair1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (∃∃K2. G ⊢ K1 ⫃⁝ K2 & L2 = K2.ⓑ{I}X) ∨
                           ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G ⊢ K1 ⁝⊑ K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
+                                      G ⊢ K1 ⫃⁝ K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #G #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
-| #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #X #H destruct /3 width=9/
+| #I #L1 #L2 #V #HL12 #J #K1 #X #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #X #H destruct /3 width=9 by or_intror, ex6_4_intro/
 ]
 qed-.
 
-lemma lsuba_inv_pair1: ∀I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⁝⊑ L2 →
-                       (∃∃K2. G ⊢ K1 ⁝⊑ K2 & L2 = K2.ⓑ{I}X) ∨
-                       ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⁝⊑ K2 &
+lemma lsuba_inv_pair1: ∀I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⫃⁝ L2 →
+                       (∃∃K2. G ⊢ K1 ⫃⁝ K2 & L2 = K2.ⓑ{I}X) ∨
+                       ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⫃⁝ K2 &
                                    I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsuba_inv_pair1_aux/ qed-.
 
-fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L2 = ⋆ → L1 = ⋆.
+fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L2 = ⋆ → L1 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -67,34 +66,28 @@ fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L2 = ⋆ → L1 = 
 ]
 qed-.
 
-lemma lsubc_inv_atom2: ∀G,L1. G ⊢ L1 ⁝⊑ ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: ∀G,L1. G ⊢ L1 ⫃⁝ ⋆ → L1 = ⋆.
 /2 width=4 by lsuba_inv_atom2_aux/ qed-.
 
-fact lsuba_inv_pair2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                          (∃∃K1. G ⊢ K1 ⁝⊑ K2 & L1 = K1.ⓑ{I}W) ∨
+fact lsuba_inv_pair2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
+                          (∃∃K1. G ⊢ K1 ⫃⁝ K2 & L1 = K1.ⓑ{I}W) ∨
                           ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                    G ⊢ K1 ⁝⊑ K2 & I = Abst & L1 = K1.ⓓⓝW.V.
+                                    G ⊢ K1 ⫃⁝ K2 & I = Abst & L1 = K1.ⓓⓝW.V.
 #G #L1 #L2 * -L1 -L2
 [ #J #K2 #U #H destruct
-| #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3/
-| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #U #H destruct /3 width=7/
+| #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #U #H destruct /3 width=7 by or_intror, ex5_3_intro/
 ]
 qed-.
 
-lemma lsuba_inv_pair2: ∀I,G,L1,K2,W. G ⊢ L1 ⁝⊑ K2.ⓑ{I}W →
-                       (∃∃K1. G ⊢ K1 ⁝⊑ K2 & L1 = K1.ⓑ{I}W) ∨
-                       ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⁝⊑ K2 &
+lemma lsuba_inv_pair2: ∀I,G,L1,K2,W. G ⊢ L1 ⫃⁝ K2.ⓑ{I}W →
+                       (∃∃K1. G ⊢ K1 ⫃⁝ K2 & L1 = K1.ⓑ{I}W) ∨
+                       ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⫃⁝ K2 &
                                  I = Abst & L1 = K1.ⓓⓝW.V.
 /2 width=3 by lsuba_inv_pair2_aux/ qed-.
 
-(* Basic forward lemmas *****************************************************)
-
-lemma lsuba_fwd_lsubr: ∀G,L1,L2. G ⊢ L1 ⁝⊑ L2 → L1 ⊑ L2.
-#G #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
-qed-.
-
 (* Basic properties *********************************************************)
 
-lemma lsuba_refl: ∀G,L. G ⊢ L ⁝⊑ L.
-#G #L elim L -L // /2 width=1/
+lemma lsuba_refl: ∀G,L. G ⊢ L ⫃⁝ L.
+#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_pair/
 qed.