renaming in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
index 613a8f3210195cc5a5804db738f00a483cb48c61..e16decefa890fb42f0fc11a20730c8e92cff8f37 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
@@ -13,14 +13,13 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lrsubeqa_3.ma".
-include "basic_2/static/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_bind: ∀I,L1,L2. lsuba G L1 L2 → lsuba G (L1.ⓘ{I}) (L2.ⓘ{I})
 | 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)
 .
@@ -34,7 +33,7 @@ interpretation
 fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L1 = ⋆ → L2 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
-| #I #L1 #L2 #V #_ #H destruct
+| #I #L1 #L2 #_ #H destruct
 | #L1 #L2 #W #V #A #_ #_ #_ #H destruct
 ]
 qed-.
@@ -42,27 +41,27 @@ qed-.
 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 →
-                          (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.â\93\91{I}X) ∨
+fact lsuba_inv_bind1_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K1. L1 = K1.ⓘ{I} →
+                          (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.â\93\98{I}) ∨
                           ∃∃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 = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
 #G #L1 #L2 * -L1 -L2
-[ #J #K1 #X #H destruct
-| #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/
+[ #J #K1 #H destruct
+| #I #L1 #L2 #HL12 #J #K1 #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K1 #H destruct /3 width=9 by ex5_4_intro, or_intror/
 ]
 qed-.
 
-lemma lsuba_inv_pair1: ∀I,G,K1,L2,X. G ⊢ K1.ⓑ{I}X ⫃⁝ L2 →
-                       (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.â\93\91{I}X) ∨
+lemma lsuba_inv_bind1: ∀I,G,K1,L2. G ⊢ K1.ⓘ{I} ⫃⁝ L2 →
+                       (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.â\93\98{I}) ∨
                        ∃∃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-.
+                                   I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
+/2 width=3 by lsuba_inv_bind1_aux/ qed-.
 
 fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → L2 = ⋆ → L1 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
-| #I #L1 #L2 #V #_ #H destruct
+| #I #L1 #L2 #_ #H destruct
 | #L1 #L2 #W #V #A #_ #_ #_ #H destruct
 ]
 qed-.
@@ -70,75 +69,25 @@ qed-.
 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 →
-                          (â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & L1 = K1.â\93\91{I}W) ∨
-                          ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                    G ⊢ K1 ⫃⁝ K2 & I = Abst & L1 = K1.ⓓⓝW.V.
+fact lsuba_inv_bind2_aux: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → ∀I,K2. L2 = K2.ⓘ{I} →
+                          (â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & L1 = K1.â\93\98{I}) ∨
+                          ∃∃K1,V,W, A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
+                                       G ⊢ K1 ⫃⁝ K2 & I = BPair Abst W & 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 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/
+[ #J #K2 #H destruct
+| #I #L1 #L2 #HL12 #J #K2 #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #W #V #A #HV #HW #HL12 #J #K2 #H destruct /3 width=9 by ex5_4_intro, or_intror/
 ]
 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 &
-                                 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 by lsubr_pair, lsubr_beta/
-qed-.
+lemma lsuba_inv_bind2: ∀I,G,L1,K2. G ⊢ L1 ⫃⁝ K2.ⓘ{I} →
+                       (∃∃K1. G ⊢ K1 ⫃⁝ K2 & L1 = K1.ⓘ{I}) ∨
+                       ∃∃K1,V,W,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A & G ⊢ K1 ⫃⁝ K2 &
+                                   I = BPair Abst W & L1 = K1.ⓓⓝW.V.
+/2 width=3 by lsuba_inv_bind2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
 lemma lsuba_refl: ∀G,L. G ⊢ L ⫃⁝ L.
-#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_pair/
+#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_bind/
 qed.
-
-(* 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.
-#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/
-  ]
-| #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/
-  ]
-]
-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.
-#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/
-  ]
-| #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/
-  ]
-]
-qed-.