some renaming and some typos corrected ...

[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 e996418dc04f90e785d1c44cf96fa16f3a515f5b..be8b2a38b657e91fe447fb6519df1346091f42c7 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
@@ -21,17 +21,17 @@ include "basic_2/static/aaa.ma".
 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: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L1 = ⋆ → L2 = ⋆.
+fact lsuba_inv_atom1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → L1 = ⋆ → L2 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -39,13 +39,13 @@ fact lsuba_inv_atom1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → L1 = ⋆ → L2 = 
 ]
 qed-.
 
-lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â\81\9dâ«\83 L2 → L2 = ⋆.
+lemma lsuba_inv_atom1: â\88\80G,L2. G â\8a¢ â\8b\86 â«\83â\81\9d L2 → L2 = ⋆.
 /2 width=4 by lsuba_inv_atom1_aux/ qed-.
 
-fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
+fact lsuba_inv_pair1_aux: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → ∀I,K1,X. L1 = K1.ⓑ{I}X →
+                          (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.ⓑ{I}X) ∨
                           ∃∃K2,W,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                      G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
+                                      G â\8a¢ K1 â«\83â\81\9d 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 by ex2_intro, or_introl/
@@ -53,13 +53,13 @@ fact lsuba_inv_pair1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀I,K1,X. L1 = K1.
 ]
 qed-.
 
-lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\81\9dâ«\83 L2 →
-                       (â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & L2 = K2.ⓑ{I}X) ∨
-                       â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
+lemma lsuba_inv_pair1: â\88\80I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â«\83â\81\9d L2 →
+                       (â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & L2 = K2.ⓑ{I}X) ∨
+                       â\88\83â\88\83K2,W,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â«\83â\81\9d K2 &
                                    I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsuba_inv_pair1_aux/ qed-.
 
-fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L2 = ⋆ → L1 = ⋆.
+fact lsuba_inv_atom2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → L2 = ⋆ → L1 = ⋆.
 #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -67,13 +67,13 @@ fact lsuba_inv_atom2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → L2 = ⋆ → L1 = 
 ]
 qed-.
 
-lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â\81\9dâ«\83 ⋆ → L1 = ⋆.
+lemma lsubc_inv_atom2: â\88\80G,L1. G â\8a¢ L1 â«\83â\81\9d ⋆ → L1 = ⋆.
 /2 width=4 by lsuba_inv_atom2_aux/ qed-.
 
-fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                          (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
+fact lsuba_inv_pair2_aux: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → ∀I,K2,W. L2 = K2.ⓑ{I}W →
+                          (â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & L1 = K1.ⓑ{I}W) ∨
                           ∃∃K1,V,A. ⦃G, K1⦄ ⊢ ⓝW.V ⁝ A & ⦃G, K2⦄ ⊢ W ⁝ A &
-                                    G â\8a¢ K1 â\81\9dâ«\83 K2 & I = Abst & L1 = K1.ⓓⓝW.V.
+                                    G â\8a¢ K1 â«\83â\81\9d 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 by ex2_intro, or_introl/
@@ -81,27 +81,27 @@ fact lsuba_inv_pair2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀I,K2,W. L2 = K2.
 ]
 qed-.
 
-lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â\81\9dâ«\83 K2.ⓑ{I}W →
-                       (â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & L1 = K1.ⓑ{I}W) ∨
-                       â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â\81\9dâ«\83 K2 &
+lemma lsuba_inv_pair2: â\88\80I,G,L1,K2,W. G â\8a¢ L1 â«\83â\81\9d K2.ⓑ{I}W →
+                       (â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & L1 = K1.ⓑ{I}W) ∨
+                       â\88\83â\88\83K1,V,A. â¦\83G, K1â¦\84 â\8a¢ â\93\9dW.V â\81\9d A & â¦\83G, K2â¦\84 â\8a¢ W â\81\9d A & G â\8a¢ K1 â«\83â\81\9d K2 &
                                  I = Abst & L1 = K1.ⓓⓝW.V.
 /2 width=3 by lsuba_inv_pair2_aux/ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → L1 ⫃ L2.
-#G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_bind, lsubr_abst/
+lemma lsuba_fwd_lsubr: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → L1 ⫃ L2.
+#G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_pair, lsubr_beta/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â\81\9dâ«\83 L.
+lemma lsuba_refl: â\88\80G,L. G â\8a¢ L â«\83â\81\9d L.
 #G #L elim L -L /2 width=1 by lsuba_atom, lsuba_pair/
 qed.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsuba_drop_O1_conf: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
-                          â\88\83â\88\83K2. G â\8a¢ K1 â\81\9dâ«\83 K2 & ⇩[s, 0, e] L2 ≡ K2.
+lemma lsuba_drop_O1_conf: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                          â\88\83â\88\83K2. G â\8a¢ K1 â«\83â\81\9d K2 & ⇩[s, 0, e] L2 ≡ K2.
 #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
 | #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
@@ -115,15 +115,15 @@ lemma lsuba_drop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K1,s,e. ⇩[s, 0
   elim (drop_inv_O1_pair1 … H) -H * #He #HLK1
   [ destruct
     elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, drop_pair, ex2_intro/
+    <(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: â\88\80G,L1,L2. G â\8a¢ L1 â\81\9dâ«\83 L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
-                           â\88\83â\88\83K1. G â\8a¢ K1 â\81\9dâ«\83 K2 & ⇩[s, 0, e] L1 ≡ K1.
+lemma lsuba_drop_O1_trans: â\88\80G,L1,L2. G â\8a¢ L1 â«\83â\81\9d L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+                           â\88\83â\88\83K1. G â\8a¢ K1 â«\83â\81\9d K2 & ⇩[s, 0, e] L1 ≡ K1.
 #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
 | #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H
@@ -137,7 +137,7 @@ lemma lsuba_drop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K2,s,e. ⇩[s,
   elim (drop_inv_O1_pair1 … H) -H * #He #HLK2
   [ destruct
     elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
-    <(drop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, drop_pair, ex2_intro/
+    <(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/
   ]
 ]