- partial commit of rt_transition ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
index 5845bcb632410e34eeabace0c0b7795c3d08fa37..c4ec6dd188e36c6eeca2148debbfd0d9380e00c4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubr.ma
@@ -24,7 +24,7 @@ inductive lsubr: relation lenv ≝
 .
 
 interpretation
-  "local environment refinement (restricted)"
+  "restricted refinement (local environment)"
   'LRSubEqC L1 L2 = (lsubr L1 L2).
 
 (* Basic properties *********************************************************)
@@ -58,8 +58,8 @@ lemma lsubr_inv_abst1: ∀K1,L2,W. K1.ⓛW ⫃ L2 →
                        L2 = ⋆ ∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓛW.
 /2 width=3 by lsubr_inv_abst1_aux/ qed-.
 
-fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓓW →
-                          ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓW.
+fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,V. L2 = K2.ⓓV →
+                          ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓV.
 #L1 #L2 * -L1 -L2
 [ #L #K2 #W #H destruct
 | #I #L1 #L2 #V #HL12 #K2 #W #H destruct /2 width=3 by ex2_intro/
@@ -67,6 +67,30 @@ fact lsubr_inv_abbr2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓓW →
 ]
 qed-.
 
-lemma lsubr_inv_abbr2: ∀L1,K2,W. L1 ⫃ K2.ⓓW →
-                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓW.
+lemma lsubr_inv_abbr2: ∀L1,K2,V. L1 ⫃ K2.ⓓV →
+                       ∃∃K1. K1 ⫃ K2 & L1 = K1.ⓓV.
 /2 width=3 by lsubr_inv_abbr2_aux/ qed-.
+
+fact lsubr_inv_abst2_aux: ∀L1,L2. L1 ⫃ L2 → ∀K2,W. L2 = K2.ⓛW →
+                          (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓛW) ∨
+                          ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V.
+#L1 #L2 * -L1 -L2
+[ #L #K2 #W #H destruct
+| #I #L1 #L2 #V #HL12 #K2 #W #H destruct /3 width=3 by ex2_intro, or_introl/
+| #L1 #L2 #V1 #V2 #HL12 #K2 #W #H destruct /3 width=4 by ex2_2_intro, or_intror/
+]
+qed-.
+
+lemma lsubr_inv_abst2: ∀L1,K2,W. L1 ⫃ K2.ⓛW →
+                       (∃∃K1. K1 ⫃ K2 & L1 = K1.ⓛW) ∨
+                       ∃∃K1,V. K1 ⫃ K2 & L1 = K1.ⓓⓝW.V.
+/2 width=3 by lsubr_inv_abst2_aux/ qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma lsubr_fwd_pair2: ∀I2,L1,K2,V2. L1 ⫃ K2.ⓑ{I2}V2 →
+                       ∃∃I1,K1,V1. K1 ⫃ K2 & L1 = K1.ⓑ{I1}V1.
+* #L1 #K2 #V2 #H
+[ elim (lsubr_inv_abbr2 … H) | elim (lsubr_inv_abst2 … H) * ] -H
+/2 width=5 by ex2_3_intro/
+qed-.