reorganization of the "static" component:

[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 8c8aa228686d6863a7bf349e8e271e15742f7484..a353d95dfb10169a7bbcff032ad8912e3abb5c8a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsuba.ma
@@ -48,8 +48,8 @@ fact lsuba_inv_pair1_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀I,K1,X. L1 = K1.
                                       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-.
 
@@ -76,8 +76,8 @@ fact lsuba_inv_pair2_aux: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀I,K2,W. L2 = K2.
                                     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-.
 
@@ -90,11 +90,55 @@ lemma lsuba_inv_pair2: ∀I,G,L1,K2,W. G ⊢ L1 ⁝⫃ K2.ⓑ{I}W →
 (* 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/
+#G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_bind, lsubr_abst/
 qed-.
 
 (* Basic properties *********************************************************)
 
 lemma lsuba_refl: ∀G,L. G ⊢ L ⁝⫃ L.
-#G #L elim L -L // /2 width=1/
+#G #L elim L -L /2 width=1 by lsuba_atom, lsuba_pair/
 qed.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsuba_ldrop_O1_conf: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                           ∃∃K2. G ⊢ K1 ⁝⫃ 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
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K1 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsuba_ldrop_O1_trans: ∀G,L1,L2. G ⊢ L1 ⁝⫃ L2 → ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
+                            ∃∃K1. G ⊢ K1 ⁝⫃ 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
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #A #HV #HW #_ #IHL12 #K2 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsuba_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.