update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / lsubv.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
index bba857ac84e1bffb6b6b48a4f2108974507d4b38..6549c361e6b61f2b0538efd713608c367ea9de35 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubv.ma
@@ -17,11 +17,10 @@ include "basic_2/dynamic/cnv.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR NATIVE VALIDITY *************************)
 
-(* Note: this is not transitive *)
 inductive lsubv (a) (h) (G): relation lenv ≝
 | lsubv_atom: lsubv a h G (⋆) (⋆)
 | lsubv_bind: ∀I,L1,L2. lsubv a h G L1 L2 → lsubv a h G (L1.ⓘ{I}) (L2.ⓘ{I})
-| lsubv_beta: ∀L1,L2,W,V. ⦃G, L1⦄ ⊢ ⓝW.V ![a,h] → ⦃G, L2⦄ ⊢ W ![a,h] →
+| lsubv_beta: ∀L1,L2,W,V. ⦃G, L1⦄ ⊢ ⓝW.V ![a,h] →
               lsubv a h G L1 L2 → lsubv a h G (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
@@ -35,7 +34,7 @@ fact lsubv_inv_atom_sn_aux (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 → L1 =
 #a #h #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #W #V #_ #_ #_ #H destruct
+| #L1 #L2 #W #V #_ #_ #H destruct
 ]
 qed-.
 
@@ -46,20 +45,20 @@ lemma lsubv_inv_atom_sn (a) (h) (G): ∀L2. G ⊢ ⋆ ⫃![a,h] L2 → L2 = ⋆.
 fact lsubv_inv_bind_sn_aux (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
                            ∀I,K1. L1 = K1.ⓘ{I} →
                            ∨∨ ∃∃K2. G ⊢ K1 ⫃![a,h] K2 & L2 = K2.ⓘ{I}
-                            | ∃∃K2,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] & ⦃G, K2⦄ ⊢ W ![a,h] &
+                            | ∃∃K2,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] &
                                         G ⊢ K1 ⫃![a,h] K2 &
                                         I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
 #a #h #G #L1 #L2 * -L1 -L2
 [ #J #K1 #H destruct
 | #I #L1 #L2 #HL12 #J #K1 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #W #V #HWV #HW #HL12 #J #K1 #H destruct /3 width=8 by ex5_3_intro, or_intror/
+| #L1 #L2 #W #V #HWV #HL12 #J #K1 #H destruct /3 width=7 by ex4_3_intro, or_intror/
 ]
 qed-.
 
 (* Basic_2A1: uses: lsubsv_inv_pair1 *)
 lemma lsubv_inv_bind_sn (a) (h) (G): ∀I,K1,L2. G ⊢ K1.ⓘ{I} ⫃![a,h] L2 →
                         ∨∨ ∃∃K2. G ⊢ K1 ⫃![a,h] K2 & L2 = K2.ⓘ{I}
-                         | ∃∃K2,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] & ⦃G, K2⦄ ⊢ W ![a,h] &
+                         | ∃∃K2,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] &
                                      G ⊢ K1 ⫃![a,h] K2 &
                                      I = BPair Abbr (ⓝW.V) & L2 = K2.ⓛW.
 /2 width=3 by lsubv_inv_bind_sn_aux/ qed-.
@@ -68,7 +67,7 @@ fact lsubv_inv_atom_dx_aux (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 → L2 =
 #a #h #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #_ #H destruct
-| #L1 #L2 #W #V #_ #_ #_ #H destruct
+| #L1 #L2 #W #V #_ #_ #H destruct
 ]
 qed-.
 
@@ -79,22 +78,31 @@ lemma lsubv_inv_atom2 (a) (h) (G): ∀L1. G ⊢ L1 ⫃![a,h] ⋆ → L1 = ⋆.
 fact lsubv_inv_bind_dx_aux (a) (h) (G): ∀L1,L2. G ⊢ L1 ⫃![a,h] L2 →
                            ∀I,K2. L2 = K2.ⓘ{I} →
                            ∨∨ ∃∃K1. G ⊢ K1 ⫃![a,h] K2 & L1 = K1.ⓘ{I}
-                            | ∃∃K1,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] & ⦃G, K2⦄ ⊢ W ![a,h] &
+                            | ∃∃K1,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] &
                                         G ⊢ K1 ⫃![a,h] K2 & I = BPair Abst W & L1 = K1.ⓓⓝW.V.
 #a #h #G #L1 #L2 * -L1 -L2
 [ #J #K2 #H destruct
 | #I #L1 #L2 #HL12 #J #K2 #H destruct /3 width=3 by ex2_intro, or_introl/
-| #L1 #L2 #W #V #HWV #HW #HL12 #J #K2 #H destruct /3 width=8 by ex5_3_intro, or_intror/
+| #L1 #L2 #W #V #HWV #HL12 #J #K2 #H destruct /3 width=7 by ex4_3_intro, or_intror/
 ]
 qed-.
 
 (* Basic_2A1: uses: lsubsv_inv_pair2 *)
 lemma lsubv_inv_bind_dx (a) (h) (G): ∀I,L1,K2. G ⊢ L1 ⫃![a,h] K2.ⓘ{I} →
                         ∨∨ ∃∃K1. G ⊢ K1 ⫃![a,h] K2 & L1 = K1.ⓘ{I}
-                         | ∃∃K1,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] & ⦃G, K2⦄ ⊢ W ![a,h] &
+                         | ∃∃K1,W,V. ⦃G, K1⦄ ⊢ ⓝW.V ![a,h] &
                                      G ⊢ K1 ⫃![a,h] K2 & I = BPair Abst W & L1 = K1.ⓓⓝW.V.
 /2 width=3 by lsubv_inv_bind_dx_aux/ qed-.
 
+(* Advanced inversion lemmas ************************************************)
+
+lemma lsubv_inv_abst_sn (a) (h) (G): ∀K1,L2,W. G ⊢ K1.ⓛW ⫃![a,h] L2 →
+                        ∃∃K2. G ⊢ K1 ⫃![a,h] K2 & L2 = K2.ⓛW.
+#a #h #G #K1 #L2 #W #H
+elim (lsubv_inv_bind_sn … H) -H // *
+#K2 #XW #XV #_ #_ #H1 #H2 destruct
+qed-.
+
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: uses: lsubsv_refl *)