partial commit: just the components before "static" ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
index 8d4e9b67a0ea6e9ab0e8ee9bcafb2cc813071b9b..29d6151fe877e584e1ccb65efa0c1caa6fc5cd8c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
@@ -22,8 +22,8 @@ inductive lsubsv (h:sh) (g:sd h): relation lenv ≝
 | lsubsv_atom: lsubsv h g (⋆) (⋆)
 | lsubsv_pair: ∀I,L1,L2,V. lsubsv h g L1 L2 →
                lsubsv h g (L1.ⓑ{I}V) (L2.ⓑ{I}V)
-| lsubsv_abbr: ∀L1,L2,W,V,W1,V2,l. ⦃h, L1⦄ ⊢ ⓝW.V ¡[g] → ⦃h, L2⦄ ⊢ W ¡[g] →
-               ⦃h, L1⦄ ⊢ V •[g] ⦃l+1, W1⦄ → ⦃h, L2⦄ ⊢ W •[g] ⦃l, V2⦄ →
+| lsubsv_abbr: ∀L1,L2,W,V,W1,V2,l. ⦃h, L1⦄ ⊢ ⓝW.V ¡[h, g] → ⦃h, L2⦄ ⊢ W ¡[h, g] →
+               ⦃h, L1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ → ⦃h, L2⦄ ⊢ W •[h, g] ⦃l, V2⦄ →
                lsubsv h g L1 L2 → lsubsv h g (L1.ⓓⓝW.V) (L2.ⓛW)
 .
 
@@ -33,7 +33,7 @@ interpretation
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubsv_inv_atom1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubsv_inv_atom1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L1 = ⋆ → L2 = ⋆.
 #h #g #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -41,15 +41,15 @@ fact lsubsv_inv_atom1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 = ⋆ → L
 ]
 qed-.
 
-lemma lsubsv_inv_atom1: ∀h,g,L2. h ⊢ ⋆ ¡⊑[g] L2 → L2 = ⋆.
+lemma lsubsv_inv_atom1: ∀h,g,L2. h ⊢ ⋆ ¡⊑[h, g] L2 → L2 = ⋆.
 /2 width=5 by lsubsv_inv_atom1_aux/ qed-.
 
-fact lsubsv_inv_pair1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
+fact lsubsv_inv_pair1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
                            ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                           (∃∃K2. h ⊢ K1 ¡⊑[g] K2 & L2 = K2.ⓑ{I}X) ∨
-                           ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[g] & ⦃h, K2⦄ ⊢ W ¡[g] &
-                                             ⦃h, K1⦄ ⊢ V •[g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[g] ⦃l, V2⦄ &
-                                             h ⊢ K1 ¡⊑[g] K2 &
+                           (∃∃K2. h ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                           ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
+                                             ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                             h ⊢ K1 ¡⊑[h, g] K2 &
                                              I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #h #g #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
@@ -58,15 +58,15 @@ fact lsubsv_inv_pair1_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair1: ∀h,g,I,K1,L2,X. h ⊢ K1.ⓑ{I}X ¡⊑[g] L2 →
-                        (∃∃K2. h ⊢ K1 ¡⊑[g] K2 & L2 = K2.ⓑ{I}X) ∨
-                        ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[g] & ⦃h, K2⦄ ⊢ W ¡[g] &
-                                          ⦃h, K1⦄ ⊢ V •[g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[g] ⦃l, V2⦄ &
-                                          h ⊢ K1 ¡⊑[g] K2 &
+lemma lsubsv_inv_pair1: ∀h,g,I,K1,L2,X. h ⊢ K1.ⓑ{I}X ¡⊑[h, g] L2 →
+                        (∃∃K2. h ⊢ K1 ¡⊑[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                        ∃∃K2,W,V,W1,V2,l. ⦃h, K1⦄ ⊢ X ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
+                                          ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                          h ⊢ K1 ¡⊑[h, g] K2 &
                                           I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsubsv_inv_pair1_aux/ qed-.
 
-fact lsubsv_inv_atom2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubsv_inv_atom2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L2 = ⋆ → L1 = ⋆.
 #h #g #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -74,15 +74,15 @@ fact lsubsv_inv_atom2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L2 = ⋆ → L
 ]
 qed-.
 
-lemma lsubsv_inv_atom2: ∀h,g,L1. h ⊢ L1 ¡⊑[g] ⋆ → L1 = ⋆.
+lemma lsubsv_inv_atom2: ∀h,g,L1. h ⊢ L1 ¡⊑[h, g] ⋆ → L1 = ⋆.
 /2 width=5 by lsubsv_inv_atom2_aux/ qed-.
 
-fact lsubsv_inv_pair2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
+fact lsubsv_inv_pair2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
                            ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                           (∃∃K1. h ⊢ K1 ¡⊑[g] K2 & L1 = K1.ⓑ{I}W) ∨
-                           ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[g] & ⦃h, K2⦄ ⊢ W ¡[g] &
-                                           ⦃h, K1⦄ ⊢ V •[g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[g] ⦃l, V2⦄ &
-                                           h ⊢ K1 ¡⊑[g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                           (∃∃K1. h ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                           ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
+                                           ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                           h ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 #h #g #L1 #L2 * -L1 -L2
 [ #J #K2 #U #H destruct
 | #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3/
@@ -90,26 +90,26 @@ fact lsubsv_inv_pair2_aux: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair2: ∀h,g,I,L1,K2,W. h ⊢ L1 ¡⊑[g] K2.ⓑ{I}W →
-                        (∃∃K1. h ⊢ K1 ¡⊑[g] K2 & L1 = K1.ⓑ{I}W) ∨
-                        ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[g] & ⦃h, K2⦄ ⊢ W ¡[g] &
-                                        ⦃h, K1⦄ ⊢ V •[g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[g] ⦃l, V2⦄ &
-                                        h ⊢ K1 ¡⊑[g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+lemma lsubsv_inv_pair2: ∀h,g,I,L1,K2,W. h ⊢ L1 ¡⊑[h, g] K2.ⓑ{I}W →
+                        (∃∃K1. h ⊢ K1 ¡⊑[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                        ∃∃K1,V,W1,V2,l. ⦃h, K1⦄ ⊢ ⓝW.V ¡[h, g] & ⦃h, K2⦄ ⊢ W ¡[h, g] &
+                                        ⦃h, K1⦄ ⊢ V •[h, g] ⦃l+1, W1⦄ & ⦃h, K2⦄ ⊢ W •[h, g] ⦃l, V2⦄ &
+                                        h ⊢ K1 ¡⊑[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 /2 width=3 by lsubsv_inv_pair2_aux/ qed-.
 
 (* Basic_forward lemmas *****************************************************)
 
-lemma lsubsv_fwd_lsubr: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ⊑ L2.
+lemma lsubsv_fwd_lsubr: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 → L1 ⊑ L2.
 #h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubsv_refl: ∀h,g,L. h ⊢ L ¡⊑[g] L.
+lemma lsubsv_refl: ∀h,g,L. h ⊢ L ¡⊑[h, g] L.
 #h #g #L elim L -L // /2 width=1/
 qed.
 
-lemma lsubsv_cprs_trans: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 →
+lemma lsubsv_cprs_trans: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[h, g] L2 →
                          ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
 /3 width=5 by lsubsv_fwd_lsubr, lsubr_cprs_trans/
 qed-.