notational change for snv and lsubsv: inverted "!" used for now

[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 7958de9183a3d324eff338536506fb43c267bb3a..089dbed26c81657eb8c2c14225adfc8ba422c856 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: â\88\80L1,L2,V1,V2,W1,W2,l. â¦\83h, L1â¦\84 â\8a© V1 :[g] → ⦃h, L1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ →
-               L1 â\8a¢ W1 â¬\8c* W2 â\86\92 â¦\83h, L2â¦\84 â\8a© W2 :[g] → ⦃h, L2⦄ ⊢ W2 •[g] ⦃l, V2⦄ →
+| lsubsv_abbr: â\88\80L1,L2,V1,V2,W1,W2,l. â¦\83h, L1â¦\84 â\8a¢ V1 ¡[g] → ⦃h, L1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ →
+               L1 â\8a¢ W1 â¬\8c* W2 â\86\92 â¦\83h, L2â¦\84 â\8a¢ W2 ¡[g] → ⦃h, L2⦄ ⊢ W2 •[g] ⦃l, V2⦄ →
                lsubsv h g L1 L2 → lsubsv h g (L1. ⓓV1) (L2. ⓛW2)
 .
 
@@ -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 ¡⊑[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 = ⋆ →
 ]
 qed-.
 
-lemma lsubsv_inv_atom1: ∀h,g,L2. h ⊢ ⋆ ⊩:⊑[g] L2 → L2 = ⋆.
+lemma lsubsv_inv_atom1: ∀h,g,L2. 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 ¡⊑[g] L2 →
                            ∀I,K1,V1. L1 = K1. ⓑ{I} V1 →
-                           (∃∃K2. h ⊢ K1 ⊩:⊑[g] K2 & L2 = K2. ⓑ{I} V1) ∨
-                           â\88\83â\88\83K2,V2,W1,W2,l. â¦\83h, K1â¦\84 â\8a© V1 :[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
-                                            K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a© W2 :[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
-                                            h ⊢ K1 ⊩:⊑[g] K2 & L2 = K2. ⓛW2 & I = Abbr.
+                           (∃∃K2. h ⊢ K1 ¡⊑[g] K2 & L2 = K2. ⓑ{I} V1) ∨
+                           â\88\83â\88\83K2,V2,W1,W2,l. â¦\83h, K1â¦\84 â\8a¢ V1 ¡[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
+                                            K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a¢ W2 ¡[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
+                                            h ⊢ K1 ¡⊑[g] K2 & L2 = K2. ⓛW2 & I = Abbr.
 #h #g #L1 #L2 * -L1 -L2
 [ #J #K1 #U1 #H destruct
 | #I #L1 #L2 #V #HL12 #J #K1 #U1 #H destruct /3 width=3/
@@ -57,14 +57,14 @@ fact lsubsv_inv_pair1_aux: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair1: ∀h,g,I,K1,L2,V1. h ⊢ K1. ⓑ{I} V1 ⊩:⊑[g] L2 →
-                        (∃∃K2. h ⊢ K1 ⊩:⊑[g] K2 & L2 = K2. ⓑ{I} V1) ∨
-                        â\88\83â\88\83K2,V2,W1,W2,l. â¦\83h, K1â¦\84 â\8a© V1 :[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
-                                         K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a© W2 :[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
-                                         h ⊢ K1 ⊩:⊑[g] K2 & L2 = K2. ⓛW2 & I = Abbr.
+lemma lsubsv_inv_pair1: ∀h,g,I,K1,L2,V1. h ⊢ K1. ⓑ{I} V1 ¡⊑[g] L2 →
+                        (∃∃K2. h ⊢ K1 ¡⊑[g] K2 & L2 = K2. ⓑ{I} V1) ∨
+                        â\88\83â\88\83K2,V2,W1,W2,l. â¦\83h, K1â¦\84 â\8a¢ V1 ¡[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
+                                         K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a¢ W2 ¡[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
+                                         h ⊢ K1 ¡⊑[g] K2 & L2 = K2. ⓛW2 & I = Abbr.
 /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 ¡⊑[g] L2 → L2 = ⋆ → L1 = ⋆.
 #h #g #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -72,15 +72,15 @@ fact lsubsv_inv_atom2_aux: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 → L2 = ⋆ →
 ]
 qed-.
 
-lemma lsubsv_inv_atom2: ∀h,g,L1. h ⊢ L1 ⊩:⊑[g] ⋆ → L1 = ⋆.
+lemma lsubsv_inv_atom2: ∀h,g,L1. h ⊢ L1 ¡⊑[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 ¡⊑[g] L2 →
                            ∀I,K2,W2. L2 = K2. ⓑ{I} W2 →
-                           (∃∃K1. h ⊢ K1 ⊩:⊑[g] K2 & L1 = K1. ⓑ{I} W2) ∨
-                           â\88\83â\88\83K1,W1,V1,V2,l. â¦\83h, K1â¦\84 â\8a© V1 :[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
-                                            K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a© W2 :[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
-                                            h ⊢ K1 ⊩:⊑[g] K2 & L1 = K1. ⓓV1 & I = Abst.
+                           (∃∃K1. h ⊢ K1 ¡⊑[g] K2 & L1 = K1. ⓑ{I} W2) ∨
+                           â\88\83â\88\83K1,W1,V1,V2,l. â¦\83h, K1â¦\84 â\8a¢ V1 ¡[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
+                                            K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a¢ W2 ¡[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
+                                            h ⊢ K1 ¡⊑[g] K2 & L1 = K1. ⓓV1 & I = Abst.
 #h #g #L1 #L2 * -L1 -L2
 [ #J #K2 #U2 #H destruct
 | #I #L1 #L2 #V #HL12 #J #K2 #U2 #H destruct /3 width=3/
@@ -88,34 +88,34 @@ fact lsubsv_inv_pair2_aux: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 →
 ]
 qed-.
 
-lemma lsubsv_inv_pair2: ∀h,g,I,L1,K2,W2. h ⊢ L1 ⊩:⊑[g] K2. ⓑ{I} W2 →
-                        (∃∃K1. h ⊢ K1 ⊩:⊑[g] K2 & L1 = K1. ⓑ{I} W2) ∨
-                        â\88\83â\88\83K1,W1,V1,V2,l. â¦\83h, K1â¦\84 â\8a© V1 :[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
-                                         K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a© W2 :[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
-                                         h ⊢ K1 ⊩:⊑[g] K2 & L1 = K1. ⓓV1 & I = Abst.
+lemma lsubsv_inv_pair2: ∀h,g,I,L1,K2,W2. h ⊢ L1 ¡⊑[g] K2. ⓑ{I} W2 →
+                        (∃∃K1. h ⊢ K1 ¡⊑[g] K2 & L1 = K1. ⓑ{I} W2) ∨
+                        â\88\83â\88\83K1,W1,V1,V2,l. â¦\83h, K1â¦\84 â\8a¢ V1 ¡[g] & ⦃h, K1⦄ ⊢ V1 •[g] ⦃l+1, W1⦄ &
+                                         K1 â\8a¢ W1 â¬\8c* W2 & â¦\83h, K2â¦\84 â\8a¢ W2 ¡[g] & ⦃h, K2⦄ ⊢ W2 •[g] ⦃l, V2⦄ &
+                                         h ⊢ K1 ¡⊑[g] K2 & L1 = K1. ⓓV1 & I = Abst.
 /2 width=3 by lsubsv_inv_pair2_aux/ qed-.
 
 (* Basic_forward lemmas *****************************************************)
 
-lemma lsubsv_fwd_lsubss: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 → h ⊢ L1 •⊑[g] L2.
+lemma lsubsv_fwd_lsubss: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → h ⊢ L1 •⊑[g] L2.
 #h #g #L1 #L2 #H elim H -L1 -L2 // /2 width=1/ /2 width=6/
 qed-.
 
-lemma lsubsv_fwd_lsubs1: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 → L1 ≼[0, |L1|] L2.
+lemma lsubsv_fwd_lsubs1: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ≼[0, |L1|] L2.
 /3 width=3 by lsubsv_fwd_lsubss, lsubss_fwd_lsubs1/
 qed-.
 
-lemma lsubsv_fwd_lsubs2: ∀h,g,L1,L2. h ⊢ L1 ⊩:⊑[g] L2 → L1 ≼[0, |L2|] L2.
+lemma lsubsv_fwd_lsubs2: ∀h,g,L1,L2. h ⊢ L1 ¡⊑[g] L2 → L1 ≼[0, |L2|] L2.
 /3 width=3 by lsubsv_fwd_lsubss, lsubss_fwd_lsubs2/
 qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubsv_refl: ∀h,g,L. h ⊢ L ⊩:⊑[g] L.
+lemma lsubsv_refl: ∀h,g,L. h ⊢ L ¡⊑[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 ¡⊑[g] L2 →
                          ∀T1,T2. L2 ⊢ T1 ➡* T2 → L1 ⊢ T1 ➡* T2.
 /3 width=5 by lsubsv_fwd_lsubss, lsubss_cprs_trans/
 qed-.