- the relation for pointwise extensions now takes a binder as argument

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
index c79161304fbd59a97b9e063e59c93570f274abbf..d6cf867a8d0e54700f489abced21249f84398408 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lsubd.ma
@@ -32,13 +32,13 @@ interpretation
 
 (* Basic_forward lemmas *****************************************************)
 
-lemma lsubd_fwd_lsubr: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 â\86\92 L1 â\8a\91 L2.
+lemma lsubd_fwd_lsubr: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 â\86\92 L1 â«\83 L2.
 #h #g #G #L1 #L2 #H elim H -L1 -L2 /2 width=1 by lsubr_bind, lsubr_abst/
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lsubd_inv_atom1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 → L1 = ⋆ → L2 = ⋆.
+fact lsubd_inv_atom1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 → L1 = ⋆ → L2 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -46,14 +46,14 @@ fact lsubd_inv_atom1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 → L1 = ⋆
 ]
 qed-.
 
-lemma lsubd_inv_atom1: â\88\80h,g,G,L2. G â\8a¢ â\8b\86 â\96ªâ\8a\91[h, g] L2 → L2 = ⋆.
+lemma lsubd_inv_atom1: â\88\80h,g,G,L2. G â\8a¢ â\8b\86 â\96ªâ«\83[h, g] L2 → L2 = ⋆.
 /2 width=6 by lsubd_inv_atom1_aux/ qed-.
 
-fact lsubd_inv_pair1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 →
+fact lsubd_inv_pair1_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 →
                           ∀I,K1,X. L1 = K1.ⓑ{I}X →
-                          (â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+                          (â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
                           ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                      G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 &
+                                      G â\8a¢ K1 â\96ªâ«\83[h, g] K2 &
                                       I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 #h #g #G #L1 #L2 * -L1 -L2
 [ #J #K1 #X #H destruct
@@ -62,14 +62,14 @@ fact lsubd_inv_pair1_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
 ]
 qed-.
 
-lemma lsubd_inv_pair1: â\88\80h,g,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\96ªâ\8a\91[h, g] L2 →
-                       (â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
+lemma lsubd_inv_pair1: â\88\80h,g,I,G,K1,L2,X. G â\8a¢ K1.â\93\91{I}X â\96ªâ«\83[h, g] L2 →
+                       (â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & L2 = K2.ⓑ{I}X) ∨
                        ∃∃K2,W,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                   G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 &
+                                   G â\8a¢ K1 â\96ªâ«\83[h, g] K2 &
                                    I = Abbr & L2 = K2.ⓛW & X = ⓝW.V.
 /2 width=3 by lsubd_inv_pair1_aux/ qed-.
 
-fact lsubd_inv_atom2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 → L2 = ⋆ → L1 = ⋆.
+fact lsubd_inv_atom2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 → L2 = ⋆ → L1 = ⋆.
 #h #g #G #L1 #L2 * -L1 -L2
 [ //
 | #I #L1 #L2 #V #_ #H destruct
@@ -77,14 +77,14 @@ fact lsubd_inv_atom2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 → L2 = ⋆
 ]
 qed-.
 
-lemma lsubd_inv_atom2: â\88\80h,g,G,L1. G â\8a¢ L1 â\96ªâ\8a\91[h, g] ⋆ → L1 = ⋆.
+lemma lsubd_inv_atom2: â\88\80h,g,G,L1. G â\8a¢ L1 â\96ªâ«\83[h, g] ⋆ → L1 = ⋆.
 /2 width=6 by lsubd_inv_atom2_aux/ qed-.
 
-fact lsubd_inv_pair2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 →
+fact lsubd_inv_pair2_aux: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 →
                           ∀I,K2,W. L2 = K2.ⓑ{I}W →
-                          (â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+                          (â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
                           ∃∃K1,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                    G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                                    G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 #h #g #G #L1 #L2 * -L1 -L2
 [ #J #K2 #U #H destruct
 | #I #L1 #L2 #V #HL12 #J #K2 #U #H destruct /3 width=3 by ex2_intro, or_introl/
@@ -92,22 +92,22 @@ fact lsubd_inv_pair2_aux: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
 ]
 qed-.
 
-lemma lsubd_inv_pair2: â\88\80h,g,I,G,L1,K2,W. G â\8a¢ L1 â\96ªâ\8a\91[h, g] K2.ⓑ{I}W →
-                       (â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
+lemma lsubd_inv_pair2: â\88\80h,g,I,G,L1,K2,W. G â\8a¢ L1 â\96ªâ«\83[h, g] K2.ⓑ{I}W →
+                       (â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & L1 = K1.ⓑ{I}W) ∨
                        ∃∃K1,V,l. ⦃G, K1⦄ ⊢ V ▪[h, g] l+1 & ⦃G, K2⦄ ⊢ W ▪[h, g] l &
-                                 G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
+                                 G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & I = Abst & L1 = K1. ⓓⓝW.V.
 /2 width=3 by lsubd_inv_pair2_aux/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma lsubd_refl: â\88\80h,g,G,L. G â\8a¢ L â\96ªâ\8a\91[h, g] L.
+lemma lsubd_refl: â\88\80h,g,G,L. G â\8a¢ L â\96ªâ«\83[h, g] L.
 #h #g #G #L elim L -L /2 width=1 by lsubd_pair/
 qed.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubd_ldrop_O1_conf: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 →
+lemma lsubd_ldrop_O1_conf: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 →
                            ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
-                           â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & ⇩[s, 0, e] L2 ≡ K2.
+                           â\88\83â\88\83K2. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & ⇩[s, 0, e] L2 ≡ K2.
 #h #g #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
 | #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
@@ -128,9 +128,9 @@ lemma lsubd_ldrop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ▪⊑[h, g] L2 →
 qed-.
 
 (* Note: the constant 0 cannot be generalized *)
-lemma lsubd_ldrop_O1_trans: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ\8a\91[h, g] L2 →
+lemma lsubd_ldrop_O1_trans: â\88\80h,g,G,L1,L2. G â\8a¢ L1 â\96ªâ«\83[h, g] L2 →
                             ∀K2,s,e. ⇩[s, 0, e] L2 ≡ K2 →
-                            â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ\8a\91[h, g] K2 & ⇩[s, 0, e] L1 ≡ K1.
+                            â\88\83â\88\83K1. G â\8a¢ K1 â\96ªâ«\83[h, g] K2 & ⇩[s, 0, e] L1 ≡ K1.
 #h #g #G #L1 #L2 #H elim H -L1 -L2
 [ /2 width=3 by ex2_intro/
 | #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H