notational change for lexs

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_static / tc_lfxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
index b8976cbd9d46eded64124ba74a948acfb61244db..e1dd22673900719167ee343232a6bf4a06422fc4 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs.ma
@@ -25,40 +25,40 @@ interpretation "iterated extension on referred entries (local environment)"
 
 (* Basic properties *********************************************************)
 
-lemma tc_lfxs_step_dx: â\88\80R,L1,L,T. L1 ⦻**[R, T] L →
-                       â\88\80L2. L ⦻*[R, T] L2 â\86\92 L1 ⦻**[R, T] L2.
+lemma tc_lfxs_step_dx: â\88\80R,L1,L,T. L1 ⪤**[R, T] L →
+                       â\88\80L2. L ⪤*[R, T] L2 â\86\92 L1 ⪤**[R, T] L2.
 #R #L1 #L2 #T #HL1 #L2 @step @HL1 (**) (* auto fails *)
 qed-.
 
-lemma tc_lfxs_step_sn: â\88\80R,L1,L,T. L1 ⦻*[R, T] L →
-                       â\88\80L2. L ⦻**[R, T] L2 â\86\92 L1 ⦻**[R, T] L2.
+lemma tc_lfxs_step_sn: â\88\80R,L1,L,T. L1 ⪤*[R, T] L →
+                       â\88\80L2. L ⪤**[R, T] L2 â\86\92 L1 ⪤**[R, T] L2.
 #R #L1 #L2 #T #HL1 #L2 @TC_strap @HL1 (**) (* auto fails *)
 qed-.
 
-lemma tc_lfxs_atom: â\88\80R,I. â\8b\86 ⦻**[R, ⓪{I}] ⋆.
+lemma tc_lfxs_atom: â\88\80R,I. â\8b\86 ⪤**[R, ⓪{I}] ⋆.
 /2 width=1 by inj/ qed.
 
 lemma tc_lfxs_sort: ∀R,I,L1,L2,V1,V2,s.
-                    L1 ⦻**[R, â\8b\86s] L2 â\86\92 L1.â\93\91{I}V1 ⦻**[R, ⋆s] L2.ⓑ{I}V2.
+                    L1 ⪤**[R, â\8b\86s] L2 â\86\92 L1.â\93\91{I}V1 ⪤**[R, ⋆s] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #s #H elim H -L2
 /3 width=4 by lfxs_sort, tc_lfxs_step_dx, inj/
 qed.
 
 lemma tc_lfxs_zero: ∀R. (∀L. reflexive … (R L)) →
-                    â\88\80I,L1,L2,V. L1 ⦻**[R, V] L2 →
-                    L1.â\93\91{I}V ⦻**[R, #0] L2.ⓑ{I}V.
+                    â\88\80I,L1,L2,V. L1 ⪤**[R, V] L2 →
+                    L1.â\93\91{I}V ⪤**[R, #0] L2.ⓑ{I}V.
 #R #HR #I #L1 #L2 #V #H elim H -L2
 /3 width=5 by lfxs_zero, tc_lfxs_step_dx, inj/
 qed.
 
 lemma tc_lfxs_lref: ∀R,I,L1,L2,V1,V2,i.
-                    L1 ⦻**[R, #i] L2 â\86\92 L1.â\93\91{I}V1 ⦻**[R, #⫯i] L2.ⓑ{I}V2.
+                    L1 ⪤**[R, #i] L2 â\86\92 L1.â\93\91{I}V1 ⪤**[R, #⫯i] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #i #H elim H -L2
 /3 width=4 by lfxs_lref, tc_lfxs_step_dx, inj/
 qed.
 
 lemma tc_lfxs_gref: ∀R,I,L1,L2,V1,V2,l.
-                    L1 ⦻**[R, §l] L2 â\86\92 L1.â\93\91{I}V1 ⦻**[R, §l] L2.ⓑ{I}V2.
+                    L1 ⪤**[R, §l] L2 â\86\92 L1.â\93\91{I}V1 ⪤**[R, §l] L2.ⓑ{I}V2.
 #R #I #L1 #L2 #V1 #V2 #l #H elim H -L2
 /3 width=4 by lfxs_gref, tc_lfxs_step_dx, inj/
 qed.
@@ -71,7 +71,7 @@ lemma tc_lfxs_sym: ∀R. lexs_frees_confluent R cfull →
 qed-.
 
 lemma tc_lfxs_co: ∀R1,R2. (∀L,T1,T2. R1 L T1 T2 → R2 L T1 T2) →
-                  â\88\80L1,L2,T. L1 ⦻**[R1, T] L2 â\86\92 L1 ⦻**[R2, T] L2.
+                  â\88\80L1,L2,T. L1 ⪤**[R1, T] L2 â\86\92 L1 ⪤**[R2, T] L2.
 #R1 #R2 #HR #L1 #L2 #T #H elim H -L2
 /4 width=5 by lfxs_co, tc_lfxs_step_dx, inj/
 qed-.
@@ -79,19 +79,19 @@ qed-.
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: TC_lpx_sn_inv_atom1 *)
-lemma tc_lfxs_inv_atom_sn: â\88\80R,I,Y2. â\8b\86 ⦻**[R, ⓪{I}] Y2 → Y2 = ⋆.
+lemma tc_lfxs_inv_atom_sn: â\88\80R,I,Y2. â\8b\86 ⪤**[R, ⓪{I}] Y2 → Y2 = ⋆.
 #R #I #Y2 #H elim H -Y2 /3 width=3 by inj, lfxs_inv_atom_sn/
 qed-.
 
 (* Basic_2A1: uses: TC_lpx_sn_inv_atom2 *)
-lemma tc_lfxs_inv_atom_dx: â\88\80R,I,Y1. Y1 ⦻**[R, ⓪{I}] ⋆ → Y1 = ⋆.
+lemma tc_lfxs_inv_atom_dx: â\88\80R,I,Y1. Y1 ⪤**[R, ⓪{I}] ⋆ → Y1 = ⋆.
 #R #I #Y1 #H @(TC_ind_dx ??????? H) -Y1
 /3 width=3 by inj, lfxs_inv_atom_dx/
 qed-.
 
-lemma tc_lfxs_inv_sort: â\88\80R,Y1,Y2,s. Y1 ⦻**[R, ⋆s] Y2 →
+lemma tc_lfxs_inv_sort: â\88\80R,Y1,Y2,s. Y1 ⪤**[R, ⋆s] Y2 →
                         (Y1 = ⋆ ∧ Y2 = ⋆) ∨
-                        â\88\83â\88\83I,L1,L2,V1,V2. L1 ⦻**[R, ⋆s] L2 &
+                        â\88\83â\88\83I,L1,L2,V1,V2. L1 ⪤**[R, ⋆s] L2 &
                                          Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 #s #H elim H -Y2
 [ #Y2 #H elim (lfxs_inv_sort … H) -H *
@@ -107,9 +107,9 @@ lemma tc_lfxs_inv_sort: ∀R,Y1,Y2,s. Y1 ⦻**[R, ⋆s] Y2 →
 ] 
 qed-.
 
-lemma tc_lfxs_inv_gref: â\88\80R,Y1,Y2,l. Y1 ⦻**[R, §l] Y2 →
+lemma tc_lfxs_inv_gref: â\88\80R,Y1,Y2,l. Y1 ⪤**[R, §l] Y2 →
                         (Y1 = ⋆ ∧ Y2 = ⋆) ∨ 
-                        â\88\83â\88\83I,L1,L2,V1,V2. L1 ⦻**[R, §l] L2 &
+                        â\88\83â\88\83I,L1,L2,V1,V2. L1 ⪤**[R, §l] L2 &
                                          Y1 = L1.ⓑ{I}V1 & Y2 = L2.ⓑ{I}V2.
 #R #Y1 #Y2 #l #H elim H -Y2
 [ #Y2 #H elim (lfxs_inv_gref … H) -H *
@@ -126,16 +126,16 @@ lemma tc_lfxs_inv_gref: ∀R,Y1,Y2,l. Y1 ⦻**[R, §l] Y2 →
 qed-.
 
 lemma tc_lfxs_inv_bind: ∀R. (∀L. reflexive … (R L)) →
-                        â\88\80p,I,L1,L2,V,T. L1 ⦻**[R, ⓑ{p,I}V.T] L2 →
-                        L1 ⦻**[R, V] L2 â\88§ L1.â\93\91{I}V ⦻**[R, T] L2.ⓑ{I}V.
+                        â\88\80p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 →
+                        L1 ⪤**[R, V] L2 â\88§ L1.â\93\91{I}V ⪤**[R, T] L2.ⓑ{I}V.
 #R #HR #p #I #L1 #L2 #V #T #H elim H -L2
 [ #L2 #H elim (lfxs_inv_bind … V ? H) -H /3 width=1 by inj, conj/
 | #L #L2 #_ #H * elim (lfxs_inv_bind … V ? H) -H /3 width=3 by tc_lfxs_step_dx, conj/
 ]
 qed-.
 
-lemma tc_lfxs_inv_flat: â\88\80R,I,L1,L2,V,T. L1 ⦻**[R, ⓕ{I}V.T] L2 →
-                        L1 ⦻**[R, V] L2 â\88§ L1 ⦻**[R, T] L2.
+lemma tc_lfxs_inv_flat: â\88\80R,I,L1,L2,V,T. L1 ⪤**[R, ⓕ{I}V.T] L2 →
+                        L1 ⪤**[R, V] L2 â\88§ L1 ⪤**[R, T] L2.
 #R #I #L1 #L2 #V #T #H elim H -L2
 [ #L2 #H elim (lfxs_inv_flat … H) -H /3 width=1 by inj, conj/
 | #L #L2 #_ #H * elim (lfxs_inv_flat … H) -H /3 width=3 by tc_lfxs_step_dx, conj/
@@ -144,32 +144,32 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma tc_lfxs_inv_sort_pair_sn: â\88\80R,I,Y2,L1,V1,s. L1.â\93\91{I}V1 ⦻**[R, ⋆s] Y2 →
-                                â\88\83â\88\83L2,V2. L1 ⦻**[R, ⋆s] L2 & Y2 = L2.ⓑ{I}V2.
+lemma tc_lfxs_inv_sort_pair_sn: â\88\80R,I,Y2,L1,V1,s. L1.â\93\91{I}V1 ⪤**[R, ⋆s] Y2 →
+                                â\88\83â\88\83L2,V2. L1 ⪤**[R, ⋆s] L2 & Y2 = L2.ⓑ{I}V2.
 #R #I #Y2 #L1 #V1 #s #H elim (tc_lfxs_inv_sort … H) -H *
 [ #H destruct
 | #J #Y1 #L2 #X1 #V2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_sort_pair_dx: â\88\80R,I,Y1,L2,V2,s. Y1 ⦻**[R, ⋆s] L2.ⓑ{I}V2 →
-                                â\88\83â\88\83L1,V1. L1 ⦻**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1.
+lemma tc_lfxs_inv_sort_pair_dx: â\88\80R,I,Y1,L2,V2,s. Y1 ⪤**[R, ⋆s] L2.ⓑ{I}V2 →
+                                â\88\83â\88\83L1,V1. L1 ⪤**[R, ⋆s] L2 & Y1 = L1.ⓑ{I}V1.
 #R #I #Y1 #L2 #V2 #s #H elim (tc_lfxs_inv_sort … H) -H *
 [ #_ #H destruct
 | #J #L1 #Y2 #V1 #X2 #Hs #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_gref_pair_sn: â\88\80R,I,Y2,L1,V1,l. L1.â\93\91{I}V1 ⦻**[R, §l] Y2 →
-                                â\88\83â\88\83L2,V2. L1 ⦻**[R, §l] L2 & Y2 = L2.ⓑ{I}V2.
+lemma tc_lfxs_inv_gref_pair_sn: â\88\80R,I,Y2,L1,V1,l. L1.â\93\91{I}V1 ⪤**[R, §l] Y2 →
+                                â\88\83â\88\83L2,V2. L1 ⪤**[R, §l] L2 & Y2 = L2.ⓑ{I}V2.
 #R #I #Y2 #L1 #V1 #l #H elim (tc_lfxs_inv_gref … H) -H *
 [ #H destruct
 | #J #Y1 #L2 #X1 #V2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
 ]
 qed-.
 
-lemma tc_lfxs_inv_gref_pair_dx: â\88\80R,I,Y1,L2,V2,l. Y1 ⦻**[R, §l] L2.ⓑ{I}V2 →
-                                â\88\83â\88\83L1,V1. L1 ⦻**[R, §l] L2 & Y1 = L1.ⓑ{I}V1.
+lemma tc_lfxs_inv_gref_pair_dx: â\88\80R,I,Y1,L2,V2,l. Y1 ⪤**[R, §l] L2.ⓑ{I}V2 →
+                                â\88\83â\88\83L1,V1. L1 ⪤**[R, §l] L2 & Y1 = L1.ⓑ{I}V1.
 #R #I #Y1 #L2 #V2 #l #H elim (tc_lfxs_inv_gref … H) -H *
 [ #_ #H destruct
 | #J #L1 #Y2 #V1 #X2 #Hl #H1 #H2 destruct /2 width=4 by ex2_2_intro/
@@ -178,18 +178,18 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma tc_lfxs_fwd_pair_sn: â\88\80R,I,L1,L2,V,T. L1 ⦻**[R, â\91¡{I}V.T] L2 â\86\92 L1 ⦻**[R, V] L2.
+lemma tc_lfxs_fwd_pair_sn: â\88\80R,I,L1,L2,V,T. L1 ⪤**[R, â\91¡{I}V.T] L2 â\86\92 L1 ⪤**[R, V] L2.
 #R #I #L1 #L2 #V #T #H elim H -L2
 /3 width=5 by lfxs_fwd_pair_sn, tc_lfxs_step_dx, inj/
 qed-.
 
 lemma tc_lfxs_fwd_bind_dx: ∀R. (∀L. reflexive … (R L)) →
-                           â\88\80p,I,L1,L2,V,T. L1 ⦻**[R, ⓑ{p,I}V.T] L2 →
-                           L1.â\93\91{I}V ⦻**[R, T] L2.ⓑ{I}V.
+                           â\88\80p,I,L1,L2,V,T. L1 ⪤**[R, ⓑ{p,I}V.T] L2 →
+                           L1.â\93\91{I}V ⪤**[R, T] L2.ⓑ{I}V.
 #R #HR #p #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_bind … H) -H //
 qed-.
 
-lemma tc_lfxs_fwd_flat_dx: â\88\80R,I,L1,L2,V,T. L1 ⦻**[R, â\93\95{I}V.T] L2 â\86\92 L1 ⦻**[R, T] L2.
+lemma tc_lfxs_fwd_flat_dx: â\88\80R,I,L1,L2,V,T. L1 ⪤**[R, â\93\95{I}V.T] L2 â\86\92 L1 ⪤**[R, T] L2.
 #R #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_flat … H) -H //
 qed-.