some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / i_static / rexs_fqup.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
index c21d8201700847f34929c3de4b03a74a6ed53dcd..fbb41879cf8d2827e0009108c50b82247625e7cc 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/i_static/rexs_fqup.ma
@@ -25,13 +25,13 @@ lemma rexs_refl: ∀R. c_reflexive … R →
 
 (* Basic_2A1: uses: TC_lpx_sn_pair TC_lpx_sn_pair_refl *)
 lemma rexs_pair_refl: ∀R. c_reflexive … R →
-                      ∀L,V1,V2. CTC … R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤*[R, T] L.ⓑ{I}V2.
+                      ∀L,V1,V2. CTC … R L V1 V2 → ∀I,T. L.ⓑ{I}V1 ⪤*[R,T] L.ⓑ{I}V2.
 #R #HR #L #V1 #V2 #H elim H -V2
 /3 width=3 by rexs_step_dx, rex_pair_refl, inj/
 qed.
 
 lemma rexs_tc: ∀R,L1,L2,T,f. 𝐈⦃f⦄ → TC … (sex cfull (cext2 R) f) L1 L2 →
-               L1 ⪤*[R, T] L2.
+               L1 ⪤*[R,T] L2.
 #R #L1 #L2 #T #f #Hf #H elim H -L2
 [ elim (frees_total L1 T) | #L elim (frees_total L T) ]
 /5 width=7 by sex_sdj, rexs_step_dx, sdj_isid_sn, inj, ex2_intro/
@@ -41,16 +41,16 @@ qed.
 
 lemma rexs_ind_sn: ∀R. c_reflexive … R →
                    ∀L1,T. ∀Q:predicate …. Q L1 →
-                   (∀L,L2. L1 ⪤*[R, T] L → L ⪤[R, T] L2 → Q L → Q L2) →
-                   ∀L2. L1 ⪤*[R, T] L2 → Q L2.
+                   (∀L,L2. L1 ⪤*[R,T] L → L ⪤[R,T] L2 → Q L → Q L2) →
+                   ∀L2. L1 ⪤*[R,T] L2 → Q L2.
 #R #HR #L1 #T #Q #HL1 #IHL1 #L2 #HL12
 @(TC_star_ind … HL1 IHL1 … HL12) /2 width=1 by rex_refl/
 qed-.
 
 lemma rexs_ind_dx: ∀R. c_reflexive … R →
                    ∀L2,T. ∀Q:predicate …. Q L2 →
-                   (∀L1,L. L1 ⪤[R, T] L → L ⪤*[R, T] L2 → Q L → Q L1) →
-                   ∀L1. L1 ⪤*[R, T] L2 → Q L1.
+                   (∀L1,L. L1 ⪤[R,T] L → L ⪤*[R,T] L2 → Q L → Q L1) →
+                   ∀L1. L1 ⪤*[R,T] L2 → Q L1.
 #R #HR #L2 #Q #HL2 #IHL2 #L1 #HL12
 @(TC_star_ind_dx … HL2 IHL2 … HL12) /2 width=4 by rex_refl/
 qed-.
@@ -58,8 +58,8 @@ qed-.
 (* Advanced inversion lemmas ************************************************)
 
 lemma rexs_inv_bind_void: ∀R. c_reflexive … R →
-                          ∀p,I,L1,L2,V,T. L1 ⪤*[R, ⓑ{p,I}V.T] L2 →
-                          ∧∧ L1 ⪤*[R, V] L2 & L1.ⓧ ⪤*[R, T] L2.ⓧ.
+                          ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ{p,I}V.T] L2 →
+                          ∧∧ L1 ⪤*[R,V] L2 & L1.ⓧ ⪤*[R,T] L2.ⓧ.
 #R #HR #p #I #L1 #L2 #V #T #H @(rexs_ind_sn … HR … H) -L2
 [ /3 width=1 by rexs_refl, conj/
 | #L #L2 #_ #H * elim (rex_inv_bind_void … H) -H /3 width=3 by rexs_step_dx, conj/
@@ -69,7 +69,7 @@ qed-.
 (* Advanced forward lemmas **************************************************)
 
 lemma rexs_fwd_bind_dx_void: ∀R. c_reflexive … R →
-                             ∀p,I,L1,L2,V,T. L1 ⪤*[R, ⓑ{p,I}V.T] L2 →
-                             L1.ⓧ ⪤*[R, T] L2.ⓧ.
+                             ∀p,I,L1,L2,V,T. L1 ⪤*[R,ⓑ{p,I}V.T] L2 →
+                             L1.ⓧ ⪤*[R,T] L2.ⓧ.
 #R #HR #p #I #L1 #L2 #V #T #H elim (rexs_inv_bind_void … H) -H //
 qed-.