- ground_2: rtmap: disjointness relation

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
index c92a4ad7b861832d3fa34ca6233ecc2e466e186d..bc7061ba7a400aae24268eddf8a030c6f55a07e2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_fqup.ma
@@ -19,11 +19,12 @@ include "basic_2/i_static/tc_lfxs.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma tc_lfxs_refl: ∀R. (∀L. reflexive … (R L)) → ∀T. reflexive … (tc_lfxs R T).
+lemma tc_lfxs_refl: ∀R. c_reflexive … R →
+                    ∀T. reflexive … (tc_lfxs R T).
 /3 width=1 by lfxs_refl, inj/ qed.
 
 (* Basic_2A1: uses: TC_lpx_sn_pair TC_lpx_sn_pair_refl *)
-lemma tc_lfxs_pair_refl: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_pair_refl: ∀R. c_reflexive … R →
                          ∀L,V1,V2. LTC … 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 tc_lfxs_step_dx, lfxs_pair_refl, inj/
@@ -31,7 +32,7 @@ qed.
 
 (* Advanced eliminators *****************************************************)
 
-lemma tc_lfxs_ind_sn: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_ind_sn: ∀R. c_reflexive … R →
                       ∀L1,T. ∀R0:predicate …. R0 L1 →
                       (∀L,L2. L1 ⪤**[R, T] L → L ⪤*[R, T] L2 → R0 L → R0 L2) →
                       ∀L2. L1 ⪤**[R, T] L2 → R0 L2.
@@ -39,7 +40,7 @@ lemma tc_lfxs_ind_sn: ∀R. (∀L. reflexive … (R L)) →
 @(TC_star_ind … HL1 IHL1 … HL12) /2 width=1 by lfxs_refl/
 qed-.
 
-lemma tc_lfxs_ind_dx: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_ind_dx: ∀R. c_reflexive … R →
                       ∀L2,T. ∀R0:predicate …. R0 L2 →
                       (∀L1,L. L1 ⪤*[R, T] L → L ⪤**[R, T] L2 → R0 L → R0 L1) →
                       ∀L1. L1 ⪤**[R, T] L2 → R0 L1.
@@ -49,7 +50,7 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma tc_lfxs_inv_bind_void: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_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.ⓧ.
 #R #HR #p #I #L1 #L2 #V #T #H @(tc_lfxs_ind_sn … HR … H) -L2
@@ -60,7 +61,7 @@ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-lemma tc_lfxs_fwd_bind_dx_void: ∀R. (∀L. reflexive … (R L)) →
+lemma tc_lfxs_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.ⓧ.
 #R #HR #p #I #L1 #L2 #V #T #H elim (tc_lfxs_inv_bind_void … H) -H //