update in static_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / nta_preserve_cpcs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma
index cbcd378a4d774ce1a01444150e5d0cccc5a254e8..383742b7ad93beb5d44e6a3e7d4598199e2344f5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve_cpcs.ma
@@ -20,43 +20,43 @@ include "basic_2/dynamic/nta_preserve.ma".
 (* Properties based on type equivalence and preservation *******************)
 
 (* Basic_1: uses: ty3_tred *)
-lemma nta_cprs_trans (a) (h) (G) (L):
-      ∀T,U1. ⦃G,L⦄ ⊢ T :[a,h] U1 → ∀U2.  ⦃G,L⦄ ⊢ U1 ➡*[h] U2 → ⦃G,L⦄ ⊢ T :[a,h] U2.
-#a #h #G #L #T #U1 #H #U2 #HU12
+lemma nta_cprs_trans (h) (a) (G) (L):
+      ∀T,U1. ⦃G,L⦄ ⊢ T :[h,a] U1 → ∀U2. ⦃G,L⦄ ⊢ U1 ➡*[h] U2 → ⦃G,L⦄ ⊢ T :[h,a] U2.
+#h #a #G #L #T #U1 #H #U2 #HU12
 /4 width=4 by nta_conv_cnv, nta_fwd_cnv_dx, cnv_cpms_trans, cpcs_cprs_dx/
 qed-.
 
 (* Basic_1: uses: ty3_sred_back *)
-lemma cprs_nta_trans (a) (h) (G) (L):
-      ∀T1,U0. ⦃G,L⦄ ⊢ T1 :[a,h] U0 → ∀T2.  ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
-      ∀U. ⦃G,L⦄ ⊢ T2 :[a,h] U →  ⦃G,L⦄ ⊢ T1 :[a,h] U.
-#a #h #G #L #T1 #U0 #HT1 #T2 #HT12 #U #H
+lemma cprs_nta_trans (h) (a) (G) (L):
+      ∀T1,U0. ⦃G,L⦄ ⊢ T1 :[h,a] U0 → ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
+      ∀U. ⦃G,L⦄ ⊢ T2 :[h,a] U →  ⦃G,L⦄ ⊢ T1 :[h,a] U.
+#h #a #G #L #T1 #U0 #HT1 #T2 #HT12 #U #H
 lapply (nta_cprs_conf … HT1 … HT12) -HT12 #HT2
 /4 width=6 by nta_mono, nta_conv_cnv, nta_fwd_cnv_dx/
 qed-.
 
-lemma cprs_nta_trans_cnv (a) (h) (G) (L):
-      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] → ∀T2.  ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
-      ∀U. ⦃G,L⦄ ⊢ T2 :[a,h] U →  ⦃G,L⦄ ⊢ T1 :[a,h] U.
-#a #h #G #L #T1 #HT1 #T2 #HT12 #U #H
+lemma cprs_nta_trans_cnv (h) (a) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T1 ➡*[h] T2 →
+      ∀U. ⦃G,L⦄ ⊢ T2 :[h,a] U → ⦃G,L⦄ ⊢ T1 :[h,a] U.
+#h #a #G #L #T1 #HT1 #T2 #HT12 #U #H
 elim (cnv_nta_sn … HT1) -HT1 #U0 #HT1
 /2 width=3 by cprs_nta_trans/
 qed-.
 
 (* Basic_1: uses: ty3_sconv *)
-lemma nta_cpcs_conf (a) (h) (G) (L):
-      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U → ∀T2.  ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 →
-      ∀U0. ⦃G,L⦄ ⊢ T2 :[a,h] U0 →  ⦃G,L⦄ ⊢ T2 :[a,h] U.
-#a #h #G #L #T1 #U #HT1 #T2 #HT12 #U0 #HT2
+lemma nta_cpcs_conf (h) (a) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[h,a] U → ∀T2. ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 →
+      ∀U0. ⦃G,L⦄ ⊢ T2 :[h,a] U0 → ⦃G,L⦄ ⊢ T2 :[h,a] U.
+#h #a #G #L #T1 #U #HT1 #T2 #HT12 #U0 #HT2
 elim (cpcs_inv_cprs … HT12) -HT12 #T0 #HT10 #HT02
 /3 width=5 by  cprs_nta_trans, nta_cprs_conf/
 qed-.
 
 (* Note: type preservation by valid r-equivalence *)
-lemma nta_cpcs_conf_cnv (a) (h) (G) (L):
-      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[a,h] U →
-      ∀T2.  ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h] →  ⦃G,L⦄ ⊢ T2 :[a,h] U.
-#a #h #G #L #T1 #U #HT1 #T2 #HT12 #HT2
+lemma nta_cpcs_conf_cnv (h) (a) (G) (L):
+      ∀T1,U. ⦃G,L⦄ ⊢ T1 :[h,a] U →
+      ∀T2. ⦃G,L⦄ ⊢ T1 ⬌*[h] T2 → ⦃G,L⦄ ⊢ T2 ![h,a] → ⦃G,L⦄ ⊢ T2 :[h,a] U.
+#h #a #G #L #T1 #U #HT1 #T2 #HT12 #HT2
 elim (cnv_nta_sn … HT2) -HT2 #U0 #HT2
 /2 width=3 by nta_cpcs_conf/
 qed-.