some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lpxs_lpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
index 52a4186179ff5f7f358d4d69c61ee78ce87a7ac0..c275077765fae748d0d98d64bd42c381e2657701 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs_lpx.ma
@@ -20,31 +20,31 @@ include "basic_2/rt_computation/lpxs.ma".
 
 (* Properties with unbound rt-transition for full local environments ********)
 
-lemma lpx_lpxs (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+lemma lpx_lpxs (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → ⦃G,L1⦄ ⊢ ⬈*[h] L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lpxs_strap2 *)
-lemma lpxs_step_sn (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L →
-                            ∀L2. ⦃G, L⦄ ⊢ ⬈*[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+lemma lpxs_step_sn (h) (G): ∀L1,L. ⦃G,L1⦄ ⊢ ⬈[h] L →
+                            ∀L2. ⦃G,L⦄ ⊢ ⬈*[h] L2 → ⦃G,L1⦄ ⊢ ⬈*[h] L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_strap1 *)
-lemma lpxs_step_dx (h) (G): ∀L1,L. ⦃G, L1⦄ ⊢ ⬈*[h] L →
-                            ∀L2. ⦃G, L⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈*[h] L2.
+lemma lpxs_step_dx (h) (G): ∀L1,L. ⦃G,L1⦄ ⊢ ⬈*[h] L →
+                            ∀L2. ⦃G,L⦄ ⊢ ⬈[h] L2 → ⦃G,L1⦄ ⊢ ⬈*[h] L2.
 /3 width=3 by lpx_cpxs_trans, lex_CTC_step_dx/ qed-.
 
 (* Eliminators with unbound rt-transition for full local environments *******)
 
 (* Basic_2A1: was: lpxs_ind_dx *)
 lemma lpxs_ind_sn (h) (G) (L2): ∀Q:predicate lenv. Q L2 →
-                                (∀L1,L. ⦃G, L1⦄ ⊢ ⬈[h] L → ⦃G, L⦄ ⊢ ⬈*[h] L2 → Q L → Q L1) →
-                                ∀L1. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → Q L1.
+                                (∀L1,L. ⦃G,L1⦄ ⊢ ⬈[h] L → ⦃G,L⦄ ⊢ ⬈*[h] L2 → Q L → Q L1) →
+                                ∀L1. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → Q L1.
 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_ind *)
 lemma lpxs_ind_dx (h) (G) (L1): ∀Q:predicate lenv. Q L1 →
-                                (∀L,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L → ⦃G, L⦄ ⊢ ⬈[h] L2 → Q L → Q L2) →
-                                ∀L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 → Q L2.
+                                (∀L,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L → ⦃G,L⦄ ⊢ ⬈[h] L2 → Q L → Q L2) →
+                                ∀L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 → Q L2.
 /3 width=7 by lpx_cpxs_trans, cpx_refl, lex_CTC_ind_dx/ qed-.
 
 (* Properties with context-sensitive extended rt-transition for terms *******)
@@ -65,7 +65,7 @@ qed-.
 (* Advanced properties ******************************************************)
 
 (* Basic_2A1: was: lpxs_pair2 *)
-lemma lpxs_pair_dx (h) (G): ∀L1,L2. ⦃G, L1⦄ ⊢ ⬈*[h] L2 →
-                            ∀V1,V2. ⦃G, L2⦄ ⊢ V1 ⬈*[h] V2 →
-                            ∀I. ⦃G, L1.ⓑ{I}V1⦄ ⊢ ⬈*[h] L2.ⓑ{I}V2.
+lemma lpxs_pair_dx (h) (G): ∀L1,L2. ⦃G,L1⦄ ⊢ ⬈*[h] L2 →
+                            ∀V1,V2. ⦃G,L2⦄ ⊢ V1 ⬈*[h] V2 →
+                            ∀I. ⦃G,L1.ⓑ{I}V1⦄ ⊢ ⬈*[h] L2.ⓑ{I}V2.
 /3 width=3 by lpxs_pair, lpxs_cpxs_trans/ qed.