update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
index 6424733db5b25067a5c7c1815c325f27961bb158..b1ce9c2429a659f6a9703b890cb7d859647b2c9a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_lpr.ma
@@ -19,33 +19,39 @@ include "basic_2/rt_computation/lprs_tc.ma".
 (* Eliminators with r-transition for full local environments ****************)
 
 (* Basic_2A1: was: lprs_ind_dx *)
-lemma lprs_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.
+lemma lprs_ind_sn (h) (G) (L2):
+      ∀Q:predicate lenv. Q L2 →
+      (∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L → ❪G,L❫ ⊢ ➡*[h,0] L2 → Q L → Q L1) →
+      ∀L1. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L1.
 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_sn/ qed-.
 
 (* Basic_2A1: was: lprs_ind *)
-lemma lprs_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.
+lemma lprs_ind_dx (h) (G) (L1):
+      ∀Q:predicate lenv. Q L1 →
+      (∀L,L2. ❪G,L1❫ ⊢ ➡*[h,0] L → ❪G,L❫ ⊢ ➡[h,0] L2 → Q L → Q L2) →
+      ∀L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L2.
 /4 width=8 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, cpr_refl, lex_CTC_ind_dx/ qed-.
 
 (* Properties with unbound rt-transition for full local environments ********)
 
-lemma lpr_lprs (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡[h] L2 → ❪G,L1❫ ⊢ ➡*[h] L2.
+lemma lpr_lprs (h) (G):
+      ∀L1,L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
 /4 width=3 by lprs_CTC, lpr_cprs_trans, lex_CTC_inj/ qed.
 
 (* Basic_2A1: was: lprs_strap2 *)
-lemma lprs_step_sn (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ➡[h] L →
-                            ∀L2.❪G,L❫ ⊢ ➡*[h] L2 → ❪G,L1❫ ⊢ ➡*[h] L2.
+lemma lprs_step_sn (h) (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ➡[h,0] L →
+      ∀L2.❪G,L❫ ⊢ ➡*[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_strap1 *)
-lemma lprs_step_dx (h) (G): ∀L1,L. ❪G,L1❫ ⊢ ➡*[h] L →
-                            ∀L2. ❪G,L❫ ⊢ ➡[h] L2 → ❪G,L1❫ ⊢ ➡*[h] L2.
+lemma lprs_step_dx (h) (G):
+      ∀L1,L. ❪G,L1❫ ⊢ ➡*[h,0] L →
+      ∀L2. ❪G,L❫ ⊢ ➡[h,0] L2 → ❪G,L1❫ ⊢ ➡*[h,0] L2.
 /4 width=3 by lprs_inv_CTC, lprs_CTC, lpr_cprs_trans, lex_CTC_step_dx/ qed-.
 
-lemma lprs_strip (h) (G): confluent2 … (lprs h G) (lpr h G).
+lemma lprs_strip (h) (G):
+      confluent2 … (lprs h 0 G) (lpr h 0 G).
 #h #G #L0 #L1 #HL01 #L2 #HL02
 elim (TC_strip1 … L1 ?? HL02) -HL02
 [ /3 width=3 by lprs_TC, ex2_intro/ | skip