milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
index 9e93c859d4c096bbedda88d2c206f69bdfb3e096..483ea690e474445d45732dfc15511d7b84143d40 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_preserve.ma
@@ -23,11 +23,10 @@ lemma cnv_preserve (a) (h): ∀G,L,T. ⦃G,L⦄ ⊢ T ![a,h] →
                             ∧∧ IH_cnv_cpms_conf_lpr a h G L T
                              & IH_cnv_cpm_trans_lpr a h G L T.
 #a #h #G #L #T #HT
-letin o ≝ (sd_O h)
-lapply (cnv_fwd_fsb … o … HT) -HT #H
+lapply (cnv_fwd_fsb … HT) -HT #H
 @(fsb_ind_fpbg … H) -G -L -T #G #L #T #_ #IH
 @conj [ letin aux ≝ cnv_cpms_conf_lpr_aux | letin aux ≝ cnv_cpm_trans_lpr_aux ]
-@(aux … o … G L T) // #G0 #L0 #T0 #H
+@(aux … G L T) // #G0 #L0 #T0 #H
 elim (IH … H) -IH -H //
 qed-.
 
@@ -54,7 +53,23 @@ lemma cnv_cpms_trans_lpr (a) (h) (G) (L) (T): IH_cnv_cpms_trans_lpr a h G L T.
 @(cpms_ind_dx … H) -n -T2 /3 width=6 by cnv_cpm_trans_lpr/
 qed-.
 
+lemma cnv_cpm_trans (a) (h) (G) (L):
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
+      ∀n,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
+/2 width=6 by cnv_cpm_trans_lpr/ qed-.
+
+(* Note: this is the preservation property *)
 lemma cnv_cpms_trans (a) (h) (G) (L):
       ∀T1. ⦃G,L⦄ ⊢ T1 ![a,h] →
       ∀n,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T2 ![a,h].
 /2 width=6 by cnv_cpms_trans_lpr/ qed-.
+
+lemma cnv_lpr_trans (a) (h) (G):
+      ∀L1,T. ⦃G,L1⦄ ⊢ T ![a,h] → ∀L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L2⦄ ⊢ T ![a,h].
+/2 width=6 by cnv_cpm_trans_lpr/ qed-.
+
+lemma cnv_lprs_trans (a) (h) (G):
+      ∀L1,T. ⦃G,L1⦄ ⊢ T ![a,h] → ∀L2. ⦃G,L1⦄ ⊢ ➡*[h] L2 → ⦃G,L2⦄ ⊢ T ![a,h].
+#a #h #G #L1 #T #HT #L2 #H
+@(lprs_ind_dx … H) -L2 /2 width=3 by cnv_lpr_trans/
+qed-.