milestone in basic_2 with additions in static_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 4ea01e53417a1eaa72f4f3a840ae2dfb9d7bbf10..297a86498220e60fbcbf38df9caecd7f8bbe5337 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-.
 
@@ -42,8 +41,56 @@ qed-.
 
 (* Advanced preservation properties *****************************************)
 
+lemma cnv_cpms_conf (a) (h) (G) (L):
+      ∀T0. ⦃G,L⦄ ⊢ T0 ![a,h] →
+      ∀n1,T1. ⦃G,L⦄ ⊢ T0 ➡*[n1,h] T1 → ∀n2,T2. ⦃G,L⦄ ⊢ T0 ➡*[n2,h] T2 →
+      ∃∃T. ⦃G,L⦄ ⊢ T1 ➡*[n2-n1,h] T & ⦃G,L⦄ ⊢ T2 ➡*[n1-n2,h] T.
+/2 width=8 by cnv_cpms_conf_lpr/ qed-.
+
 (* Basic_2A1: uses: snv_cprs_lpr *)
 lemma cnv_cpms_trans_lpr (a) (h) (G) (L) (T): IH_cnv_cpms_trans_lpr a h G L T.
 #a #h #G #L1 #T1 #HT1 #n #T2 #H
 @(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-.
+
+(* Advanced inversion lemmas ************************************************)
+
+lemma cnv_inv_appl_SO (a) (h) (G) (L):
+      ∀V,T. ⦃G, L⦄ ⊢ ⓐV.T ![a, h] →
+      ∃∃n,p,W0,U0. a = Ⓣ → n = 1 & ⦃G, L⦄ ⊢ V ![a, h] & ⦃G, L⦄ ⊢ T ![a, h] &
+                   ⦃G, L⦄ ⊢ V ➡*[1, h] W0 & ⦃G, L⦄ ⊢ T ➡*[n, h] ⓛ{p}W0.U0.
+* #h #G #L #V #T #H
+elim (cnv_inv_appl … H) -H [ * [| #n ] | #n ] #p #W #U #Ha #HV #HT #HVW #HTU
+[ elim (cnv_fwd_cpm_SO … (ⓛ{p}W.U))
+  [|*: /2 width=8 by cnv_cpms_trans/ ] #X #HU0
+  elim (cpm_inv_abst1 … HU0) #W0 #U0 #HW0 #_ #H0 destruct
+  lapply (cpms_step_dx … HVW … HW0) -HVW -HW0 #HVW0
+  lapply (cpms_step_dx … HTU … HU0) -HTU -HU0 #HTU0
+  /2 width=7 by ex5_4_intro/
+| lapply (Ha ?) -Ha [ // ] #Ha
+  lapply (le_n_O_to_eq n ?) [ /3 width=1 by le_S_S_to_le/ ] -Ha #H destruct
+  /2 width=7 by ex5_4_intro/
+| @(ex5_4_intro … HV HT HVW HTU) #H destruct
+]
+qed-.