update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpts.ma
@@ -0,0 +1,74 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/rt_computation/cpts_cpms.ma".
+include "basic_2/rt_equivalence/cpcs_cpcs.ma".
+include "basic_2/rt_equivalence/cpes.ma".
+include "basic_2/dynamic/cnv_preserve_cpcs.ma".
+
+(* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
+
+(* Forward lemmas with t-bound t-computarion for terms **********************)
+
+lemma cpts_cpms_conf_eq (h) (n) (a) (G) (L):
+      ∀T0. ⦃G,L⦄ ⊢ T0 ![h,a] → ∀T1. ⦃G,L⦄ ⊢ T0 ⬆*[h,n] T1 →
+      ∀T2. ⦃G,L⦄ ⊢ T0 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
+#h #a #n #G #L #T0 #HT0 #T1 #HT01 #T2 #HT02
+/3 width=6 by cpts_fwd_cpms, cnv_cpms_conf_eq/
+qed-.
+
+(* Inversion lemmas with t-bound t-computarion for terms ********************)
+
+lemma cnv_inv_cast_cpts (h) (a) (nu) (nt) (G) (L):
+      ∀U1. ⦃G,L⦄ ⊢ U1 ![h,a] → ∀U2. ⦃G,L⦄ ⊢ U1 ⬆*[h,nu] U2 →
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,nt] T2 →
+      ⦃G,L⦄ ⊢ U1 ⬌*[h,nu,nt] T1 → ⦃G,L⦄ ⊢ U2 ⬌*[h] T2.
+#h #a #nu #nt #G #L #U1 #HU1 #U2 #HU12 #T1 #HT1 #T2 #HT12 * #X1 #HUX1 #HTX1
+/3 width=8 by cpts_cpms_conf_eq, cpcs_canc_dx/
+qed-.
+
+lemma cnv_inv_appl_cpts (h) (a) (nv) (nt) (p) (G) (L):
+      ∀V1. ⦃G,L⦄ ⊢ V1 ![h,a] → ∀V2. ⦃G,L⦄ ⊢ V1 ⬆*[h,nv] V2 →
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,nt] T2 →
+      ∀V0. ⦃G,L⦄ ⊢ V1 ➡*[nv,h] V0 → ∀T0. ⦃G,L⦄ ⊢ T1 ➡*[nt,h] ⓛ{p}V0.T0 →
+      ∃∃W0,U0. ⦃G,L⦄ ⊢ V2 ➡*[h] W0 & ⦃G,L⦄ ⊢ T2 ➡*[h] ⓛ{p}W0.U0.
+#h #a #nv #nt #p #G #L #V1 #HV1 #V2 #HV12 #T1 #HT1 #T2 #HT12 #V0 #HV20 #T0 #HT20
+lapply (cpts_cpms_conf_eq … HV1 … HV12 … HV20) -nv -V1 #HV20
+lapply (cpts_cpms_conf_eq … HT1 … HT12 … HT20) -nt -T1 #HT20
+lapply (cpcs_bind_sn … Abst … T0 HV20 p) -HV20 #HV20
+lapply (cpcs_canc_dx … HT20 … HV20) -V0 #HT20
+elim (cpcs_inv_cprs … HT20) -HT20 #X #HT2X #HT0X
+elim (cpms_inv_abst_sn … HT0X) -HT0X #V0 #X0 #HV20 #_ #H destruct
+/2 width=4 by ex2_2_intro/
+qed-.
+
+(* Properties with t-bound t-computarion for terms **************************)
+
+lemma cnv_cast_cpts (h) (a) (nu) (nt) (G) (L):
+      ∀U1. ⦃G,L⦄ ⊢ U1 ![h,a] → ∀U2. ⦃G,L⦄ ⊢ U1 ⬆*[h,nu] U2 →
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,nt] T2 →
+      ⦃G,L⦄ ⊢ U2 ⬌*[h] T2 → ⦃G,L⦄ ⊢ U1 ⬌*[h,nu,nt] T1.
+#h #a #nu #nt #G #L #U1 #HU1 #U2 #HU12 #T1 #HT1 #T2 #HT12 #HUT2
+elim (cpcs_inv_cprs … HUT2) -HUT2 #X2 #HUX2 #HTX2
+/3 width=5 by cpts_cprs_trans, cpms_div/
+qed-.
+
+lemma cnv_appl_cpts (h) (a) (nv) (nt) (p) (G) (L):
+      ∀V1. ⦃G,L⦄ ⊢ V1 ![h,a] → ∀V2. ⦃G,L⦄ ⊢ V1 ⬆*[h,nv] V2 →
+      ∀T1. ⦃G,L⦄ ⊢ T1 ![h,a] → ∀T2. ⦃G,L⦄ ⊢ T1 ⬆*[h,nt] T2 →
+      ∀V0. ⦃G,L⦄ ⊢ V2 ➡*[h] V0 → ∀T0. ⦃G,L⦄ ⊢ T2 ➡*[h] ⓛ{p}V0.T0 →
+      ∃∃W0,U0. ⦃G,L⦄ ⊢ V1 ➡*[nv,h] W0 & ⦃G,L⦄ ⊢ T1 ➡*[nt,h] ⓛ{p}W0.U0.
+#h #a #nv #nt #p #G #L #V1 #HV1 #V2 #HV12 #T1 #HT1 #T2 #HT12 #V0 #HV20 #T0 #HT20
+/3 width=6 by cpts_cprs_trans, ex2_2_intro/
+qed-.