partial commit of the "dynamic" component

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
index 9451e34d296991f312e5fff11864c77dc44a327c..643bf6569fde0a82ea166f1278fccf5117e9fc90 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_cpcs.ma
@@ -12,9 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/unwind/sstas_sstas.ma".
-include "basic_2/equivalence/cpcs_ltpr.ma".
-include "basic_2/dynamic/snv_ltpss_dx.ma".
+include "basic_2/unfold/sstas_sstas.ma".
+include "basic_2/equivalence/cpcs_cpcs.ma".
 include "basic_2/dynamic/snv_sstas.ma".
 include "basic_2/dynamic/ygt.ma".
 
@@ -22,15 +21,15 @@ include "basic_2/dynamic/ygt.ma".
 
 (* Inductive premises for the preservation results **************************)
 
-definition IH_snv_ltpr_tpr: ∀h:sh. sd h → relation2 lenv term ≝
-                            λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                            ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 ¡[g].
+definition IH_snv_cpr_lpr: ∀h:sh. sd h → relation2 lenv term ≝
+                           λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] →
+                           ∀T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ⊢ ➡ L2 → ⦃h, L2⦄ ⊢ T2 ¡[g].
 
-definition IH_ssta_ltpr_tpr: ∀h:sh. sd h → relation2 lenv term ≝
-                             λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                             ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
-                             ∀L2. L1 ➡ L2 → ∀T2. T1 ➡ T2 →
-                             ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2.
+definition IH_ssta_cpr_lpr: ∀h:sh. sd h → relation2 lenv term ≝
+                            λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] →
+                            ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
+                            ∀T2. L1 ⊢ T1 ➡ T2 → ∀L2. L1 ⊢ ➡ L2 →
+                            ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ⬌* U2.
 
 definition IH_snv_ssta: ∀h:sh. sd h → relation2 lenv term ≝
                         λh,g,L1,T1. ⦃h, L1⦄ ⊢ T1 ¡[g] →
@@ -42,64 +41,45 @@ definition IH_snv_lsubsv: ∀h:sh. sd h → relation2 lenv term ≝
 
 (* Properties for the preservation results **********************************)
 
-fact snv_ltpr_cpr_aux: ∀h,g,L1,T1. IH_snv_ltpr_tpr h g L1 T1 →
-                       ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                       ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 → ⦃h, L2⦄ ⊢ T2 ¡[g].
-#h #g #L1 #T1 #IH #HT1 #L2 #HL12 #T2 * #T #HT1T #HTT2
-lapply (IH … HL12 … HT1T) -HL12 // -T1 #HT0
-lapply (snv_tpss_conf … HT0 … HTT2) -T //
+fact snv_cprs_lpr_aux: ∀h,g,L0,T0.
+                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
+                       ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] →
+                       ∀T2. L1 ⊢ T1 ➡* T2 → ∀L2. L1 ⊢ ➡ L2 → ⦃h, L2⦄ ⊢ T2 ¡[g].
+#h #g #L0 #T0 #IH #L1 #T1 #HLT0 #HT1 #T2 #H
+elim H -T2 [ /2 width=6/ ] -HT1
+/4 width=6 by ygt_yprs_trans, cprs_yprs/
 qed-.
 
-fact ssta_ltpr_cpr_aux: ∀h,g,L1,T1. IH_ssta_ltpr_tpr h g L1 T1 →
-                        ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                        ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
-                        ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡ T2 →
-                        ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2.
-#h #g #L1 #T1 #IH #HT1 #U1 #l #HTU1 #L2 #HL12 #T2 * #T #HT1T #HTT2
-elim (IH … HTU1 … HL12 … HT1T) // -L1 -T1 #U #HTU #HU1
-elim (ssta_tpss_conf … HTU … HTT2) -T #U2 #HTU2 #HU2
-lapply (cpcs_cpr_strap1 … HU1 U2 ?) /2 width=3/
-qed-.
-
-fact snv_ltpr_cprs_aux: ∀h,g,L0,T0.
-                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
+fact ssta_cprs_lpr_aux: ∀h,g,L0,T0.
+                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
+                        (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
                         ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                        ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 → ⦃h, L2⦄ ⊢ T2 ¡[g].
-#h #g #L0 #T0 #IH #L1 #T1 #HLT0 #HT1 #L2 #HL12 #T2 #H
-@(cprs_ind … H) -T2 [ /2 width=6 by snv_ltpr_cpr_aux/ ] -HT1
-/5 width=6 by snv_ltpr_cpr_aux, ygt_yprs_trans, ltpr_cprs_yprs/
-qed-.
-
-fact ssta_ltpr_cprs_aux: ∀h,g,L0,T0.
-                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
-                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
-                         ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                         ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
-                         ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 →
-                         ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L2 ⊢ U1 ⬌* U2.
-#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #l #HTU1 #L2 #HL12 #T2 #H
-@(cprs_ind … H) -T2 [ /2 width=7 by ssta_ltpr_cpr_aux/ ]
-#T #T2 #HT1T #HTT2 * #U #HTU #HU1
-elim (ssta_ltpr_cpr_aux … HTU … HTT2) //
-[2: /3 width=9 by snv_ltpr_cprs_aux/
-|3: /5 width=6 by ygt_yprs_trans, ltpr_cprs_yprs/
-] -L0 -L1 -T0 -T1 -T #U2 #HTU2 #HU2
+                        ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l, U1⦄ →
+                        ∀T2. L1 ⊢ T1 ➡* T2 → ∀L2. L1 ⊢ ➡ L2 → 
+                        ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l, U2⦄ & L1 ⊢ U1 ⬌* U2.
+#h #g #L0 #T0 #IH2 #IH1 #L1 #T1 #H01 #HT1 #U1 #l #HTU1 #T2 #H
+elim H -T2 [ /2 width=5/ ]
+#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12
+elim (IHT1 L1) // -IHT1 #U #HTU #HU1
+elim (IH1 … HTU … HTT2 … HL12) -IH1 -HTU -HTT2 -HL12
+[2: /3 width=9 by snv_cprs_lpr_aux/
+|3: /5 width=6 by ygt_yprs_trans, cprs_yprs/
+] -L0 -T0 -T1 -T #U2 #HTU2 #HU2
 lapply (cpcs_trans … HU1 … HU2) -U /2 width=3/
 qed-.
 
-fact ssta_ltpr_cpcs_aux: ∀h,g,L0,T0.
-                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
-                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
-                         ∀L1,L2,T1,T2. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → h ⊢ ⦃L0, T0⦄ >[g] ⦃L2, T2⦄ →
-                         ⦃h, L1⦄ ⊢ T1 ¡[g] → ⦃h, L2⦄ ⊢ T2 ¡[g] →
-                         ∀U1,l1. ⦃h, L1⦄ ⊢ T1 •[g] ⦃l1, U1⦄ →
-                         ∀U2,l2. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l2, U2⦄ →
-                         L1 ➡ L2 → L2 ⊢ T1 ⬌* T2 →
-                         l1 = l2 ∧ L2 ⊢ U1 ⬌* U2.
-#h #g #L0 #T0 #IH2 #IH1 #L1 #L2 #T1 #T2 #HLT01 #HLT02 #HT1 #HT2 #U1 #l1 #HTU1 #U2 #l2 #HTU2 #HL12 #H
+fact ssta_cpcs_aux: ∀h,g,L0,T0.
+                    (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
+                    (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
+                    ∀L,T1,T2. h ⊢ ⦃L0, T0⦄ >[g] ⦃L, T1⦄ → h ⊢ ⦃L0, T0⦄ >[g] ⦃L, T2⦄ →
+                        ⦃h, L⦄ ⊢ T1 ¡[g] → ⦃h, L⦄ ⊢ T2 ¡[g] →
+                    ∀U1,l1. ⦃h, L⦄ ⊢ T1 •[g] ⦃l1, U1⦄ →
+                    ∀U2,l2. ⦃h, L⦄ ⊢ T2 •[g] ⦃l2, U2⦄ →
+                    L ⊢ T1 ⬌* T2 → l1 = l2 ∧ L ⊢ U1 ⬌* U2.
+#h #g #L0 #T0 #IH2 #IH1 #L #T1 #T2 #HLT01 #HLT02 #HT1 #HT2 #U1 #l1 #HTU1 #U2 #l2 #HTU2 #H
 elim (cpcs_inv_cprs … H) -H #T #H1 #H2
-elim (ssta_ltpr_cprs_aux … HLT01 HT1 … HTU1 … H1) -T1 /2 width=1/ #W1 #H1 #HUW1
-elim (ssta_ltpr_cprs_aux … HLT02 HT2 … HTU2 … H2) -T2 /2 width=1/ #W2 #H2 #HUW2 -L1 -L0 -T0
+elim (ssta_cprs_lpr_aux … HLT01 HT1 … HTU1 … H1 L) -T1 // /2 width=1/ #W1 #H1 #HUW1
+elim (ssta_cprs_lpr_aux … HLT02 HT2 … HTU2 … H2 L) -T2 // /2 width=1/ #W2 #H2 #HUW2 -L0 -T0
 elim (ssta_mono … H1 … H2) -h -T #H1 #H2 destruct
 lapply (cpcs_canc_dx … HUW1 … HUW2) -W2 /2 width=1/
 qed-.
@@ -112,13 +92,13 @@ fact snv_sstas_aux: ∀h,g,L0,T0.
 @(sstas_ind … H) -U1 // -HT1 /4 width=5 by ygt_yprs_trans, sstas_yprs/
 qed-.
 
-fact sstas_ltpr_cprs_aux: ∀h,g,L0,T0.
-                          (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
-                          (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
-                          (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
-                          ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] →
-                          ∀L2. L1 ➡ L2 → ∀T2. L2 ⊢ T1 ➡* T2 → ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 →
-                          ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L2 ⊢ U1 ⬌* U2.
+fact sstas_cprs_lpr_aux: ∀h,g,L0,T0.
+                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
+                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
+                         (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
+                         ∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → ⦃h, L1⦄ ⊢ T1 ¡[g] →
+                         ∀T2. L1 ⊢ T1 ➡* T2 → ∀U1. ⦃h, L1⦄ ⊢ T1 •*[g] U1 → ∀L2. L1 ⊢ ➡ L2 →
+                         ∃∃U2. ⦃h, L2⦄ ⊢ T2 •*[g] U2 & L1 ⊢ U1 ⬌* U2.
 #h #g #L0 #T0 #IH3 #IH2 #IH1 #L1 #T1 #H01 #HT1 #L2 #HL12 #T2 #HT12 #U1 #H
 @(sstas_ind … H) -U1 [ /3 width=3/ ]
 #U1 #W1 #l1 #HTU1 #HUW1 * #U2 #HTU2 #HU12