passive support for global environments completed!

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_cpds.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_cpds.ma
index 55a7e9a136803c524aa71508b90d0e4afb601c6c..d9b21a9f6370dc0daf012f01a8da1f999106db59 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_cpds.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv_cpds.ma
@@ -19,38 +19,38 @@ include "basic_2/dynamic/lsubsv_ssta.ma".
 
 (* Properties for the preservation results **********************************)
 
-fact lsubsv_sstas_aux: ∀h,g,L0,T0.
-                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
-                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
-                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
-                       (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
-                       ∀L2,T. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L2, T⦄ → ⦃h, L2⦄ ⊢ T ¡[h, g] →
-                       ∀L1. h ⊢ L1 ¡⊑[h, g] L2 → ∀U2. ⦃h, L2⦄ ⊢ T •*[h, g] U2 →
-                       ∃∃U1. ⦃h, L1⦄ ⊢ T •*[h, g] U1 & L1 ⊢ U1 ⬌* U2.
-#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 #T #HLT0 #HT #L1 #HL12 #U2 #H @(sstas_ind … H) -U2 [ /2 width=3/ ]
+fact lsubsv_sstas_aux: ∀h,g,G0,L0,T0.
+                       (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
+                       (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_ssta_cpr_lpr h g G1 L1 T1) →
+                       (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_ssta h g G1 L1 T1) →
+                       (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_lsubsv h g G1 L1 T1) →
+                       ∀G,L2,T. ⦃G0, L0, T0⦄ >[h, g] ⦃G, L2, T⦄ → ⦃G, L2⦄ ⊢ T ¡[h, g] →
+                       ∀L1. G ⊢ L1 ¡⊑[h, g] L2 → ∀U2. ⦃G, L2⦄ ⊢ T •*[h, g] U2 →
+                       ∃∃U1. ⦃G, L1⦄ ⊢ T •*[h, g] U1 & ⦃G, L1⦄ ⊢ U1 ⬌* U2.
+#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G #L2 #T #HLT0 #HT #L1 #HL12 #U2 #H @(sstas_ind … H) -U2 [ /2 width=3/ ]
 #U2 #W #l #HTU2 #HU2W * #U1 #HTU1 #HU12
 lapply (IH1 … HT … HL12) // #H
-lapply (snv_sstas_aux … IH2 … HTU1) // /3 width=4 by ygt_yprs_trans, lsubsv_yprs/ -H #HU1
+lapply (snv_sstas_aux … IH2 … HTU1) // /3 width=5 by ygt_yprs_trans, lsubsv_yprs/ -H #HU1
 lapply (snv_sstas_aux … IH2 … HTU2) // #H
-lapply (IH1 … H … HL12) [ /3 width=4 by ygt_yprs_trans, sstas_yprs/ ] -H #HU2
+lapply (IH1 … H … HL12) [ /3 width=5 by ygt_yprs_trans, sstas_yprs/ ] -H #HU2
 elim (snv_fwd_ssta … HU1) #l1 #W1 #HUW1
 elim (lsubsv_ssta_trans … HU2W … HL12) -HU2W #W2 #HUW2 #HW2
 elim (ssta_cpcs_lpr_aux … IH4 IH3 … HU1 HU2 … HUW1 … HUW2 … HU12 L1) -HU1 -HU2 -HUW2 -HU12 //
-[2,3: /4 width=4 by ygt_yprs_trans, sstas_yprs, lsubsv_yprs/ ] -L2 -L0 -T0 -U2 #H #HW12 destruct
+[2,3: /4 width=5 by ygt_yprs_trans, sstas_yprs, lsubsv_yprs/ ] -G0 -L2 -L0 -T0 -U2 #H #HW12 destruct
 lapply (cpcs_trans … HW12 … HW2) -W2 /3 width=4/
 qed-.
 
-fact lsubsv_cpds_aux: ∀h,g,L0,T0.
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
-                      (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
-                      ∀L2,T1. h ⊢ ⦃L0, T0⦄ >[h, g] ⦃L2, T1⦄ → ⦃h, L2⦄ ⊢ T1 ¡[h, g] →
-                      ∀L1. h ⊢ L1 ¡⊑[h, g] L2 → ∀T2. ⦃h, L2⦄ ⊢ T1 •*➡*[h, g] T2 →
-                      ∃∃T. ⦃h, L1⦄ ⊢ T1 •*➡*[h, g] T & L1 ⊢ T2 ➡* T.
-#h #g #L0 #T0 #IH4 #IH3 #IH2 #IH1 #L2 #T1 #HLT0 #HT1 #L1 #HL12 #T2 * #T #HT1T #HTT2
+fact lsubsv_cpds_aux: ∀h,g,G0,L0,T0.
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_ssta_cpr_lpr h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_ssta h g G1 L1 T1) →
+                      (∀G1,L1,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G1, L1, T1⦄ → IH_snv_lsubsv h g G1 L1 T1) →
+                      ∀G,L2,T1. ⦃G0, L0, T0⦄ >[h, g] ⦃G,L2, T1⦄ → ⦃G, L2⦄ ⊢ T1 ¡[h, g] →
+                      ∀L1. G ⊢ L1 ¡⊑[h, g] L2 → ∀T2. ⦃G, L2⦄ ⊢ T1 •*➡*[h, g] T2 →
+                      ∃∃T. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] T & ⦃G, L1⦄ ⊢ T2 ➡* T.
+#h #g #G0 #L0 #T0 #IH4 #IH3 #IH2 #IH1 #G #L2 #T1 #HLT0 #HT1 #L1 #HL12 #T2 * #T #HT1T #HTT2
 lapply (lsubsv_cprs_trans … HL12 … HTT2) -HTT2 #HTT2
-elim (lsubsv_sstas_aux … IH4 IH3 IH2 IH1 … HLT0 … HL12 … HT1T) // -L2 -L0 -T0 #T0 #HT10 #HT0
+elim (lsubsv_sstas_aux … IH4 IH3 IH2 IH1 … HLT0 … HL12 … HT1T) // -G0 -L2 -L0 -T0 #T0 #HT10 #HT0
 lapply (cpcs_cprs_strap1 … HT0 … HTT2) -T #HT02
 elim (cpcs_inv_cprs … HT02) -HT02 /3 width=3/
 qed-.