syntactic components detached from basic_2 become static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / lsubc_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/lsubc_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/lsubc_drops.ma
new file mode 100644 (file)
index 0000000..9fe4888
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/static_2/static/lsubc_drops.ma
@@ -0,0 +1,70 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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 "static_2/static/aaa_drops.ma".
+include "static_2/static/lsubc.ma".
+
+(* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
+
+(* Properties with generic slicing ******************************************)
+
+(* Note: the premise 𝐔⦃f⦄ cannot be removed *)
+(* Basic_1: includes: csubc_drop_conf_O *)
+(* Basic_2A1: includes: lsubc_drop_O1_trans *)
+lemma lsubc_drops_trans_isuni: ∀RP,G,L1,L2. G ⊢ L1 ⫃[RP] L2 →
+                               ∀b,f,K2. 𝐔⦃f⦄ → ⬇*[b, f] L2 ≘ K2 →
+                               ∃∃K1. ⬇*[b, f] L1 ≘ K1 & G ⊢ K1 ⫃[RP] K2.
+#RP #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsubc_bind, drops_refl, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+| #L1 #L2 #V #W #A #HV #H1W #H2W #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_bind1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=8 by drops_refl, lsubc_beta, ex2_intro/
+  | #g #Hg #HLK2 #H destruct -HL12
+    elim (IH … Hg HLK2) -L2 -Hg /3 width=3 by drops_drop, ex2_intro/
+  ]
+]
+qed-.
+
+(* Basic_1: was: csubc_drop1_conf_rev *)
+(* Basic_1: includes: csubc_drop_conf_rev *)
+(* Basic_2A1: includes: drop_lsubc_trans *)
+lemma drops_lsubc_trans: ∀RR,RS,RP. gcp RR RS RP →
+                         ∀b,f,G,L1,K1. ⬇*[b, f] L1 ≘ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
+                         ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[b, f] L2 ≘ K2.
+#RR #RS #RP #HR #b #f #G #L1 #K1 #H elim H -f -L1 -K1
+[ #f #Hf #Y #H lapply (lsubc_inv_atom1 … H) -H
+  #H destruct /4 width=3 by lsubc_atom, drops_atom, ex2_intro/
+| #f #I #L1 #K1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
+  /3 width=5 by lsubc_bind, drops_drop, ex2_intro/
+| #f #Z #I #L1 #K1 #HLK1 #HZ #IH #Y #H elim (lsubc_inv_bind1 … H) -H *
+  [ #K2 #HK12 #H destruct -HLK1
+    elim (IH … HK12) -K1 /3 width=5 by lsubc_bind, drops_skip, ex2_intro/
+  | #K2 #V2 #W2 #A #HV2 #H1W2 #H2W2 #HK12 #H1 #H2 destruct
+    elim (liftsb_inv_pair_sn … HZ) -HZ #V1 #HV21 #H destruct
+    elim (lifts_inv_flat1 … HV21) -HV21 #W3 #V3 #HW23 #HV3 #H destruct
+    elim (IH … HK12) -IH -HK12 #K #HL1K #HK2
+    lapply (acr_lifts … HR … HV2 … HLK1 … HV3) -HV2
+    lapply (acr_lifts … HR … H1W2 … HLK1 … HW23) -H1W2
+    /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ext2_pair, ex2_intro/
+  ]
+]
+qed-.