support for generic reducibility ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lsubc_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubc_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubc_drops.ma
index 8fa9adfefcd0f9b673d85b0b5a1674dc687b4c7b..59ba61ad2dfedc9a1e0dd4919a5f7cba23d5e9c2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubc_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubc_drops.ma
@@ -12,20 +12,58 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/computation/lsubc_drop.ma".
+include "basic_2/static/aaa_drops.ma".
+include "basic_2/rt_computation/lsubc.ma".
 
 (* LOCAL ENVIRONMENT REFINEMENT FOR GENERIC REDUCIBILITY ********************)
 
-(* Properties concerning generic local environment slicing ******************)
+(* 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 #V #HL12 #IH #b #f #K2 #Hf #H
+  elim (drops_inv_pair1_isuni … Hf H) -Hf -H *
+  [ #Hf #H destruct -IH
+    /3 width=3 by lsubc_pair, 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_pair1_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 →
-                         ∀G,L1,K1,cs. ⬇*[Ⓕ, cs] L1 ≡ K1 → ∀K2. G ⊢ K1 ⫃[RP] K2 →
-                         ∃∃L2. G ⊢ L1 ⫃[RP] L2 & ⬇*[Ⓕ, cs] L2 ≡ K2.
-#RR #RS #RP #Hgcp #G #L1 #K1 #cs #H elim H -L1 -K1 -cs
-[ /2 width=3 by drops_nil, ex2_intro/
-| #L1 #L #K1 #cs #l #k #_ #HLK1 #IHL #K2 #HK12
-  elim (drop_lsubc_trans … Hgcp … HLK1 … HK12) -Hgcp -K1 #K #HLK #HK2
-  elim (IHL … HLK) -IHL -HLK /3 width=5 by drops_cons, ex2_intro/
+                         ∀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 #V1 #_ #IH #K2 #HK12 elim (IH … HK12) -K1
+  /3 width=5 by lsubc_pair, drops_drop, ex2_intro/
+| #f #I #L1 #K1 #V1 #V2 #HLK1 #HV21 #IH #X #H elim (lsubc_inv_pair1 … H) -H *
+  [ #K2 #HK12 #H destruct -HLK1
+    elim (IH … HK12) -K1 /3 width=5 by lsubc_pair, drops_skip, ex2_intro/
+  | #K2 #V #W2 #A #HV #H1W2 #H2W2 #HK12 #H1 #H2 #H3 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 … HV … HLK1 … HV3) -HV
+    lapply (acr_lifts … HR … H1W2 … HLK1 … HW23) -H1W2
+    /4 width=10 by lsubc_beta, aaa_lifts, drops_skip, ex2_intro/
+  ]
 ]
 qed-.