theory of generic slicing almost completed ....

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / drops_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
index c2b0b30d1550a2ac4b238989dbcad7864fcc423d..34c446f649b8d5863693a4194d2839be57dafefa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/drops_drops.ma
@@ -12,14 +12,78 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/multiple/drops_drop.ma".
+include "basic_2/relocation/lifts_lifts.ma".
+include "basic_2/relocation/drops.ma".
 
-(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
+(* GENERAL SLICING FOR LOCAL ENVIRONMENTS ***********************************)
 
 (* Main properties **********************************************************)
 
+(* Basic_2A1: includes: drop_conf_ge drop_conf_be drop_conf_le *)
+theorem drops_conf: ∀L1,L,s1,t1. ⬇*[s1, t1] L1 ≡ L →
+                    ∀L2,s2,t. ⬇*[s2, t] L1 ≡ L2 →
+                    ∀t2. t1 ⊚ t2 ≡ t → ⬇*[s2, t2] L ≡ L2.
+#L1 #L #s1 #t1 #H elim H -L1 -L -t1
+[ #t1 #_ #L2 #s2 #t #H #t2 #Ht12 elim (drops_inv_atom1 … H) -s1 -H
+  #H #Ht destruct @drops_atom
+  #H elim (after_inv_isid3 … Ht12) -Ht12 /2 width=1 by/
+| #I #K1 #K #V1 #t1 #_ #IH #L2 #s2 #t #H12 #t2 #Ht elim (after_inv_false1 … Ht) -Ht
+  #u #H #Hu destruct /3 width=3 by drops_inv_drop1/
+| #I #K1 #K #V1 #V #t1 #_ #HV1 #IH #L2 #s2 #t #H #t2 #Ht elim (after_inv_true1 … Ht) -Ht
+  #u2 #u * #H1 #H2 #Hu destruct
+  [ elim (drops_inv_skip1 … H) -H /3 width=6 by drops_skip, lifts_div/
+  | /4 width=3 by drops_inv_drop1, drops_drop/
+  ]
+]
+qed-.
+
 (* Basic_1: was: drop1_trans *)
-theorem drops_trans: ∀L,L2,s,cs2. ⬇*[s, cs2] L ≡ L2 → ∀L1,cs1. ⬇*[s, cs1] L1 ≡ L →
-                     ⬇*[s, cs2 @@ cs1] L1 ≡ L2.
-#L #L2 #s #cs2 #H elim H -L -L2 -cs2 /3 width=3 by drops_cons/
+(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm 
+                        drops_drop_trans
+*)
+theorem drops_trans: ∀L1,L,s1,t1. ⬇*[s1, t1] L1 ≡ L →
+                     ∀L2,s2,t2. ⬇*[s2, t2] L ≡ L2 →
+                     ∀t. t1 ⊚ t2 ≡ t → ⬇*[s1∨s2, t] L1 ≡ L2.
+#L1 #L #s1 #t1 #H elim H -L1 -L -t1
+[ #t1 #Ht1 #L2 #s2 #t2 #H #t #Ht elim (drops_inv_atom1 … H) -H
+  #H #Ht2 destruct @drops_atom #H elim (orb_false_r … H) -H
+  #H1 #H2 >(after_isid_inv_sn … Ht) -Ht /2 width=1 by/
+| #I #K1 #K #V1 #t1 #_ #IH #L #s2 #t2 #HKL #t #Ht elim (after_inv_false1 … Ht) -Ht
+  /3 width=3 by drops_drop/
+| #I #K1 #K #V1 #V #t1 #_ #HV1 #IH #L #s2 #t2 #H #t #Ht elim (after_inv_true1 … Ht) -Ht
+  #u2 #u * #H1 #H2 #Hu destruct
+  [ elim (drops_inv_skip1 … H) -H /3 width=6 by drops_skip, lifts_trans/
+  | /4 width=3 by drops_inv_drop1, drops_drop/
+  ]
+]
+qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: includes: drop_mono *)
+lemma drops_mono: ∀L,L1,s1,t. ⬇*[s1, t] L ≡ L1 →
+                  ∀L2,s2. ⬇*[s2, t] L ≡ L2 → L1 = L2.
+#L #L1 #s1 #t elim (isid_after_dx t)
+/3 width=8 by drops_conf, drops_fwd_isid/
+qed-.
+
+(* Basic_2A1: includes: drop_conf_lt *)
+lemma drops_conf_skip1: ∀L,L2,s2,t. ⬇*[s2, t] L ≡ L2 →
+                        ∀I,K1,V1,s1,t1. ⬇*[s1, t1] L ≡ K1.ⓑ{I}V1 →
+                        ∀t2. t1 ⊚ Ⓣ@t2 ≡ t →
+                        ∃∃K2,V2. L2 = K2.ⓑ{I}V2 &
+                                 ⬇*[s2, t2] K1 ≡ K2 & ⬆*[t2] V2 ≡ V1.
+#L #L2 #s2 #t #H2 #I #K1 #V1 #s1 #t1 #H1 #t2 #Ht lapply (drops_conf … H1 … H2 … Ht) -L -Ht
+#H elim (drops_inv_skip1 … H) -H /2 width=5 by ex3_2_intro/
+qed-.
+
+(* Basic_2A1: includes: drop_trans_lt *)
+lemma drops_trans_skip2: ∀L1,L,s1,t1. ⬇*[s1, t1] L1 ≡ L →
+                         ∀I,K2,V2,s2,t2. ⬇*[s2, t2] L ≡ K2.ⓑ{I}V2 →
+                         ∀t. t1 ⊚ t2 ≡ Ⓣ@t →
+                         ∃∃K1,V1. L1 = K1.ⓑ{I}V1 &
+                                  ⬇*[s1∨s2, t] K1 ≡ K2 & ⬆*[t] V2 ≡ V1.
+#L1 #L #s1 #t1 #H1 #I #K2 #V2 #s2 #t2 #H2 #t #Ht
+lapply (drops_trans … H1 … H2 … Ht) -L -Ht
+#H elim (drops_inv_skip2 … H) -H /2 width=5 by ex3_2_intro/
 qed-.