reorganization of the "static" component:

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
index ec0832ad4f49a1af4a63a7ff14ba1b169a196594..7d1faa892fe5763d3c9709757af400832f83da3f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/lsubsv.ma
@@ -118,3 +118,49 @@ lemma lsubsv_cprs_trans: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
                          ∀T1,T2. ⦃G, L2⦄ ⊢ T1 ➡* T2 → ⦃G, L1⦄ ⊢ T1 ➡* T2.
 /3 width=6 by lsubsv_fwd_lsubr, lsubr_cprs_trans/
 qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubsv_ldrop_O1_conf: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                            ∀K1,s,e. ⇩[s, 0, e] L1 ≡ K1 →
+                            ∃∃K2. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L2 ≡ K2.
+#h #g #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K1 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #IHL12 #K1 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK1
+  [ destruct
+    elim (IHL12 L1 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=4 by lsubsv_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK1) -L1 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.
+
+(* Note: the constant 0 cannot be generalized *)
+lemma lsubsv_ldrop_O1_trans: ∀h,g,G,L1,L2. G ⊢ L1 ¡⫃[h, g] L2 →
+                             ∀K2,s, e. ⇩[s, 0, e] L2 ≡ K2 →
+                             ∃∃K1. G ⊢ K1 ¡⫃[h, g] K2 & ⇩[s, 0, e] L1 ≡ K1.
+#h #g #G #L1 #L2 #H elim H -L1 -L2
+[ /2 width=3 by ex2_intro/
+| #I #L1 #L2 #V #_ #IHL12 #K2 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=3 by lsubsv_pair, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+| #L1 #L2 #W #V #l #H1W #HV #HVW #H2W #H1l #H2l #_ #IHL12 #K2 #s #e #H
+  elim (ldrop_inv_O1_pair1 … H) -H * #He #HLK2
+  [ destruct
+    elim (IHL12 L2 s 0) -IHL12 // #X #HL12 #H
+    <(ldrop_inv_O2 … H) in HL12; -H /3 width=4 by lsubsv_abbr, ldrop_pair, ex2_intro/
+  | elim (IHL12 … HLK2) -L2 /3 width=3 by ldrop_drop_lt, ex2_intro/
+  ]
+]
+qed-.