two more main properties of drop closed

[helm.git] / matita / matita / lib / lambda-delta / substitution / drop_main.ma

diff --git a/matita/matita/lib/lambda-delta/substitution/drop_main.ma b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
index 67a1df4c1588c7d5ff6b3ca7f31c716e97ca66be..72d980e9bf183784f494a1d69a8ef30253bf7a66 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/drop_main.ma
+++ b/matita/matita/lib/lambda-delta/substitution/drop_main.ma
@@ -30,19 +30,48 @@ lemma drop_conf_ge: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
   lapply (transitive_le 1 … Hdee2) // #He2
   lapply (drop_inv_drop1 … H ?) -H // -He2 #HL2
   lapply (transitive_le (1+e) … Hdee2) // #Hee2
-  >(plus_minus_m_m (e2-e) 1 ?) [ @drop_drop >minus_minus_comm /3/ | /2/ ]
+  @drop_drop_lt >minus_minus_comm /3/ (**) (* explicit constructor *)
 ]
 qed.
 
-axiom drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
+lemma drop_conf_lt: ∀d1,e1,L,L1. ↑[d1, e1] L1 ≡ L →
                     ∀e2,K2,I,V2. ↑[0, e2] K2. 𝕓{I} V2 ≡ L →
                     e2 < d1 → let d ≝ d1 - e2 - 1 in
                     ∃∃K1,V1. ↑[0, e2] K1. 𝕓{I} V1 ≡ L1 & 
                              ↑[d, e1] K1 ≡ K2 & ↑[d,e1] V1 ≡ V2.
+#d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
+[ #L0 #e2 #K2 #I #V2 #_ #H
+  elim (lt_zero_false … H)
+| #L1 #L2 #I #V #e #_ #_ #e2 #K2 #J #V2 #_ #H
+  elim (lt_zero_false … H)
+| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #K2 #J #V #H #He2d
+  elim (drop_inv_O1 … H) -H *
+  [ -IHL12 He2d #H1 #H2 destruct -e2 K2 J V /2 width=5/
+  | -HL12 -HV12 #He #HLK
+    elim (IHL12 … HLK ?) -IHL12 HLK [ <minus_minus /3 width=5/ | /2/ ] (**) (* a bit slow *)
+  ]
+]
+qed.
 
-axiom drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
+lemma drop_trans_le: ∀d1,e1,L1. ∀L:lenv. ↑[d1, e1] L ≡ L1 →
                      ∀e2,L2. ↑[0, e2] L2 ≡ L → e2 ≤ d1 →
                      ∃∃L0. ↑[0, e2] L0 ≡ L1 & ↑[d1 - e2, e1] L2 ≡ L0.
+#d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
+[ #L #e2 #L2 #HL2 #H
+  lapply (le_O_to_eq_O … H) -H #H destruct -e2 /2/
+| #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H
+  lapply (le_O_to_eq_O … H) -H #H destruct -e2;
+  elim (IHL12 … HL2 ?) -IHL12 HL2 // #L0 #H #HL0
+  lapply (drop_inv_refl … H) -H #H destruct -L1 /3 width=5/
+| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #L #H #He2d
+  elim (drop_inv_O1 … H) -H *
+  [ -He2d IHL12 #H1 #H2 destruct -e2 L /3 width=5/
+  | -HL12 HV12 #He2 #HL2
+    elim (IHL12 … HL2 ?) -IHL12 HL2 L2
+    [ <minus_le_minus_minus_comm /3/ | /2/ ]
+  ]
+]
+qed.
 
 axiom drop_trans_ge: ∀d1,e1,L1,L. ↑[d1, e1] L ≡ L1 →
                      ∀e2,L2. ↑[0, e2] L2 ≡ L → d1 ≤ e2 → ↑[0, e1 + e2] L2 ≡ L1.