advances on append allow to complete the long awaited "big tree" theorem by closing...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / multiple / llor_ldrop.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
index f8458d3c63a4a7e39e3361e766032e25e21a6db3..5f82638e030bfb104cb2973d504cc1bfb71e4001 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/multiple/llor_ldrop.ma
@@ -13,13 +13,13 @@
 (**************************************************************************)
 
 include "basic_2/multiple/frees_lift.ma".
-include "basic_2/multiple/llor.ma".
+include "basic_2/multiple/llor_alt.ma".
 
 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
 
 (* Advanced properties ******************************************************)
 
-lemma llor_skip: ∀L1,L2,U,d. |L1| ≤ |L2| → yinj (|L1|) ≤ d → L1 ⩖[U, d] L2 ≡ L1.
+lemma llor_skip: ∀L1,L2,U,d. |L1| = |L2| → yinj (|L1|) ≤ d → L1 ⩖[U, d] L2 ≡ L1.
 #L1 #L2 #U #d #HL12 #Hd @and3_intro // -HL12
 #I1 #I2 #I #K1 #K2 #K #W1 #W2 #W #i #HLK1 #_ #HLK -L2 -K2
 lapply (ldrop_mono … HLK … HLK1) -HLK #H destruct
@@ -27,4 +27,18 @@ lapply (ldrop_fwd_length_lt2 … HLK1) -K1
 /5 width=3 by ylt_yle_trans, ylt_inj, or3_intro0, and3_intro/
 qed.
 
-axiom llor_total: ∀L1,L2,T,d. |L1| ≤ |L2| → ∃L. L1 ⩖[T, d] L2 ≡ L.
+lemma llor_total: ∀L1,L2,T,d. |L1| = |L2| → ∃L. L1 ⩖[T, d] L2 ≡ L.
+#L1 @(lenv_ind_alt … L1) -L1
+[ #L2 #T #d #H >(length_inv_zero_sn … H) -L2 /2 width=2 by ex_intro/
+| #I1 #L1 #V1 #IHL1 #Y #T #d >ltail_length #H
+  elim (length_inv_pos_sn_ltail … H) -H #I2 #L2 #V2 #HL12 #H destruct
+  elim (ylt_split d (|ⓑ{I1}V1.L1|))
+  [ elim (frees_dec (ⓑ{I1}V1.L1) T d (|L1|)) #HnU
+    elim (IHL1 L2 T d) // -IHL1 -HL12
+    [ #L #HL12 >ltail_length /4 width=2 by llor_tail_frees, ylt_fwd_succ2, ex_intro/ 
+    | /4 width=2 by llor_tail_cofrees, ex_intro/
+    ]
+  | -IHL1 /4 width=3 by llor_skip, plus_to_minus, ex_intro/
+  ]
+]
+qed-.