- some corrections and additions

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_leq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_leq.ma
index e5a7555313bbd7f28cc196f846f6664aa79a9cfa..1355827f7f7a55681b731cf948051b420f1b85f5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_leq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_leq.ma
@@ -68,3 +68,15 @@ lemma dedropable_sn_TC: ∀R. dedropable_sn R → dedropable_sn (TC … R).
   /3 width=6 by leq_trans, step, ex3_intro/
 ]
 qed-.
+
+(* Inversion lemmas on equivalence ******************************************)
+
+lemma ldrop_O_inj: ∀i,L1,L2,K. ⇩[i] L1 ≡ K → ⇩[i] L2 ≡ K → L1 ≃[i, ∞] L2.
+#i @(nat_ind_plus … i) -i
+[ #L1 #L2 #K #H <(ldrop_inv_O2 … H) -K #H <(ldrop_inv_O2 … H) -L1 //
+| #i #IHi * [2: #L1 #I1 #V1 ] * [2,4: #L2 #I2 #V2 ] #K #HLK1 #HLK2 //
+  lapply (ldrop_fwd_length … HLK1)
+  <(ldrop_fwd_length … HLK2) [ /4 width=5 by ldrop_inv_drop1, leq_succ/ ]
+  normalize <plus_n_Sm #H destruct
+]
+qed-.