- advances in the theory of cofrees

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / lleq_lleq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
index ea10429970bb1268aff64b1cd3953de3ceec374b..abee448a3bc70740bb8cf207e1bc4a47044a828b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq_lleq.ma
@@ -12,35 +12,21 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/substitution/cpys_cpys.ma".
-include "basic_2/substitution/lleq.ma".
+include "basic_2/substitution/lleq_ldrop.ma".
 
-(* Advanced forward lemmas **************************************************)
+(* Main properties **********************************************************)
 
-lemma lleq_fwd_lref: ∀L1,L2,d,i. L1 ⋕[#i, d] L2 →
-                     ∨∨ |L1| ≤ i ∧ |L2| ≤ i
-                      | i < d
-                      | ∃∃I1,I2,K1,K2,V. ⇩[0, i] L1 ≡ K1.ⓑ{I1}V &
-                                         ⇩[0, i] L2 ≡ K2.ⓑ{I2}V &
-                                         K1 ⋕[V, 0] K2 & d ≤ i.
-#L1 #L2 #d #i * #HL12 #IH elim (lt_or_ge i (|L1|)) /3 width=3 by or3_intro0, conj/
-elim (lt_or_ge i d) /2 width=1 by or3_intro1/ #Hdi #Hi
-elim (ldrop_O1_lt … Hi) #I1 #K1 #V1 #HLK1
-elim (ldrop_O1_lt L2 i) // -Hi #I2 #K2 #V2 #HLK2
-lapply (ldrop_fwd_length_minus2 … HLK2) #H
-lapply (ldrop_fwd_length_minus2 … HLK1) >HL12 <H -HL12 -H
-#H lapply (injective_plus_l … H) -H #HK12
-elim (lift_total V1 0 (i+1)) #W1 #HVW1
-elim (lift_total V2 0 (i+1)) #W2 #HVW2
-elim (IH W1) elim (IH W2) #_ #H2 #H1 #_
-elim (cpys_inv_lref1_ldrop … (H1 ?) … HLK2 … HVW1) -H1
-[ elim (cpys_inv_lref1_ldrop … (H2 ?) … HLK1 … HVW2) -H2 ]
-/3 width=7 by cpys_subst, yle_inj/ -W1 -W2 #H12 #_ #_ #H21 #_ #_
-lapply (cpys_antisym_eq … H12 … H21) -H12 -H21 #H destruct
-@or3_intro2 @(ex4_5_intro … HLK1 HLK2) // @conj // -HK12
-#V elim (lift_total V 0 (i+1))
-#W #HVW elim (IH W) -IH #H12 #H21 @conj #H
-[ elim (cpys_inv_lref1_ldrop … (H12 ?) … HLK2 … HVW) -H12 -H21
-| elim (cpys_inv_lref1_ldrop … (H21 ?) … HLK1 … HVW) -H21 -H12
-] /3 width=7 by cpys_subst, yle_inj/
-qed-.
+theorem lleq_trans: ∀d,T. Transitive … (lleq d T).
+/2 width=3 by lleq_llpx_sn_trans/ qed-.
+
+theorem lleq_canc_sn: ∀L,L1,L2,T,d. L ≡[d, T] L1→ L ≡[d, T] L2 → L1 ≡[d, T] L2.
+/3 width=3 by lleq_trans, lleq_sym/ qed-.
+
+theorem lleq_canc_dx: ∀L1,L2,L,T,d. L1 ≡[d, T] L → L2 ≡[d, T] L → L1 ≡[d, T] L2.
+/3 width=3 by lleq_trans, lleq_sym/ qed-.
+
+(* Note: lleq_nlleq_trans: ∀d,T,L1,L. L1≡[T, d] L →
+                           ∀L2. (L ≡[T, d] L2 → ⊥) → (L1 ≡[T, d] L2 → ⊥).
+/3 width=3 by lleq_canc_sn/ qed-.
+works with /4 width=8/ so lleq_canc_sn is more convenient
+*)