- commit of the "reduction" component with two additions ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq.ma
index 75833e23bb2d42a63d8cb1a8c7e3669744c79e9b..d6bef52ecee8cd7d227cba435507efee7c37b330 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/lleq.ma
@@ -50,12 +50,7 @@ lemma lleq_bind: ∀a,I,L1,L2,V,T,d.
 #a #I #L1 #L2 #V #T #d * #HL12 #IHV * #_ #IHT @conj // -HL12
 #X @conj #H elim (cpys_inv_bind1 … H) -H
 #W #U #HVW #HTU #H destruct
-elim (IHV W) -IHV #H1VW #H1WV
-elim (IHT U) -IHT #H1TU #H1UT
-@cpys_bind /2 width=1 by/ -HVW -H1VW -H1WV
-[ @(lsuby_cpys_trans … (L2.ⓑ{I}V))
-| @(lsuby_cpys_trans … (L1.ⓑ{I}V))
-] /4 width=5 by lsuby_cpys_trans, lsuby_succ/ (**) (* full auto too slow *)
+elim (IHV W) -IHV elim (IHT U) -IHT /3 width=1 by cpys_bind/
 qed.
 
 lemma lleq_flat: ∀I,L1,L2,V,T,d.
@@ -74,20 +69,40 @@ lemma lleq_be: ∀L1,L2,U,dt. L1 ⋕[U, dt] L2 → ∀T,d,e. ⇧[d, e] T ≡ U 
 #HU0 elim (cpys_up … HU0 … HTU) // -HU0 /4 width=5 by cpys_weak/
 qed-.
 
+lemma lsuby_lleq_trans: ∀L2,L,T,d. L2 ⋕[T, d] L →
+                        ∀L1. L1 ⊑×[d, ∞] L2 → |L1| = |L2| → L1 ⋕[T, d] L.
+#L2 #L #T #d * #HL2 #IH #L1 #HL12 #H @conj // -HL2
+#U elim (IH U) -IH #Hdx #Hsn @conj #HTU
+[ @Hdx -Hdx -Hsn @(lsuby_cpys_trans … HTU) -HTU
+  /2 width=1 by lsuby_sym/ (**) (* full auto does not work *)
+| -H -Hdx /3 width=3 by lsuby_cpys_trans/
+]
+qed-.
+
+lemma lleq_lsuby_trans: ∀L,L1,T,d. L ⋕[T, d] L1 →
+                        ∀L2. L1 ⊑×[d, ∞] L2 → |L1| = |L2| → L ⋕[T, d] L2.
+/5 width=4 by lsuby_lleq_trans, lleq_sym, lsuby_sym/ qed-.
+
+lemma lleq_lsuby_repl: ∀L1,L2,T,d. L1 ⋕[T, d] L2 →
+                       ∀K1. K1 ⊑×[d, ∞] L1 → |K1| = |L1| →
+                       ∀K2. L2 ⊑×[d, ∞] K2 → |L2| = |K2| →
+                       K1 ⋕[T, d] K2.
+/3 width=4 by lleq_lsuby_trans, lsuby_lleq_trans/ qed-.
+
 (* Basic forward lemmas *****************************************************)
 
 lemma lleq_fwd_length: ∀L1,L2,T,d. L1 ⋕[T, d] L2 → |L1| = |L2|.
 #L1 #L2 #T #d * //
 qed-.
 
-lemma lleq_fwd_ldrop_sn: ∀L1,L2,T,d. L1 ⋕[d, T] L2 → ∀K1,i. ⇩[0, i] L1 ≡ K1 →
-                         ∃K2. ⇩[0, i] L2 ≡ K2.
+lemma lleq_fwd_ldrop_sn: ∀L1,L2,T,d. L1 ⋕[d, T] L2 → ∀K1,i. ⇩[i] L1 ≡ K1 →
+                         ∃K2. ⇩[i] L2 ≡ K2.
 #L1 #L2 #T #d #H #K1 #i #HLK1 lapply (lleq_fwd_length … H) -H
 #HL12 lapply (ldrop_fwd_length_le2 … HLK1) -HLK1 /2 width=1 by ldrop_O1_le/
 qed-.
 
-lemma lleq_fwd_ldrop_dx: ∀L1,L2,T,d. L1 ⋕[d, T] L2 → ∀K2,i. ⇩[0, i] L2 ≡ K2 →
-                         ∃K1. ⇩[0, i] L1 ≡ K1.
+lemma lleq_fwd_ldrop_dx: ∀L1,L2,T,d. L1 ⋕[d, T] L2 → ∀K2,i. ⇩[i] L2 ≡ K2 →
+                         ∃K1. ⇩[i] L1 ≡ K1.
 /3 width=6 by lleq_fwd_ldrop_sn, lleq_sym/ qed-.
 
 lemma lleq_fwd_bind_sn: ∀a,I,L1,L2,V,T,d.