X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Ffsle_drops.ma;h=441c6b468df6ca86817de617fcbf9ad63ad468c7;hp=273a2755a452f79f87543ded34679571c62b27f4;hb=222044da28742b24584549ba86b1805a87def070;hpb=990f97071a9939d47be16b36f6045d3b23f218e0

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma
index 273a2755a..441c6b468 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/fsle_drops.ma
@@ -19,7 +19,7 @@ include "basic_2/static/fsle_length.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma fsle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≡ U1 → ∀L1,L2. |L2| ≤ |L1| →
+lemma fsle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| →
                      ∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄.
 #T1 #U1 #HTU1 #L1 #L2 #H1L #T2
 * #n #m #f #g #Hf #Hg #H2L #Hfg
@@ -29,8 +29,17 @@ lapply (frees_lifts_SO (Ⓣ) (L1.ⓧ) … HTU1 … Hf)
 @(ex4_4_intro … Hf Hg) /2 width=4 by lveq_void_sn/ (**) (* explict constructor *)
 qed-.
 
+lemma fsle_lifts_SO_sn: ∀K1,K2. |K1| = |K2| → ∀V1,V2. ⦃K1, V1⦄ ⊆ ⦃K2, V2⦄ →
+                        ∀W1. ⬆*[1] V1 ≘ W1 → ∀I1,I2. ⦃K1.ⓘ{I1}, W1⦄ ⊆ ⦃K2.ⓑ{I2}V2, #O⦄.
+#K1 #K2 #HK #V1 #V2
+* #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
+#W1 #HVW1 #I1 #I2
+elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
+/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, sle_weak, ex4_4_intro/
+qed.
+
 lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ⦃K1, T1⦄ ⊆ ⦃K2, T2⦄ →
-                     ∀U1,U2. ⬆*[1] T1 ≡ U1 → ⬆*[1] T2 ≡ U2 →
+                     ∀U1,U2. ⬆*[1] T1 ≘ U1 → ⬆*[1] T2 ≘ U2 →
                      ∀I1,I2.  ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄.
 #K1 #K2 #HK #T1 #T2
 * #n1 #n2 #f1 #f2 #Hf1 #Hf2 #HK12 #Hf12
@@ -41,7 +50,7 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma fsle_inv_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≡ U1 →
+lemma fsle_inv_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 →
                          ∀I1,I2,L1,L2,V1,V2,U2. ⦃L1.ⓑ{I1}V1,U1⦄ ⊆ ⦃L2.ⓑ{I2}V2, U2⦄ →
                          ∀p. ⦃L1, T1⦄ ⊆ ⦃L2, ⓑ{p,I2}V2.U2⦄.
 #T1 #U1 #HTU1 #I1 #I2 #L1 #L2 #V1 #V2 #U2