X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fstatic_2%2Fstatic%2Ffsle_drops.ma;h=87d3864ffe6c48f1d331e78242f61706d73c596b;hb=98e786e1a6bd7b621e37ba7cd4098d4a0a6f8278;hp=8375d521a07dca47cf7f90008de8294836d98d10;hpb=ff612dc35167ec0c145864c9aa8ae5e1ebe20a48;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
index 8375d521a..87d3864ff 100644
--- a/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/fsle_drops.ma
@@ -19,8 +19,8 @@ include "static_2/static/fsle_length.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma fsle_lifts_sn: ∀T1,U1. ⬆*[1] T1 ≘ U1 → ∀L1,L2. |L2| ≤ |L1| →
-                     ∀T2. ⦃L1, T1⦄ ⊆ ⦃L2, T2⦄ → ⦃L1.ⓧ, U1⦄ ⊆ ⦃L2, T2⦄.
+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
 lapply (lveq_length_fwd_dx … H2L ?) // -H1L #H destruct
@@ -29,37 +29,48 @@ 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⦄.
+lemma fsle_lifts_dx (L1) (L2):
+                    |L1| ≤ |L2| → ∀T2,U2. ⇧[1]T2 ≘ U2 →
+                    ∀T1. ❪L1,T1❫ ⊆ ❪L2,T2❫ → ❪L1,T1❫ ⊆ ❪L2.ⓧ,U2❫.
+#L1 #L2 #HL21 #T2 #U2 #HTU2 #T1
+* #n #m #f #g #Hf #Hg #H2L #Hfg
+lapply (lveq_length_fwd_sn … H2L ?) // -HL21 #H destruct
+lapply (frees_lifts_SO (Ⓣ) (L2.ⓧ) … HTU2 … Hg)
+[ /3 width=4 by drops_refl, drops_drop/ ] -T2 #Hg
+@(ex4_4_intro … Hf Hg) /2 width=4 by lveq_void_dx/ (**) (* 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/
+/5 width=12 by frees_lifts_SO, frees_pair, drops_refl, drops_drop, lveq_bind, pr_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 →
-                     ∀I1,I2.  ⦃K1.ⓘ{I1}, U1⦄ ⊆ ⦃K2.ⓘ{I2}, U2⦄.
+lemma fsle_lifts_SO: ∀K1,K2. |K1| = |K2| → ∀T1,T2. ❪K1,T1❫ ⊆ ❪K2,T2❫ →
+                     ∀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
 #U1 #U2 #HTU1 #HTU2 #I1 #I2
 elim (lveq_inj_length … HK12) // -HK #H1 #H2 destruct
-/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, sle_push, ex4_4_intro/
+/5 width=12 by frees_lifts_SO, drops_refl, drops_drop, lveq_bind, pr_sle_push, ex4_4_intro/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-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⦄.
+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
 * #n #m #f2 #g2 #Hf2 #Hg2 #HL #Hfg2 #p
 elim (lveq_inv_pair_pair … HL) -HL #HL #H1 #H2 destruct
 elim (frees_total L2 V2) #g1 #Hg1
-elim (sor_isfin_ex g1 (⫱g2)) /3 width=3 by frees_fwd_isfin, isfin_tl/ #g #Hg #_
+elim (pr_sor_isf_bi g1 (â«°g2)) /3 width=3 by frees_fwd_isfin, pr_isf_tl/ #g #Hg #_
 lapply (frees_inv_lifts_SO (Ⓣ) … Hf2 … HTU1)
 [1,2: /3 width=4 by drops_refl, drops_drop/ ] -U1 #Hf2
-lapply (sor_inv_sle_dx … Hg) #H0g
-/5 width=10 by frees_bind, sle_tl, sle_trans, ex4_4_intro/
+lapply (pr_sor_inv_sle_dx … Hg) #H0g
+/5 width=10 by frees_bind, pr_sle_tl, pr_sle_trans, ex4_4_intro/
 qed-.