- degree assignment, static type assignment, iterated static type

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_ldrop.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_ldrop.ma
index 5a7ac853f931ce81e3a0bc5c7136e2e8fb357544..8b1e5d29206caa710c569a3b348f394f1b64405b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_ldrop.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/ldrop_ldrop.ma
@@ -28,7 +28,7 @@ theorem ldrop_mono: ∀d,e,L,L1. ⇩[d, e] L ≡ L1 →
 | #L #K #I #V #e #_ #IHLK #L2 #H
   lapply (ldrop_inv_ldrop1 … H ?) -H // /2 width=1/
 | #L #K1 #I #T #V1 #d #e #_ #HVT1 #IHLK1 #X #H
-  elim (ldrop_inv_skip1 … H ?) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct
+  elim (ldrop_inv_skip1 … H) -H // <minus_plus_m_m #K2 #V2 #HLK2 #HVT2 #H destruct
   >(lift_inj … HVT1 … HVT2) -HVT1 -HVT2
   >(IHLK1 … HLK2) -IHLK1 -HLK2 //
 ]
@@ -64,7 +64,7 @@ theorem ldrop_conf_be: ∀L0,L1,d1,e1. ⇩[d1, e1] L0 ≡ L1 →
   lapply (ldrop_inv_O1_pair1 … H) -H * * #He2 #HL20
   [ -IHLK0 -He21 destruct <minus_n_O /3 width=3/
   | -HLK0 <minus_le_minus_minus_comm //
-    elim (IHLK0 … HL20 ? ?) -L0 // /2 width=1/ /2 width=3/
+    elim (IHLK0 … HL20) -L0 // /2 width=1/ /2 width=3/
   ]
 | #L0 #K0 #I #V0 #V1 #d1 #e1 >plus_plus_comm_23 #_ #_ #IHLK0 #L2 #e2 #H #Hd1e2 #He2de1
   elim (le_inv_plus_l … Hd1e2) #_ #He2
@@ -120,7 +120,7 @@ theorem ldrop_trans_le: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L →
   lapply (le_n_O_to_eq … H) -H #H destruct /2 width=3/
 | #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H
   lapply (le_n_O_to_eq … H) -H #H destruct
-  elim (IHL12 … HL2 ?) -IHL12 -HL2 // #L0 #H #HL0
+  elim (IHL12 … HL2) -IHL12 -HL2 // #L0 #H #HL0
   lapply (ldrop_inv_O2 … H) -H #H destruct /3 width=5/
 | #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #IHL12 #e2 #L #H #He2d
   elim (ldrop_inv_O1_pair1 … H) -H *
@@ -135,6 +135,17 @@ qed.
 axiom ldrop_div: ∀e1,L1,L. ⇩[0, e1] L1 ≡ L → ∀e2,L2. ⇩[0, e2] L2 ≡ L →
                  ∃∃L0. ⇩[0, e1] L0 ≡ L2 & ⇩[e1, e2] L0 ≡ L1.
 
+(* Advanced properties ******************************************************)
+
+lemma l_liftable_llstar: ∀R. l_liftable R → ∀l. l_liftable (llstar … R l).
+#R #HR #l #K #T1 #T2 #H @(lstar_ind_r … l T2 H) -l -T2
+[ #L #d #e #_ #U1 #HTU1 #U2 #HTU2 -HR -K
+  >(lift_mono … HTU2 … HTU1) -T1 -U2 -d -e //
+| #l #T #T2 #_ #HT2 #IHT1 #L #d #e #HLK #U1 #HTU1 #U2 #HTU2
+  elim (lift_total T d e) /3 width=11 by lstar_dx/ (**) (* auto too slow without trace *)
+]
+qed.
+
 (* Basic_1: was: drop_conf_lt *)
 lemma ldrop_conf_lt: ∀d1,e1,L,L1. ⇩[d1, e1] L ≡ L1 →
                      ∀e2,K2,I,V2. ⇩[0, e2] L ≡ K2. ⓑ{I} V2 →
@@ -146,6 +157,17 @@ elim (ldrop_conf_le … H1 … H2) -L [2: /2 width=2/] #K #HL1K #HK2
 elim (ldrop_inv_skip1 … HK2) -HK2 [2: /2 width=1/] #K1 #V1 #HK21 #HV12 #H destruct /2 width=5/
 qed.
 
+(* Note: apparently this was missing in basic_1 *)
+lemma ldrop_trans_lt: ∀d1,e1,L1,L. ⇩[d1, e1] L1 ≡ L →
+                      ∀e2,L2,I,V2. ⇩[0, e2] L ≡ L2.ⓑ{I}V2 →
+                      e2 < d1 → let d ≝ d1 - e2 - 1 in
+                      ∃∃L0,V0. ⇩[0, e2] L1 ≡ L0.ⓑ{I}V0 &
+                               ⇩[d, e1] L0 ≡ L2 & ⇧[d, e1] V2 ≡ V0.
+#d1 #e1 #L1 #L #HL1 #e2 #L2 #I #V2 #HL2 #Hd21
+elim (ldrop_trans_le … HL1 … HL2) -L [2: /2 width=1/ ] #L0 #HL10 #HL02
+elim (ldrop_inv_skip2 … HL02) -HL02 [2: /2 width=1/ ] #L #V1 #HL2 #HV21 #H destruct /2 width=5/
+qed-.
+
 lemma ldrop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
                            ⇩[d1, e1] L1 ≡ L → ⇩[0, e2] L ≡ L2 → d1 ≤ e2 →
                            ⇩[0, e2 + e1] L1 ≡ L2.