- matita: reset_font_size () added after matita.conf.xml is read to set

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / substitution / ldrop.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma b/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
index 73a9ff92e373fc9bb0d3aee04849989b25191576..9ab5134581aacbae9ceee142248d4321b2986b73 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/substitution/ldrop.ma
@@ -13,8 +13,8 @@
 (**************************************************************************)
 
 include "basic_2/grammar/cl_weight.ma".
-include "basic_2/grammar/lsubs.ma".
 include "basic_2/substitution/lift.ma".
+include "basic_2/substitution/lsubs.ma".
 
 (* LOCAL ENVIRONMENT SLICING ************************************************)
 
@@ -76,6 +76,12 @@ lemma ldrop_inv_O1: ∀e,K,I,V,L2. ⇩[0, e] K. ⓑ{I} V ≡ L2 →
                     (0 < e ∧ ⇩[0, e - 1] K ≡ L2).
 /2 width=3/ qed-.
 
+lemma ldrop_inv_pair1: ∀K,I,V,L2. ⇩[0, 0] K. ⓑ{I} V ≡ L2 → L2 = K. ⓑ{I} V.
+#K #I #V #L2 #H
+elim (ldrop_inv_O1 … H) -H * // #H destruct
+elim (lt_refl_false … H)
+qed-.
+
 (* Basic_1: was: drop_gen_drop *)
 lemma ldrop_inv_ldrop1: ∀e,K,I,V,L2.
                         ⇩[0, e] K. ⓑ{I} V ≡ L2 → 0 < e → ⇩[0, e - 1] K ≡ L2.
@@ -135,20 +141,35 @@ lemma ldrop_ldrop_lt: ∀L1,L2,I,V,e.
 #L1 #L2 #I #V #e #HL12 #He >(plus_minus_m_m e 1) // /2 width=1/
 qed.
 
-lemma ldrop_O1: ∀L,i. i < |L| → ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V.
+lemma ldrop_skip_lt: ∀L1,L2,I,V1,V2,d,e.
+                     ⇩[d - 1, e] L1 ≡ L2 → ⇧[d - 1, e] V2 ≡ V1 → 0 < d →
+                     ⇩[d, e] L1. ⓑ{I} V1 ≡ L2. ⓑ{I} V2.
+#L1 #L2 #I #V1 #V2 #d #e #HL12 #HV21 #Hd >(plus_minus_m_m d 1) // /2 width=1/
+qed.
+
+lemma ldrop_O1_le: ∀i,L. i ≤ |L| → ∃K. ⇩[0, i] L ≡ K.
+#i @(nat_ind_plus … i) -i /2 width=2/
+#i #IHi *
+[ #H lapply (le_n_O_to_eq … H) -H >commutative_plus normalize #H destruct 
+| #L #I #V normalize #H
+  elim (IHi L ?) -IHi /2 width=1/ -H /3 width=2/
+]
+qed.
+
+lemma ldrop_O1_lt: ∀L,i. i < |L| → ∃∃I,K,V. ⇩[0, i] L ≡ K.ⓑ{I}V.
 #L elim L -L
 [ #i #H elim (lt_zero_false … H)
-| #L #I #V #IHL #i @(nat_ind_plus … i) -i /2 width=4/ #i #_ #H
-  lapply (lt_plus_to_lt_l … H) -H #Hi
-  elim (IHL i ?) // /3 width=4/
+| #L #I #V #IHL #i @(nat_ind_plus … i) -i /2 width=4/
+  #i #_ normalize #H
+  elim (IHL i ? ) -IHL /2 width=1/ -H /3 width=4/
 ]
-qed.   
+qed.
 
-lemma ldrop_lsubs_ldrop1_abbr: ∀L1,L2,d,e. L1 [d, e] ≼ L2 →
-                               ∀K1,V,i. ⇩[0, i] L1 ≡ K1. ⓓV →
+lemma ldrop_lsubs_ldrop2_abbr: ∀L1,L2,d,e. L1 ≼ [d, e] L2 →
+                               ∀K2,V,i. ⇩[0, i] L2 ≡ K2. ⓓV →
                                d ≤ i → i < d + e →
-                               ∃∃K2. K1 [0, d + e - i - 1] ≼ K2 &
-                                     ⇩[0, i] L2 ≡ K2. ⓓV.
+                               ∃∃K1. K1 ≼ [0, d + e - i - 1] K2 &
+                                     ⇩[0, i] L1 ≡ K1. ⓓV.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e
 [ #d #e #K1 #V #i #H
   lapply (ldrop_inv_atom1 … H) -H #H destruct
@@ -188,7 +209,7 @@ lemma ldrop_fwd_ldrop2: ∀L1,I2,K2,V2,e. ⇩[O, e] L1 ≡ K2. ⓑ{I2} V2 →
 ]
 qed-.
 
-lemma ldrop_fwd_lw: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → #[L2] ≤ #[L1].
+lemma ldrop_fwd_lw: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → #{L2} ≤ #{L1}.
 #L1 #L2 #d #e #H elim H -L1 -L2 -d -e // normalize
 [ /2 width=3/
 | #L1 #L2 #I #V1 #V2 #d #e #_ #HV21 #IHL12
@@ -197,7 +218,7 @@ lemma ldrop_fwd_lw: ∀L1,L2,d,e. ⇩[d, e] L1 ≡ L2 → #[L2] ≤ #[L1].
 qed-. 
 
 lemma ldrop_pair2_fwd_cw: ∀I,L,K,V,d,e. ⇩[d, e] L ≡ K. ⓑ{I} V →
-                          ∀T. #[K, V] < #[L, T].
+                          ∀T. #{K, V} < #{L, T}.
 #I #L #K #V #d #e #H #T
 lapply (ldrop_fwd_lw … H) -H #H
 @(le_to_lt_to_lt … H) -H /3 width=1/