X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambda-delta%2FBasic-2%2Fsubstitution%2Fdrop_drop.ma;h=9343748537ebf0b9c1a685e0e46da83b93ee544f;hb=55dc00c1c44cc21c7ae179cb9df03e7446002c46;hp=03a8e31ddaf9a7a1cf856f609c7bec2bff3359dd;hpb=b24e4faf4501e54da29dc70940101eeb160e9c9f;p=helm.git

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop_drop.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop_drop.ma
index 03a8e31dd..934374853 100644
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop_drop.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/drop_drop.ma
@@ -19,13 +19,13 @@ include "Basic-2/substitution/drop.ma".
 
 (* Main properties **********************************************************)
 
+(* Basic-1: was: drop_mono *)
 theorem drop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
                    ∀L2. ↓[d, e] L ≡ L2 → L1 = L2.
 #d #e #L #L1 #H elim H -H d e L L1
 [ #d #e #L2 #H
-  >(drop_inv_sort1 … H) -H L2 //
-| #K1 #K2 #I #V #HK12 #_ #L2 #HL12
-   <(drop_inv_refl … HK12) -HK12 K2
+  >(drop_inv_atom1 … H) -H L2 //
+| #K #I #V #L2 #HL12
    <(drop_inv_refl … HL12) -HL12 L2 //
 | #L #K #I #V #e #_ #IHLK #L2 #H
   lapply (drop_inv_drop1 … H ?) -H /2/
@@ -36,14 +36,14 @@ theorem drop_mono: ∀d,e,L,L1. ↓[d, e] L ≡ L1 →
 ]
 qed.
 
+(* Basic-1: was: drop_conf_ge *)
 theorem drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
                       ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 + e1 ≤ e2 →
                       ↓[0, e2 - e1] L1 ≡ L2.
 #d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
 [ #d #e #e2 #L2 #H
-  >(drop_inv_sort1 … H) -H L2 //
-| #K1 #K2 #I #V #HK12 #_ #e2 #L2 #H #_ <minus_n_O
-   <(drop_inv_refl … HK12) -HK12 K2 //
+  >(drop_inv_atom1 … H) -H L2 //
+| //
 | #L #K #I #V #e #_ #IHLK #e2 #L2 #H #He2
   lapply (drop_inv_drop1 … H ?) -H /2/ #HL2
   <minus_plus_comm /3/
@@ -55,6 +55,7 @@ theorem drop_conf_ge: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 ]
 qed.
 
+(* Basic-1: was: drop_conf_lt *)
 theorem drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
                       ∀e2,K2,I,V2. ↓[0, e2] L ≡ K2. 𝕓{I} V2 →
                       e2 < d1 → let d ≝ d1 - e2 - 1 in
@@ -62,8 +63,8 @@ theorem drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
                                ↓[d, e1] K2 ≡ K1 & ↑[d, e1] V1 ≡ V2.
 #d1 #e1 #L #L1 #H elim H -H d1 e1 L L1
 [ #d #e #e2 #K2 #I #V2 #H
-  lapply (drop_inv_sort1 … H) -H #H destruct
-| #L1 #L2 #I #V #_ #_ #e2 #K2 #J #V2 #_ #H
+  lapply (drop_inv_atom1 … H) -H #H destruct
+| #L #I #V #e2 #K2 #J #V2 #_ #H
   elim (lt_zero_false … H)
 | #L1 #L2 #I #V #e #_ #_ #e2 #K2 #J #V2 #_ #H
   elim (lt_zero_false … H)
@@ -76,14 +77,14 @@ theorem drop_conf_lt: ∀d1,e1,L,L1. ↓[d1, e1] L ≡ L1 →
 ]
 qed.
 
+(* Basic-1: was: drop_trans_le *)
 theorem drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
                        ∀e2,L2. ↓[0, e2] L ≡ L2 → e2 ≤ d1 →
                        ∃∃L0. ↓[0, e2] L1 ≡ L0 & ↓[d1 - e2, e1] L0 ≡ L2.
 #d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
 [ #d #e #e2 #L2 #H
-  >(drop_inv_sort1 … H) -H L2 /2/
-| #K1 #K2 #I #V #HK12 #_ #e2 #L2 #HL2 #H
-  >(drop_inv_refl … HK12) -HK12 K1;
+  >(drop_inv_atom1 … H) -H L2 /2/
+| #K #I #V #e2 #L2 #HL2 #H
   lapply (le_O_to_eq_O … H) -H #H destruct -e2 /2/
 | #L1 #L2 #I #V #e #_ #IHL12 #e2 #L #HL2 #H
   lapply (le_O_to_eq_O … H) -H #H destruct -e2;
@@ -99,13 +100,13 @@ theorem drop_trans_le: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
 ]
 qed.
 
+(* Basic-1: was: drop_trans_ge *)
 theorem drop_trans_ge: ∀d1,e1,L1,L. ↓[d1, e1] L1 ≡ L →
                        ∀e2,L2. ↓[0, e2] L ≡ L2 → d1 ≤ e2 → ↓[0, e1 + e2] L1 ≡ L2.
 #d1 #e1 #L1 #L #H elim H -H d1 e1 L1 L
 [ #d #e #e2 #L2 #H
-  >(drop_inv_sort1 … H) -H L2 //
-| #K1 #K2 #I #V #HK12 #_ #e2 #L2 #H #_ normalize
-  >(drop_inv_refl … HK12) -HK12 K1 //
+  >(drop_inv_atom1 … H) -H L2 //
+| //
 | /3/
 | #L1 #L2 #I #V1 #V2 #d #e #H_ #_ #IHL12 #e2 #L #H #Hde2
   lapply (lt_to_le_to_lt 0 … Hde2) // #He2
@@ -121,5 +122,6 @@ theorem drop_trans_ge_comm: ∀d1,e1,e2,L1,L2,L.
 #e1 #e1 #e2 >commutative_plus /2 width=5/
 qed.
 
+(* Basic-1: was: drop_conf_rev *)
 axiom drop_div: ∀e1,L1,L. ↓[0, e1] L1 ≡ L → ∀e2,L2. ↓[0, e2] L2 ≡ L →
                 ∃∃L0. ↓[0, e1] L0 ≡ L2 & ↓[e1, e2] L0 ≡ L1.