X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fsubstitution%2Fldrops.ma;h=868b8ec2aba8a541cae2bfbe1b5dc48c26a4725f;hb=6aab24b40d5d09561375959043ecd85c8b428d85;hp=659689248795b62367f490a59f3f0ece8d53a83a;hpb=65008df95049eb835941ffea1aa682c9253c4c2b;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops.ma
index 659689248..868b8ec2a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/ldrops.ma
@@ -13,77 +13,83 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/rdropstar_3.ma".
+include "basic_2/notation/relations/rdropstar_4.ma".
 include "basic_2/relocation/ldrop.ma".
 include "basic_2/substitution/gr2_minus.ma".
 include "basic_2/substitution/lifts.ma".
 
-(* GENERIC LOCAL ENVIRONMENT SLICING ****************************************)
+(* ITERATED LOCAL ENVIRONMENT SLICING ***************************************)
 
-inductive ldrops: list2 nat nat → relation lenv ≝
-| ldrops_nil : ∀L. ldrops ⟠ L L
+inductive ldrops (s:bool): list2 nat nat → relation lenv ≝
+| ldrops_nil : ∀L. ldrops s (⟠) L L
 | ldrops_cons: ∀L1,L,L2,des,d,e.
-               ldrops des L1 L → ⇩[d,e] L ≡ L2 → ldrops ({d, e} @ des) L1 L2
+               ldrops s des L1 L → ⇩[s, d, e] L ≡ L2 → ldrops s ({d, e} @ des) L1 L2
 .
 
-interpretation "generic local environment slicing"
-   'RDropStar des T1 T2 = (ldrops des T1 T2).
+interpretation "iterated slicing (local environment) abstract"
+   'RDropStar s des T1 T2 = (ldrops s des T1 T2).
+(*
+interpretation "iterated slicing (local environment) general"
+   'RDropStar des T1 T2 = (ldrops true des T1 T2).
+*)
 
 (* Basic inversion lemmas ***************************************************)
 
-fact ldrops_inv_nil_aux: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → des = ⟠ → L1 = L2.
-#L1 #L2 #des * -L1 -L2 -des //
+fact ldrops_inv_nil_aux: ∀L1,L2,s,des. ⇩*[s, des] L1 ≡ L2 → des = ⟠ → L1 = L2.
+#L1 #L2 #s #des * -L1 -L2 -des //
 #L1 #L #L2 #d #e #des #_ #_ #H destruct
-qed.
+qed-.
 
 (* Basic_1: was: drop1_gen_pnil *)
-lemma ldrops_inv_nil: ∀L1,L2. ⇩*[⟠] L1 ≡ L2 → L1 = L2.
-/2 width=3/ qed-.
+lemma ldrops_inv_nil: ∀L1,L2,s. ⇩*[s, ⟠] L1 ≡ L2 → L1 = L2.
+/2 width=4 by ldrops_inv_nil_aux/ qed-.
 
-fact ldrops_inv_cons_aux: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 →
+fact ldrops_inv_cons_aux: ∀L1,L2,s,des. ⇩*[s, des] L1 ≡ L2 →
                           ∀d,e,tl. des = {d, e} @ tl →
-                          ∃∃L. ⇩*[tl] L1 ≡ L & ⇩[d, e] L ≡ L2.
-#L1 #L2 #des * -L1 -L2 -des
+                          ∃∃L. ⇩*[s, tl] L1 ≡ L & ⇩[s, d, e] L ≡ L2.
+#L1 #L2 #s #des * -L1 -L2 -des
 [ #L #d #e #tl #H destruct
 | #L1 #L #L2 #des #d #e #HT1 #HT2 #hd #he #tl #H destruct
-  /2 width=3/
-qed.
+  /2 width=3 by ex2_intro/
+]
+qed-.
 
 (* Basic_1: was: drop1_gen_pcons *)
-lemma ldrops_inv_cons: ∀L1,L2,d,e,des. ⇩*[{d, e} @ des] L1 ≡ L2 →
-                       ∃∃L. ⇩*[des] L1 ≡ L & ⇩[d, e] L ≡ L2.
-/2 width=3/ qed-.
+lemma ldrops_inv_cons: ∀L1,L2,s,d,e,des. ⇩*[s, {d, e} @ des] L1 ≡ L2 →
+                       ∃∃L. ⇩*[s, des] L1 ≡ L & ⇩[s, d, e] L ≡ L2.
+/2 width=3 by ldrops_inv_cons_aux/ qed-.
 
-lemma ldrops_inv_skip2: ∀I,des,i,des2. des ▭ i ≡ des2 →
-                        ∀L1,K2,V2. ⇩*[des2] L1 ≡ K2. ⓑ{I} V2 →
+lemma ldrops_inv_skip2: ∀I,s,des,des2,i. des ▭ i ≡ des2 →
+                        ∀L1,K2,V2. ⇩*[s, des2] L1 ≡ K2. ⓑ{I} V2 →
                         ∃∃K1,V1,des1. des + 1 ▭ i + 1 ≡ des1 + 1 &
-                                      ⇩*[des1] K1 ≡ K2 &
+                                      ⇩*[s, des1] K1 ≡ K2 &
                                       ⇧*[des1] V2 ≡ V1 &
                                       L1 = K1. ⓑ{I} V1.
-#I #des #i #des2 #H elim H -des -i -des2
+#I #s #des #des2 #i #H elim H -des -des2 -i
 [ #i #L1 #K2 #V2 #H
-  >(ldrops_inv_nil … H) -L1 /2 width=7/
+  >(ldrops_inv_nil … H) -L1 /2 width=7 by lifts_nil, minuss_nil, ex4_3_intro, ldrops_nil/
 | #des #des2 #d #e #i #Hid #_ #IHdes2 #L1 #K2 #V2 #H
   elim (ldrops_inv_cons … H) -H #L #HL1 #H
-  elim (ldrop_inv_skip2 … H ?) -H /2 width=1/ #K #V >minus_plus #HK2 #HV2 #H destruct
+  elim (ldrop_inv_skip2 … H) -H /2 width=1 by lt_plus_to_minus_r/ #K #V >minus_plus #HK2 #HV2 #H destruct
   elim (IHdes2 … HL1) -IHdes2 -HL1 #K1 #V1 #des1 #Hdes1 #HK1 #HV1 #X destruct
-  @(ex4_3_intro … K1 V1 … ) // [3,4: /2 width=7/ | skip ]
-  normalize >plus_minus // @minuss_lt // /2 width=1/ (**) (* explicit constructors, /3 width=1/ is a bit slow *)
+  @(ex4_3_intro … K1 V1 … ) // [3,4: /2 width=7 by lifts_cons, ldrops_cons/ | skip ]
+  normalize >plus_minus /3 width=1 by minuss_lt, lt_minus_to_plus/ (**) (* explicit constructors *)
 | #des #des2 #d #e #i #Hid #_ #IHdes2 #L1 #K2 #V2 #H
   elim (IHdes2 … H) -IHdes2 -H #K1 #V1 #des1 #Hdes1 #HK1 #HV1 #X destruct
-  /4 width=7/
+  /4 width=7 by minuss_ge, ex4_3_intro, le_S_S/
 ]
 qed-.
 
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: drop1_skip_bind *)
-lemma ldrops_skip: ∀L1,L2,des. ⇩*[des] L1 ≡ L2 → ∀V1,V2. ⇧*[des] V2 ≡ V1 →
-                   ∀I. ⇩*[des + 1] L1. ⓑ{I} V1 ≡ L2. ⓑ{I} V2.
-#L1 #L2 #des #H elim H -L1 -L2 -des
+lemma ldrops_skip: ∀L1,L2,s,des. ⇩*[s, des] L1 ≡ L2 → ∀V1,V2. ⇧*[des] V2 ≡ V1 →
+                   ∀I. ⇩*[s, des + 1] L1.ⓑ{I}V1 ≡ L2.ⓑ{I}V2.
+#L1 #L2 #s #des #H elim H -L1 -L2 -des
 [ #L #V1 #V2 #HV12 #I
   >(lifts_inv_nil … HV12) -HV12 //
 | #L1 #L #L2 #des #d #e #_ #HL2 #IHL #V1 #V2 #H #I
-  elim (lifts_inv_cons … H) -H /3 width=5/
+  elim (lifts_inv_cons … H) -H /3 width=5 by ldrop_skip, ldrops_cons/
 ].
 qed.