other addition to the standard library removed

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / unfold / ltpss.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
index 4f2062a1456c9de7b69696ef18921a8e12de1d83..7c86262d9a0d0b91bf5c76466fce76396c0a2b2e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/unfold/ltpss.ma
@@ -12,8 +12,8 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/substitution/ltps.ma".
-include "Basic-2/unfold/tpss.ma".
+include "Basic_2/substitution/ltps.ma".
+include "Basic_2/unfold/tpss.ma".
 
 (* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************)
 
@@ -25,47 +25,43 @@ interpretation "partial unfold (local environment)"
 
 (* Basic eliminators ********************************************************)
 
-lemma ltpss_ind: ∀d,e,L1. ∀R: lenv → Prop. R L1 →
+lemma ltpss_ind: ∀d,e,L1. ∀R:predicate lenv. R L1 →
                  (∀L,L2. L1 [d, e] ≫* L → L [d, e] ≫ L2 → R L → R L2) →
                  ∀L2. L1 [d, e] ≫* L2 → R L2.
 #d #e #L1 #R #HL1 #IHL1 #L2 #HL12 @(TC_star_ind … HL1 IHL1 … HL12) //
-qed.
+qed-.
 
 (* Basic properties *********************************************************)
 
 lemma ltpss_strap: ∀L1,L,L2,d,e.
                    L1 [d, e] ≫ L → L [d, e] ≫* L2 → L1 [d, e] ≫* L2. 
-/2/ qed.
+/2 width=3/ qed.
 
 lemma ltpss_refl: ∀L,d,e. L [d, e] ≫* L.
-/2/ qed.
+/2 width=1/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 lemma ltpss_inv_refl_O2: ∀d,L1,L2. L1 [d, 0] ≫* L2 → L1 = L2.
 #d #L1 #L2 #H @(ltpss_ind … H) -L2 //
 #L #L2 #_ #HL2 #IHL <(ltps_inv_refl_O2 … HL2) -HL2 //
-qed.
+qed-.
 
 lemma ltpss_inv_atom1: ∀d,e,L2. ⋆ [d, e] ≫* L2 → L2 = ⋆.
 #d #e #L2 #H @(ltpss_ind … H) -L2 //
-#L #L2 #_ #HL2 #IHL destruct -L
+#L #L2 #_ #HL2 #IHL destruct
 >(ltps_inv_atom1 … HL2) -HL2 //
-qed.
-(*
-fact ltps_inv_atom2_aux: ∀d,e,L1,L2.
-                         L1 [d, e] ≫ L2 → L2 = ⋆ → L1 = ⋆.
-#d #e #L1 #L2 * -d e L1 L2
-[ //
-| #L #I #V #H destruct
-| #L1 #L2 #I #V1 #V2 #e #_ #_ #H destruct
-| #L1 #L2 #I #V1 #V2 #d #e #_ #_ #H destruct
-]
-qed.
+qed-.
 
-lemma drop_inv_atom2: ∀d,e,L1. L1 [d, e] ≫ ⋆ → L1 = ⋆.
-/2 width=5/ qed.
+fact ltpss_inv_atom2_aux: ∀d,e,L1,L2. L1 [d, e] ≫* L2 → L2 = ⋆ → L1 = ⋆.
+#d #e #L1 #L2 #H @(ltpss_ind … H) -L2 //
+#L2 #L #_ #HL2 #IHL2 #H destruct
+lapply (ltps_inv_atom2 … HL2) -HL2 /2 width=1/
+qed.
 
+lemma ltpss_inv_atom2: ∀d,e,L1. L1 [d, e] ≫* ⋆ → L1 = ⋆.
+/2 width=5/ qed-.
+(*
 fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
                          ∀K2,I,V2. L2 = K2. 𝕓{I} V2 →
                          ∃∃K1,V1. K1 [0, e - 1] ≫ K2 &
@@ -74,7 +70,7 @@ fact ltps_inv_tps22_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
 #d #e #L1 #L2 * -d e L1 L2
 [ #d #e #_ #_ #K1 #I #V1 #H destruct
 | #L1 #I #V #_ #H elim (lt_refl_false … H)
-| #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #_ #_ #K2 #J #W2 #H destruct -L2 I V2 /2 width=5/
+| #L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #_ #_ #K2 #J #W2 #H destruct /2 width=5/
 | #L1 #L2 #I #V1 #V2 #d #e #_ #_ #H elim (plus_S_eq_O_false … H)
 ]
 qed.
@@ -93,8 +89,7 @@ fact ltps_inv_tps12_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → 0 < d →
 [ #d #e #_ #I #K2 #V2 #H destruct
 | #L #I #V #H elim (lt_refl_false … H)
 | #L1 #L2 #I #V1 #V2 #e #_ #_ #H elim (lt_refl_false … H)
-| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #_ #J #K2 #W2 #H destruct -L2 I V2
-  /2 width=5/
+| #L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #_ #J #K2 #W2 #H destruct /2 width=5/
 ]
 qed.
 
@@ -102,6 +97,5 @@ lemma ltps_inv_tps12: ∀L1,K2,I,V2,d,e. L1 [d, e] ≫ K2. 𝕓{I} V2 → 0 < d
                       ∃∃K1,V1. K1 [d - 1, e] ≫ K2 &
                                   K2 ⊢ V1 [d - 1, e] ≫ V2 &
                                   L1 = K1. 𝕓{I} V1.
-/2/ qed.
-
+/2 width=1/ qed.
 *)