- lambda_delta: context-free weak head normal forms continued ...

[helm.git] / matita / matita / contribs / lambda_delta / Basic_2 / substitution / ltps.ma

diff --git a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
index 3982ed2f9be3b96431bc73d64afc64584f808bf4..43c13fb22ac69f4856727217ec2d0469fdd5bc8e 100644 (file)
--- a/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/substitution/ltps.ma
@@ -12,11 +12,11 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "Basic-2/substitution/tps.ma".
+include "Basic_2/substitution/tps.ma".
 
 (* PARALLEL SUBSTITUTION ON LOCAL ENVIRONMENTS ******************************)
 
-(* Basic-1: includes: csubst1_bind *)
+(* Basic_1: includes: csubst1_bind *)
 inductive ltps: nat → nat → relation lenv ≝
 | ltps_atom: ∀d,e. ltps d e (⋆) (⋆)
 | ltps_pair: ∀L,I,V. ltps 0 0 (L. 𝕓{I} V) (L. 𝕓{I} V)
@@ -47,7 +47,7 @@ lemma ltps_tps1_lt: ∀L1,L2,I,V1,V2,d,e.
 >(plus_minus_m_m d 1) /2/
 qed.
 
-(* Basic-1: was by definition: csubst1_refl *)
+(* Basic_1: was by definition: csubst1_refl *)
 lemma ltps_refl: ∀L,d,e. L [d, e] ≫ L.
 #L elim L -L //
 #L #I #V #IHL * /2/ * /2/
@@ -65,7 +65,7 @@ fact ltps_inv_refl_O2_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → e = 0 → L1 = L2.
 qed.
 
 lemma ltps_inv_refl_O2: ∀d,L1,L2. L1 [d, 0] ≫ L2 → L1 = L2.
-/2/ qed.
+/2/ qed-.
 
 fact ltps_inv_atom1_aux: ∀d,e,L1,L2.
                          L1 [d, e] ≫ L2 → L1 = ⋆ → L2 = ⋆.
@@ -78,7 +78,7 @@ fact ltps_inv_atom1_aux: ∀d,e,L1,L2.
 qed.
 
 lemma ltps_inv_atom1: ∀d,e,L2. ⋆ [d, e] ≫ L2 → L2 = ⋆.
-/2 width=5/ qed.
+/2 width=5/ qed-.
 
 fact ltps_inv_tps21_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → d = 0 → 0 < e →
                          ∀K1,I,V1. L1 = K1. 𝕓{I} V1 →
@@ -96,7 +96,7 @@ qed.
 lemma ltps_inv_tps21: ∀e,K1,I,V1,L2. K1. 𝕓{I} V1 [0, e] ≫ L2 → 0 < e →
                       ∃∃K2,V2. K1 [0, e - 1] ≫ K2 & K2 ⊢ V1 [0, e - 1] ≫ V2 &
                                L2 = K2. 𝕓{I} V2.
-/2 width=5/ qed.
+/2 width=5/ qed-.
 
 fact ltps_inv_tps11_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → 0 < d →
                          ∀I,K1,V1. L1 = K1. 𝕓{I} V1 →
@@ -116,7 +116,7 @@ lemma ltps_inv_tps11: ∀d,e,I,K1,V1,L2. K1. 𝕓{I} V1 [d, e] ≫ L2 → 0 < d
                       ∃∃K2,V2. K1 [d - 1, e] ≫ K2 &
                                   K2 ⊢ V1 [d - 1, e] ≫ V2 &
                                   L2 = K2. 𝕓{I} V2.
-/2/ qed.
+/2/ qed-.
 
 fact ltps_inv_atom2_aux: ∀d,e,L1,L2.
                          L1 [d, e] ≫ L2 → L2 = ⋆ → L1 = ⋆.
@@ -129,7 +129,7 @@ fact ltps_inv_atom2_aux: ∀d,e,L1,L2.
 qed.
 
 lemma ltps_inv_atom2: ∀d,e,L1. L1 [d, e] ≫ ⋆ → L1 = ⋆.
-/2 width=5/ qed.
+/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 →
@@ -147,7 +147,7 @@ qed.
 lemma ltps_inv_tps22: ∀e,L1,K2,I,V2. L1 [0, e] ≫ K2. 𝕓{I} V2 → 0 < e →
                       ∃∃K1,V1. K1 [0, e - 1] ≫ K2 & K2 ⊢ V1 [0, e - 1] ≫ V2 &
                                L1 = K1. 𝕓{I} V1.
-/2 width=5/ qed.
+/2 width=5/ qed-.
 
 fact ltps_inv_tps12_aux: ∀d,e,L1,L2. L1 [d, e] ≫ L2 → 0 < d →
                          ∀I,K2,V2. L2 = K2. 𝕓{I} V2 →
@@ -167,12 +167,12 @@ 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/ qed-.
 
-(* Basic-1: removed theorems 27:
-            csubst0_clear_O csubst0_drop_lt csubst0_drop_gt csubst0_drop_eq
+(* Basic_1: removed theorems 27:
+            csubst0_clear_O csubst0_ldrop_lt csubst0_ldrop_gt csubst0_ldrop_eq
             csubst0_clear_O_back csubst0_clear_S csubst0_clear_trans
-            csubst0_drop_gt_back csubst0_drop_eq_back csubst0_drop_lt_back
+            csubst0_ldrop_gt_back csubst0_ldrop_eq_back csubst0_ldrop_lt_back
             csubst0_gen_sort csubst0_gen_head csubst0_getl_ge csubst0_getl_lt
             csubst0_gen_S_bind_2 csubst0_getl_ge_back csubst0_getl_lt_back
             csubst0_snd_bind csubst0_fst_bind csubst0_both_bind