- weakening leq, we proved cpr_bind_dx

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / substitution / leq.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/substitution/leq.ma b/matita/matita/contribs/lambda-delta/Basic-2/substitution/leq.ma
index 7f5c12e01fe6656655b2c0317c57429fc1daa847..7612bcb85674f1284f8c8bb35e814c55056aea48 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/substitution/leq.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/substitution/leq.ma
@@ -18,8 +18,7 @@ include "Basic-2/grammar/lenv_length.ma".
 
 inductive leq: lenv → nat → nat → lenv → Prop ≝
 | leq_sort: ∀d,e. leq (⋆) d e (⋆)
-| leq_comp: ∀L1,L2,I1,I2,V1,V2.
-            leq L1 0 0 L2 → leq (L1. 𝕓{I1} V1) 0 0 (L2. 𝕓{I2} V2)
+| leq_OO:   ∀L1,L2. leq L1 0 0 L2
 | leq_eq:   ∀L1,L2,I,V,e. leq L1 0 e L2 → leq (L1. 𝕓{I} V) 0 (e + 1) (L2.𝕓{I} V)
 | leq_skip: ∀L1,L2,I1,I2,V1,V2,d,e.
             leq L1 d e L2 → leq (L1. 𝕓{I1} V1) (d + 1) e (L2. 𝕓{I2} V2)
@@ -31,7 +30,7 @@ interpretation "local environment equality" 'Eq L1 d e L2 = (leq L1 d e L2).
 
 lemma leq_refl: ∀d,e,L. L [d, e] ≈ L.
 #d elim d -d
-[ #e elim e -e [ #L elim L -L /2/ | #e #IHe #L elim L -L /2/ ]
+[ #e elim e -e // #e #IHe #L elim L -L /2/
 | #d #IHd #e #L elim L -L /2/
 ]
 qed.
@@ -43,25 +42,7 @@ qed.
 lemma leq_skip_lt: ∀L1,L2,d,e. L1 [d - 1, e] ≈ L2 → 0 < d →
                    ∀I1,I2,V1,V2. L1. 𝕓{I1} V1 [d, e] ≈ L2. 𝕓{I2} V2.
 
-#L1 #L2 #d #e #HL12 #Hd >(plus_minus_m_m d 1) /2/ 
+#L1 #L2 #d #e #HL12 #Hd >(plus_minus_m_m d 1) /2/
 qed.
 
-lemma leq_fwd_length: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → |L1| = |L2|.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e; normalize //
-qed.  
-
 (* Basic inversion lemmas ***************************************************)
-
-lemma leq_inv_sort1_aux: ∀L1,L2,d,e. L1 [d, e] ≈ L2 → L1 = ⋆ → L2 = ⋆.
-#L1 #L2 #d #e #H elim H -H L1 L2 d e
-[ //
-| #L1 #L2 #I1 #I2 #V1 #V2 #_ #_ #H destruct
-| #L1 #L2 #I #V #e #_ #_ #H destruct
-| #L1 #L2 #I1 #I2 #V1 #V2 #d #e #_ #_ #H destruct
-qed.
-
-lemma leq_inv_sort1: ∀L2,d,e. ⋆ [d, e] ≈ L2 → L2 = ⋆.
-/2 width=5/ qed.
-
-lemma leq_inv_sort2: ∀L1,d,e. L1 [d, e] ≈ ⋆ → L1 = ⋆.
-/3/ qed.