- support for transitive closures started

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

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/grammar/leq.ma b/matita/matita/contribs/lambda-delta/Basic-2/grammar/leq.ma
index 7612bcb85674f1284f8c8bb35e814c55056aea48..ac5503d28c62329c174a2e43ebc606e9ca099ee8 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/grammar/leq.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/grammar/leq.ma
@@ -16,18 +16,31 @@ include "Basic-2/grammar/lenv_length.ma".
 
 (* LOCAL ENVIRONMENT EQUALITY ***********************************************)
 
-inductive leq: lenv → nat → nat → lenv → Prop ≝
-| leq_sort: ∀d,e. leq (⋆) d e (⋆)
-| 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)
+inductive leq: nat → nat → relation lenv ≝
+| leq_sort: ∀d,e. leq d e (⋆) (⋆)
+| leq_OO:   ∀L1,L2. leq 0 0 L1 L2
+| leq_eq:   ∀L1,L2,I,V,e. leq 0 e L1 L2 →
+            leq 0 (e + 1) (L1. 𝕓{I} V) (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)
+            leq d e L1 L2 → leq (d + 1) e (L1. 𝕓{I1} V1) (L2. 𝕓{I2} V2)
 .
 
-interpretation "local environment equality" 'Eq L1 d e L2 = (leq L1 d e L2).
+interpretation "local environment equality" 'Eq L1 d e L2 = (leq d e L1 L2).
+
+definition leq_repl_dx: ∀S. (lenv → relation S) → Prop ≝ λS,R.
+                        ∀L1,s1,s2. R L1 s1 s2 →
+                        ∀L2,d,e. L1 [d, e]≈ L2 → R L2 s1 s2.
 
 (* Basic properties *********************************************************)
 
+lemma TC_leq_repl_dx: ∀S,R. leq_repl_dx S R → leq_repl_dx S (λL. (TC … (R L))).
+#S #R #HR #L1 #s1 #s2 #H elim H -H s2
+[ /3 width=5/
+| #s #s2 #_ #Hs2 #IHs1 #L2 #d #e #HL12
+  lapply (HR … Hs2 … HL12) -HR Hs2 HL12 /3/
+]
+qed.
+
 lemma leq_refl: ∀d,e,L. L [d, e] ≈ L.
 #d elim d -d
 [ #e elim e -e // #e #IHe #L elim L -L /2/