- advances on hereditarily free variables: now "frees" is primitive

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / substitution / llor.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/substitution/llor.ma b/matita/matita/contribs/lambdadelta/basic_2/substitution/llor.ma
index 9d0122cca33838024ee965b19cca5b5faf439aba..94dfeeb256e2561f16589a64add1c4efe107690d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/substitution/llor.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/substitution/llor.ma
@@ -13,19 +13,17 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lazyor_4.ma".
-include "basic_2/relocation/lpx_sn.ma".
-include "basic_2/substitution/cofrees.ma".
+include "basic_2/substitution/frees.ma".
 
 (* POINTWISE UNION FOR LOCAL ENVIRONMENTS ***********************************)
 
-inductive clor (T) (L2) (K1) (V1): predicate term ≝
-| clor_sn: |K1| < |L2| → K1 ⊢ |L2|-|K1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → clor T L2 K1 V1 V1
-| clor_dx: ∀I,K2,V2. |K1| < |L2| → (K1 ⊢ |L2|-|K1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) →
-           ⇩[|L2|-|K1|-1] L2 ≡ K2.ⓑ{I}V2 → clor T L2 K1 V1 V2
-.
-
-definition llor: relation4 term lenv lenv lenv ≝
-                 λT,L2. lpx_sn (clor T L2).
+definition llor: relation4 term lenv lenv lenv ≝ λT,L2,L1,L.
+                 ∧∧ |L1| ≤ |L2| & |L1| = |L|
+                  & (∀I1,I2,I,K1,K2,K,V1,V2,V,i.
+                       ⇩[i] L1 ≡ K1.ⓑ{I1}V1 → ⇩[i] L2 ≡ K2.ⓑ{I2}V2 → ⇩[i] L ≡ K.ⓑ{I}V →
+                       (∧∧ (L1 ⊢ i ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) & I1 = I & V1 = V) ∨
+                       (∧∧ L1 ⊢ i ϵ 𝐅*[yinj 0]⦃T⦄  & I1 = I & V2 = V)
+                    ).
 
 interpretation
    "lazy union (local environment)"
@@ -33,24 +31,8 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma llor_pair_sn: ∀I,L1,L2,L,V,T. L1 ⩖[T] L2 ≡ L →
-                    |L1| < |L2| → L1 ⊢ |L2|-|L1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ →
-                    L1.ⓑ{I}V ⩖[T] L2 ≡ L.ⓑ{I}V.
-/3 width=2 by clor_sn, lpx_sn_pair/ qed.
-
-lemma llor_pair_dx: ∀I,J,L1,L2,L,K2,V1,V2,T. L1 ⩖[T] L2 ≡ L →
-                    |L1| < |L2| → (L1 ⊢ |L2|-|L1|-1 ~ϵ 𝐅*[yinj 0]⦃T⦄ → ⊥) →
-                    ⇩[|L2|-|L1|-1] L2 ≡ K2.ⓑ{J}V2 →
-                    L1.ⓑ{I}V1 ⩖[T] L2 ≡ L.ⓑ{I}V2.
-/4 width=3 by clor_dx, lpx_sn_pair/ qed.
-
-lemma llor_total: ∀T,L2,L1. |L1| ≤ |L2| → ∃L. L1 ⩖[T] L2 ≡ L.
-#T #L2 #L1 elim L1 -L1 /2 width=2 by ex_intro/
-#L1 #I1 #V1 #IHL1 normalize
-#H elim IHL1 -IHL1 /2 width=3 by transitive_le/
-#L #HT elim (cofrees_dec L1 T 0 (|L2|-|L1|-1))
-[ /3 width=2 by llor_pair_sn, ex_intro/
-| elim (ldrop_O1_lt (Ⓕ) L2 (|L2|-|L1|-1))
-  /5 width=4 by llor_pair_dx, monotonic_lt_minus_l, ex_intro/
-]
-qed-.
+lemma llor_atom: ∀T,L2. ⋆ ⩖[T] L2 ≡ ⋆.
+#T #L2 @and3_intro //
+#I1 #I2 #I #K1 #K2 #K #V1 #V2 #V #i #HLK1
+elim (ldrop_inv_atom1 … HLK1) -HLK1 #H destruct
+qed.