- some renaming according to the written version of basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / lcosx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma
index 03187e34c8d49604d649b6b09165ed1bb9e60bcf..8997c6ec9b567531a19bae6ec23b32d0e817aa23 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lcosx.ma
@@ -18,15 +18,15 @@ include "basic_2/computation/lsx.ma".
 (* SN EXTENDED STRONGLY CONORMALIZING LOCAL ENVIRONMENTS ********************)
 
 inductive lcosx (h) (g) (G): relation2 ynat lenv ≝
-| lcosx_sort: ∀d. lcosx h g G d (⋆)
+| lcosx_sort: ∀l. lcosx h g G l (⋆)
 | lcosx_skip: ∀I,L,T. lcosx h g G 0 L → lcosx h g G 0 (L.ⓑ{I}T)
-| lcosx_pair: ∀I,L,T,d. G ⊢ ⬊*[h, g, T, d] L →
-              lcosx h g G d L → lcosx h g G (⫯d) (L.ⓑ{I}T)
+| lcosx_pair: ∀I,L,T,l. G ⊢ ⬊*[h, g, T, l] L →
+              lcosx h g G l L → lcosx h g G (⫯l) (L.ⓑ{I}T)
 .
 
 interpretation
    "sn extended strong conormalization (local environment)"
-   'CoSN h g d G L = (lcosx h g G d L).
+   'CoSN h g l G L = (lcosx h g G l L).
 
 (* Basic properties *********************************************************)
 
@@ -34,43 +34,43 @@ lemma lcosx_O: ∀h,g,G,L. G ⊢ ~⬊*[h, g, 0] L.
 #h #g #G #L elim L /2 width=1 by lcosx_skip/
 qed.
 
-lemma lcosx_drop_trans_lt: ∀h,g,G,L,d. G ⊢ ~⬊*[h, g, d] L →
-                            ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < d →
-                            G ⊢ ~⬊*[h, g, ⫰(d-i)] K ∧ G ⊢ ⬊*[h, g, V, ⫰(d-i)] K.
-#h #g #G #L #d #H elim H -L -d
-[ #d #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct
+lemma lcosx_drop_trans_lt: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, l] L →
+                            ∀I,K,V,i. ⬇[i] L ≡ K.ⓑ{I}V → i < l →
+                            G ⊢ ~⬊*[h, g, ⫰(l-i)] K ∧ G ⊢ ⬊*[h, g, V, ⫰(l-i)] K.
+#h #g #G #L #l #H elim H -L -l
+[ #l #J #K #V #i #H elim (drop_inv_atom1 … H) -H #H destruct
 | #I #L #T #_ #_ #J #K #V #i #_ #H elim (ylt_yle_false … H) -H //
-| #I #L #T #d #HT #HL #IHL #J #K #V #i #H #Hid
+| #I #L #T #l #HT #HL #IHL #J #K #V #i #H #Hil
   elim (drop_inv_O1_pair1 … H) -H * #Hi #HLK destruct
   [ >ypred_succ /2 width=1 by conj/
-  | lapply (ylt_pred … Hid ?) -Hid /2 width=1 by ylt_inj/ >ypred_succ #Hid
+  | lapply (ylt_pred … Hil ?) -Hil /2 width=1 by ylt_inj/ >ypred_succ #Hil
     elim (IHL … HLK ?) -IHL -HLK <yminus_inj >yminus_SO2 //
-    <(ypred_succ d) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/
+    <(ypred_succ l) in ⊢ (%→%→?); >yminus_pred /2 width=1 by ylt_inj, conj/
   ]
 ]
 qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-fact lcosx_inv_succ_aux: ∀h,g,G,L,x. G ⊢ ~⬊*[h, g, x] L → ∀d. x = ⫯d →
+fact lcosx_inv_succ_aux: ∀h,g,G,L,x. G ⊢ ~⬊*[h, g, x] L → ∀l. x = ⫯l →
                          L = ⋆ ∨
-                         ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, d] K &
-                                  G ⊢ ⬊*[h, g, V, d] K.
-#h #g #G #L #d * -L -d /2 width=1 by or_introl/
+                         ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K &
+                                  G ⊢ ⬊*[h, g, V, l] K.
+#h #g #G #L #l * -L -l /2 width=1 by or_introl/
 [ #I #L #T #_ #x #H elim (ysucc_inv_O_sn … H)
-| #I #L #T #d #HT #HL #x #H <(ysucc_inj … H) -x
+| #I #L #T #l #HT #HL #x #H <(ysucc_inj … H) -x
   /3 width=6 by ex3_3_intro, or_intror/
 ]
 qed-.
 
-lemma lcosx_inv_succ: ∀h,g,G,L,d. G ⊢ ~⬊*[h, g, ⫯d] L → L = ⋆ ∨
-                      ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, d] K &
-                               G ⊢ ⬊*[h, g, V, d] K.
+lemma lcosx_inv_succ: ∀h,g,G,L,l. G ⊢ ~⬊*[h, g, ⫯l] L → L = ⋆ ∨
+                      ∃∃I,K,V. L = K.ⓑ{I}V & G ⊢ ~⬊*[h, g, l] K &
+                               G ⊢ ⬊*[h, g, V, l] K.
 /2 width=3 by lcosx_inv_succ_aux/ qed-.
 
-lemma lcosx_inv_pair: ∀h,g,I,G,L,T,d. G ⊢ ~⬊*[h, g, ⫯d] L.ⓑ{I}T →
-                      G ⊢ ~⬊*[h, g, d] L ∧ G ⊢ ⬊*[h, g, T, d] L.
-#h #g #I #G #L #T #d #H elim (lcosx_inv_succ … H) -H
+lemma lcosx_inv_pair: ∀h,g,I,G,L,T,l. G ⊢ ~⬊*[h, g, ⫯l] L.ⓑ{I}T →
+                      G ⊢ ~⬊*[h, g, l] L ∧ G ⊢ ⬊*[h, g, T, l] L.
+#h #g #I #G #L #T #l #H elim (lcosx_inv_succ … H) -H
 [ #H destruct
 | * #Z #Y #X #H destruct /2 width=1 by conj/
 ]