work in progress with voids and lveq (was: the most recent voids)

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / syntax / lenv_length.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/syntax/lenv_length.ma b/matita/matita/contribs/lambdadelta/basic_2/syntax/lenv_length.ma
index 41e09d5d5ecde9497b7ecf4508d30eb4f475f09c..8b7ccd58207a7b1fc92fc4203da6f70612a7982c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/syntax/lenv_length.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/syntax/lenv_length.ma
@@ -17,24 +17,27 @@ include "basic_2/syntax/lenv.ma".
 (* LENGTH OF A LOCAL ENVIRONMENT ********************************************)
 
 rec definition length L ≝ match L with
-[ LAtom       ⇒ 0
-| LPair L _ _ ⇒ ⫯(length L)
+[ LAtom     ⇒ 0
+| LBind L _ ⇒ ⫯(length L)
 ].
 
 interpretation "length (local environment)" 'card L = (length L).
 
+definition length2 (L1) (L2): nat ≝ |L1| + |L2|. 
+
 (* Basic properties *********************************************************)
 
 lemma length_atom: |⋆| = 0.
 // qed.
 
-lemma length_pair: ∀I,L,V. |L.ⓑ{I}V| = ⫯|L|.
+(* Basic_2A1: uses: length_pair *)
+lemma length_bind: ∀I,L. |L.ⓘ{I}| = ⫯|L|.
 // qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 lemma length_inv_zero_dx: ∀L. |L| = 0 → L = ⋆.
-* // #L #I #V >length_pair
+* // #L #I >length_bind
 #H destruct
 qed-.
 
@@ -43,16 +46,18 @@ lemma length_inv_zero_sn: ∀L. 0 = |L| → L = ⋆.
 
 (* Basic_2A1: was: length_inv_pos_dx *)
 lemma length_inv_succ_dx: ∀n,L. |L| = ⫯n →
-                          ∃∃I,K,V. |K| = n & L = K. ⓑ{I}V.
-#n * [ >length_atom #H destruct ]
-#L #I #V >length_pair /3 width=5 by ex2_3_intro, injective_S/
+                          ∃∃I,K. |K| = n & L = K. ⓘ{I}.
+#n *
+[ >length_atom #H destruct
+| #L #I >length_bind /3 width=4 by ex2_2_intro, injective_S/
+]
 qed-.
 
 (* Basic_2A1: was: length_inv_pos_sn *)
 lemma length_inv_succ_sn: ∀n,L. ⫯n = |L| →
-                          ∃∃I,K,V. n = |K| & L = K. ⓑ{I}V.
-#l #L #H lapply (sym_eq ??? H) -H 
-#H elim (length_inv_succ_dx … H) -H /2 width=5 by ex2_3_intro/
+                          ∃∃I,K. n = |K| & L = K. ⓘ{I}.
+#n #L #H lapply (sym_eq ??? H) -H 
+#H elim (length_inv_succ_dx … H) -H /2 width=4 by ex2_2_intro/
 qed-.
 
 (* Basic_2A1: removed theorems 1: length_inj *)