- lambda: some parts commented out, some refactoring

[helm.git] / matita / matita / contribs / lambda / preamble.ma

diff --git a/matita/matita/contribs/lambda/preamble.ma b/matita/matita/contribs/lambda/preamble.ma
index f3884b229489f7bbe58cd0bde50e28c7086b6833..c7c736f2ce1d3cad45775d2568fa537914ca2691 100644 (file)
--- a/matita/matita/contribs/lambda/preamble.ma
+++ b/matita/matita/contribs/lambda/preamble.ma
@@ -13,16 +13,13 @@
 (**************************************************************************)
 
 include "basics/star.ma".
-include "basics/lists/list.ma".
+include "basics/lists/lstar.ma".
 include "arithmetics/exp.ma".
 
 include "xoa_notation.ma".
 include "xoa.ma".
 
-(* Note: notation for nil not involving brackets *)
-notation > "◊"
-  non associative with precedence 90
-  for @{'nil}.
+(* logic *)
 
 (* Note: For some reason this cannot be in the standard library *) 
 interpretation "logical false" 'false = False.
@@ -31,6 +28,8 @@ notation "⊥"
   non associative with precedence 90
   for @{'false}.
 
+(* arithmetics *)
+
 lemma lt_refl_false: ∀n. n < n → ⊥.
 #n #H elim (lt_to_not_eq … H) -H /2 width=1/
 qed-.
@@ -75,3 +74,30 @@ lemma tri_gt: ∀A,a1,a2,a3,n1,n2. n2 < n1 → tri A n1 n2 a1 a2 a3 = a3.
 | #n1 #IH #n2 elim n2 -n2 // /3 width=1/
 ]
 qed.
+
+(* lists *)
+
+(* Note: notation for nil not involving brackets *)
+notation > "◊"
+  non associative with precedence 90
+  for @{'nil}.
+
+definition map_cons: ∀A. A → list (list A) → list (list A) ≝ λA,a.
+                     map … (cons … a).
+
+interpretation "map_cons" 'ho_cons a l = (map_cons ? a l).
+
+notation "hvbox(a ::: break l)"
+  right associative with precedence 47
+  for @{'ho_cons $a $l}.
+
+(* lstar *)
+
+(* Note: this cannot be in lib because of the missing xoa quantifier *)
+lemma lstar_inv_pos: ∀A,B,R,l,b1,b2. lstar A B R l b1 b2 → 0 < |l| →
+                     ∃∃a,ll,b. a::ll = l & R a b1 b & lstar A B R ll b b2.
+#A #B #R #l #b1 #b2 #H @(lstar_ind_l ????????? H) -b1
+[ #H elim (lt_refl_false … H) 
+| #a #ll #b1 #b #Hb1 #Hb2 #_ #_ /2 width=6/ (**) (* auto fail if we do not remove the inductive premise *)
+]
+qed-.