Ported permutation.ma and fermat_little_theorem.ma

[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 640615d596f2aa2aa2947a23884d7a3ec9b09916..c7c736f2ce1d3cad45775d2568fa537914ca2691 100644 (file)
--- a/matita/matita/contribs/lambda/preamble.ma
+++ b/matita/matita/contribs/lambda/preamble.ma
@@ -28,16 +28,6 @@ notation "⊥"
   non associative with precedence 90
   for @{'false}.
 
-(* relations *)
-
-definition confluent1: ∀A. relation A → predicate A ≝ λA,R,a0.
-                       ∀a1. R a0 a1 → ∀a2. R a0 a2 →
-                       ∃∃a. R a1 a & R a2 a. 
-
-(* Note: confluent1 would be redundant if \Pi-reduction where enabled *)                       
-definition confluent: ∀A. predicate (relation A) ≝ λA,R.
-                      ∀a0. confluent1 … R a0.
-
 (* arithmetics *)
 
 lemma lt_refl_false: ∀n. n < n → ⊥.
@@ -100,3 +90,14 @@ 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-.