From 37905ef451d98f0c857d62876fdbe12f0ee8ccaf Mon Sep 17 00:00:00 2001
From: Andrea Asperti <andrea.asperti@unibo.it>
Date: Fri, 7 Mar 2014 13:32:16 +0000
Subject: [PATCH] Minor changes to make the script more robust to strategy
 changes.

---
 matita/matita/lib/arithmetics/binomial.ma     |  2 +-
 .../lib/arithmetics/chebyshev/bertrand.ma     |  2 +-
 matita/matita/lib/basics/finset.ma            | 14 ++++-------
 matita/matita/lib/hints_declaration.ma        | 23 ++++++++++++++++---
 4 files changed, 27 insertions(+), 14 deletions(-)

diff --git a/matita/matita/lib/arithmetics/binomial.ma b/matita/matita/lib/arithmetics/binomial.ma
index c3834c8d8..6b4d3ff52 100644
--- a/matita/matita/lib/arithmetics/binomial.ma
+++ b/matita/matita/lib/arithmetics/binomial.ma
@@ -103,7 +103,7 @@ theorem binomial_law:∀a,b,n.
 >bigop_Strue in ⊢ (??(??%)?); // <associative_plus 
 <commutative_plus in ⊢ (??(? % ?) ?); >associative_plus @eq_f2
   [<minus_n_n >bc_n_n >bc_n_n normalize //
-  |>bigop_0 >associative_plus >commutative_plus in ⊢ (??(??%)?);
+  |>(bigop_0 ??? plusA)  >associative_plus >commutative_plus in ⊢ (??(??%)?);
    <associative_plus >(bigop_0 n ?? plusA) @eq_f2 
     [cut (∀a,b. plus a b = plusAC a b) [//] #Hplus >Hplus 
      >(bigop_op n ??? plusAC) @same_bigop //
diff --git a/matita/matita/lib/arithmetics/chebyshev/bertrand.ma b/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
index 99770436b..8f41262e3 100644
--- a/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
+++ b/matita/matita/lib/arithmetics/chebyshev/bertrand.ma
@@ -166,7 +166,7 @@ elim (log p (2*n))
           [@leb_true_to_le //
           |>commutative_times in ⊢ (??%); > times_exp
            @(transitive_le ? (exp n 2))
-            [<associative_times >exp_2 in ⊢ (??%); @le_times //
+            [<associative_times >exp_2 in ⊢ (??%); @le_times [@le18|//]
             |@(le_exp1 … (lt_O_S ?))
              @(le_plus_to_le 3)
              cut (3+2*n/3*3 = S(2*n/3)*3) [//] #eq1 >eq1
diff --git a/matita/matita/lib/basics/finset.ma b/matita/matita/lib/basics/finset.ma
index 33b6b664a..df8d0a87c 100644
--- a/matita/matita/lib/basics/finset.ma
+++ b/matita/matita/lib/basics/finset.ma
@@ -64,16 +64,12 @@ lemma memb_enumn: ∀m,n,i:DeqNat. ∀h:n ≤ m. ∀k: i < m. n ≤ i →
   (¬ (memb (Nat_to m) (mk_Sig ?? i k) (enumnaux n m h))) = true.
 #m #n elim n -n // #n #Hind #i #ltm #k #ltni @sym_eq @noteq_to_eqnot @sym_not_eq
 % #H cases (orb_true_l … H)
-  [#H1 @(absurd … (\P H1)) % #Hfalse
-   cut (∀A,P,a,a1,h,h1.mk_Sig A P a h = mk_Sig A P a1 h1 → a = a1)
-   [#A #P #a #a1 #h #h1 #H destruct (H) %] #Hcut 
-    lapply (Hcut nat (λi.i<m) i n ? ? Hfalse) #Hfalse @(absurd … ltni)
-    @le_to_not_lt >Hfalse @le_n
-  |<(notb_notb (memb …)) >Hind normalize /2/
+  [whd in ⊢ (??%?→?); #H1 @(absurd  … ltni) @le_to_not_lt 
+   >(eqb_true_to_eq … H1) @le_n
+  |<(notb_notb (memb …)) >Hind normalize /2 by lt_to_le, absurd/
   ]
 qed. 
 
-
 lemma enumn_unique_aux: ∀n,m. ∀h:n ≤ m. uniqueb (Nat_to m) (enumnaux n m h) = true.
 #n elim n -n // #n #Hind #m #h @true_to_andb_true // @memb_enumn //
 qed.
@@ -209,13 +205,13 @@ unification hint  0 ≔ C1,C2;
 
 definition enum_prod ≝ λA,B:DeqSet.λl1.λl2.
   compose ??? (mk_Prod A B) l1 l2.
-  
+
 lemma enum_prod_unique: ∀A,B,l1,l2. 
   uniqueb A l1 = true → uniqueb B l2 = true →
   uniqueb ? (enum_prod A B l1 l2) = true.
 #A #B #l1 elim l1 //
   #a #tl #Hind #l2 #H1 #H2 @uniqueb_append 
-  [@unique_map_inj // 
+  [@unique_map_inj [#x #y #Heq @(eq_f … \snd … Heq) | //]
   |@Hind // @(andb_true_r … H1)
   |#p #H3 cases (memb_map_to_exists … H3) #b * 
    #Hmemb #eqp <eqp @(not_to_not ? (memb ? a tl = true))
diff --git a/matita/matita/lib/hints_declaration.ma b/matita/matita/lib/hints_declaration.ma
index d04f453f2..7dd0800d7 100644
--- a/matita/matita/lib/hints_declaration.ma
+++ b/matita/matita/lib/hints_declaration.ma
@@ -56,6 +56,23 @@ notation > "≔ (list0 ( (list1 (ident x) sep , ) opt (: T) ) sep ,) opt (; (lis
                }
        }}.
 
+(* it seems unbelivable, but it works! *)
+notation > "≔ (list0 ( (list1 (ident x) sep , ) opt (: T) ) sep ,) opt (; (list1 (ident U ≟ term 19 V ) sep ,)) ⊢ term 19 Px ≡≡ term 19 Py"
+  with precedence 90
+  for @{ ${ fold right 
+               @{ ${ default 
+                    @{ ${ fold right 
+                        @{ 'hint_decl2 $Px $Py } 
+                        rec acc1 @{ let ( ${ident U} : ?) ≝ $V in $acc1} } }
+                    @{ 'hint_decl2 $Px $Py } 
+                 }
+               } 
+               rec acc @{ 
+                 ${ fold right @{ $acc } rec acc2 
+                      @{ ∀${ident x}:${ default @{ $T } @{ ? } }.$acc2 } } 
+               }
+       }}.
+
 include "basics/pts.ma".
 
 definition hint_declaration_Type0  ≝  λA:Type[0] .λa,b:A.Prop.
@@ -65,8 +82,8 @@ definition hint_declaration_CProp0 ≝  λA:CProp[0].λa,b:A.Prop.
 definition hint_declaration_CProp1 ≝  λA:CProp[1].λa,b:A.Prop.
 definition hint_declaration_CProp2 ≝  λa,b:CProp[2].Prop.
   
-interpretation "hint_decl_Type2"  'hint_decl a b = (hint_declaration_Type2 a b).
-interpretation "hint_decl_CProp2" 'hint_decl a b = (hint_declaration_CProp2 a b).
+interpretation "hint_decl_Type2"  'hint_decl2 a b = (hint_declaration_Type2 a b).
+interpretation "hint_decl_CProp2" 'hint_decl2 a b = (hint_declaration_CProp2 a b).
 interpretation "hint_decl_Type1"  'hint_decl a b = (hint_declaration_Type1 ? a b).
 interpretation "hint_decl_CProp1" 'hint_decl a b = (hint_declaration_CProp1 ? a b).
 interpretation "hint_decl_CProp0" 'hint_decl a b = (hint_declaration_CProp0 ? a b).
@@ -104,4 +121,4 @@ unification hint 0 ≔ R : setoid;
 (* ---------------------------------------- *) ⊢ 
    setoid ≡ target1 ? MR sol.
 
-*)
\ No newline at end of file
+*)
-- 
2.39.2