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[helm.git] / helm / software / matita / tests / coercions_russell.ma

diff --git a/helm/software/matita/tests/coercions_russell.ma b/helm/software/matita/tests/coercions_russell.ma
index 203faece5d6db7e13ef284842fe397502e6a0bb3..48639b3cb54afdad3c89def91c1b04be77f3e83b 100644 (file)
--- a/helm/software/matita/tests/coercions_russell.ma
+++ b/helm/software/matita/tests/coercions_russell.ma
@@ -34,23 +34,16 @@ coercion cic:/matita/tests/coercions_russell/eject.con.
   
 alias symbol "exists" (instance 2) = "exists".
 lemma tl : ∀l:list nat. l ≠ [] → ∃l1.∃a.a :: l1 = l.
-letin program ≝ 
-  (λl:list nat. λH:l ≠ [].match l with [ nil ⇒ λH.[] | cons x l1 ⇒ λH.l1] H);
-letin program_spec ≝ (program : ∀l:list nat. l ≠ [] → ∃l1.∃a.a :: l1 = l);
- [ generalize in match H; cases l; [intros (h1); cases (h1 ?); reflexivity]
-   intros; apply (ex_intro ? ? n); apply eq_f; reflexivity; ]
-exact program_spec;
+ apply rule (λl:list nat. λ_.match l with [ nil ⇒ [] | cons x l1 ⇒ l1]);
+  [ exists; [2: reflexivity | skip]
+  | destruct; elim H; reflexivity]
 qed.
 
 alias symbol "exists" (instance 3) = "exists".
 lemma tl2 : ∀l:∃l:list nat. l ≠ []. ∃l1.∃a.a :: l1 = l.
-letin program ≝ 
-  (λl:list nat. match l with [ nil ⇒ [] | cons x l1 ⇒ l1]);
-letin program_spec ≝ 
-  (program : ∀l:∃l:list nat. l ≠ []. ∃l1.∃a.a :: l1 = l);
-  [ autobatch; | generalize in match H; clear H; cases s; simplify;
-    intros; cases (H H1); ]
-exact program_spec.
+apply rule (λl:list nat. match l with [ nil ⇒ [] | cons x l1 ⇒ l1]);
+[ autobatch; 
+| cases s in H; simplify; intros; cases (H H1); ]
 qed.
 
 definition nat_return := λn:nat. Some ? n.
@@ -101,31 +94,25 @@ simplify; apply (eqb_elim x hd); simplify; intros;
 simplify; autobatch;
 qed.
 
-definition if : ∀A:Type.bool → A → A → A ≝ 
- λA,b,t,f. match b with [ true ⇒ t | false ⇒ f].
- 
-notation < "'If' \nbsp b \nbsp 'Then' \nbsp t \nbsp 'Else' \nbsp f" for @{ 'if $b $t $f }.
-notation > "'If' b 'Then' t 'Else' f" for @{ 'if $b $t $f }.
-interpretation "if" 'if a b c = (cic:/matita/tests/coercions_russell/if.con _ a b c). 
+notation > "'If' b 'Then' t 'Else' f" non associative
+with precedence 90 for @{ match $b with [ true ⇒ $t | _ ⇒ $f ] }.
 
-definition sigma_find_spec : ∀p,l. sigma ? (λres.find_spec l p res).
-(* define the find function *) 
-letin find ≝ (λp. 
+alias symbol "exists" = "sigma".
+definition sigma_find_spec : ∀p,l. ∃res.find_spec l p res.
+apply rule (λp. 
   let rec aux l ≝
     match l with
     [ nil ⇒ raise_exn
     | cons x l ⇒ If p x Then nat_return x Else aux l]
     in aux);
-(* manca una delta?! *) unfold if in find;
-apply (find: ∀p.∀l.sigma ? (λres.find_spec l p res)); clear find;
 (* l = x::tl ∧ p x = false *)
 [1: cases (aux l1); clear aux;
-    generalize in match H2; clear H2; cases a; clear a; simplify;
-    [1: intros 2; apply (eqb_elim y n); intros (Eyn); [rewrite > Eyn; assumption]
-        apply H3; simplify in H2; assumption;
+    cases a in H2; simplify;
+    [1: intros 2; apply (eqb_elim y n); intros (Eyn); autobatch;
     |2: intros; decompose; repeat split; [2: assumption]; intros;
         [1: cases (eqb n1 n); simplify; autobatch;
-        |2: generalize in match (refl_eq ? (eqb y n)); generalize in ⊢ (? ? ? %→?); 
+        |2: generalize in match (refl_eq ? (eqb y n));
+            generalize in ⊢ (? ? ? %→?); 
             intro; cases b; clear b; intro Eyn; rewrite > Eyn in H3; simplify in H3;
             [1: rewrite > (eqb_true_to_eq ? ? Eyn) in H6; rewrite > H1 in H6; destruct H6;
             |2: lapply H4; try assumption; decompose; clear H4; rewrite > H8;
@@ -136,9 +123,9 @@ apply (find: ∀p.∀l.sigma ? (λres.find_spec l p res)); clear find;
     |2: intro; generalize in match (refl_eq ? (eqb y n)); generalize in ⊢ (? ? ? %→?);
         intro; cases b; clear b; intro Eyn; rewrite > Eyn; 
         [1: rewrite > (eqb_true_to_eq ? ? Eyn);] clear Eyn; simplify; intros;
-        [1: cases H4; reflexivity
-        |2: lapply (mem_x_to_ex_l1_l2 ? ? H2); decompose; rewrite > H6;
-            apply (ex_intro ? ? []); simplify; autobatch;]]
+          [1: cases H4; reflexivity
+          |2: lapply (mem_x_to_ex_l1_l2 ? ? H2); decompose; rewrite > H6;
+              apply (ex_intro ? ? []); simplify; autobatch;]]
 (* l = [] *)
 |3: unfold raise_exn; simplify; intros; destruct H1;]
-qed.
+qed.
\ No newline at end of file