X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Ftests%2Fcoercions_propagation.ma;h=63c48e66b9d42267b3d3455cc855565b80527095;hb=1776f357e1a69fa1133956660b65d7bafdfe5c25;hp=f87052086bda26aa80eebde5acaac1fd370531ce;hpb=e23c6d237922d7bfb0e98d165efd1ed24566106d;p=helm.git

diff --git a/matita/tests/coercions_propagation.ma b/matita/tests/coercions_propagation.ma
index f87052086..63c48e66b 100644
--- a/matita/tests/coercions_propagation.ma
+++ b/matita/tests/coercions_propagation.ma
@@ -16,7 +16,6 @@ set "baseuri" "cic:/matita/test/coercions_propagation/".
 
 include "logic/connectives.ma".
 include "nat/orders.ma".
-alias num (instance 0) = "natural number".
 
 inductive sigma (A:Type) (P:A → Prop) : Type ≝
  sigma_intro: ∀a:A. P a → sigma A P.
@@ -33,7 +32,6 @@ definition eject ≝ λP.λc: ∃n:nat.P n. match c with [ sigma_intro w _ ⇒ w
 coercion cic:/matita/test/coercions_propagation/eject.con.
 
 alias num (instance 0) = "natural number".
-
 theorem test: ∃n. 0 ≤ n.
  apply (S O : ∃n. 0 ≤ n).
  autobatch.
@@ -50,7 +48,7 @@ qed.
 
 theorem test4: (∃n. 1 ≤ n) → ∃n. 0 < n.
  apply ((λn:nat.n) : (∃n. 1 ≤ n) → ∃n. 0 < n);
- cases name_con;
+ cases s;
  assumption.
 qed.
 
@@ -64,7 +62,7 @@ apply (
  in
   aux
 : nat → ∃n. 1 ≤ n);
-[ cases (aux name_con); simplify; ] autobatch;
+[ cases (aux n1); simplify; ] autobatch;
 qed.
 
 inductive NN (A:Type) : nat -> Type ≝
@@ -110,8 +108,7 @@ qed.
 
 theorem test51: ∀A,k. NN A k → ∃n:NN A (S k). PN ? ? n.
 intros 1;
-(* MANCA UN LIFT forse NEL FIX *)
-apply (
+letin xxx ≝ (
  let rec aux (w : nat) (n : NN A w) on n : NN A (S w) ≝
   match n in NN return λx.λm:NN A x.NN A (S x) with
    [ NO ⇒ NS A ? (NO A)
@@ -119,12 +116,12 @@ apply (
    ]
  in
   aux
-: ∀n:nat. NN A n → ∃m:NN A (S n). PN ? ? m);
-[ cases (aux name_con); simplify; ] autobatch;
+: ∀n:nat. NN A n → ∃m:NN A (S n). PN ? ? m); [3: apply xxx];
+unfold PN in aux ⊢ %; [cases (aux n2 n3)] autobatch;
 qed.
 
-(* guarded troppo debole 
-theorem test5: nat → ∃n. 1 ≤ n.
+(* guarded troppo debole *)
+theorem test522: nat → ∃n. 1 ≤ n.
 apply (
  let rec aux n : nat ≝
   match n with
@@ -134,95 +131,8 @@ apply (
  in
   aux
 : nat → ∃n. 1 ≤ n);
-cases name_con;
-simplify;
- [ autobatch
- | cases (aux n);
-   simplify;
-   apply lt_O_S
- ]
+[ cases (aux n1); simplify;
+  autobatch
+| autobatch].
 qed.
-*)
 
-(*
-theorem test5: nat → ∃n. 1 ≤ n.
-apply (
- let rec aux (n : nat) : ∃n. 1 ≤ n ≝ 
-   match n with
-   [ O => (S O : ∃n. 1 ≤ n)
-   | S m => (S (aux m) : ∃n. 1 ≤ n)
-(*      
-   inject ? (S (eject ? (aux m))) ? *)
-   ]
- in
-  aux
- : nat → ∃n. 1 ≤ n);
- [ autobatch
- | elim (aux m);
-   simplify;
-   autobatch
- ]
-qed.
-
-Re1: nat => nat |- body[Rel1] : nat => nat
-Re1: nat => X |- body[Rel1] : nat => nat : nat => X
-Re1: Y => X |- body[Rel1] : nat => nat : Y => X
-
-nat => nat
-nat => X
-
-theorem test5: (∃n. 2 ≤ n) → ∃n. 1 ≤ n.
-apply (
- λk: ∃n. 2 ≤ n.
- let rec aux n : eject ? n = eject ? k → ∃n. 1 ≤ n ≝
-  match eject ? n return λx:nat. x = eject ? k → ∃n. 1 ≤ n with
-   [ O ⇒ λH: 0 = eject ? k.
-          sigma_intro ? ? 0 ?
-   | S m ⇒ λH: S m = eject ? k.
-          sigma_intro ? ? (S m) ?
-   ]
- in
-  aux k (refl_eq ? (eject ? k)));
-
-
-intro;
-cases s; clear s;
-generalize in match H; clear H;
-elim a;
- [ apply (sigma_intro ? ? 0);
- | apply (sigma_intro ? ? (S n));
- ].
-
-apply (
- λk.
- let rec aux n : ∃n. 1 ≤ n ≝
-  inject ?
-   (match n with
-     [ O ⇒ O
-     | S m ⇒ S (eject ? (aux m))
-     ]) ?
- in aux (eject ? k)).
-
-   
-apply (
- let rec aux n : nat ≝
-  match n with
-   [ O ⇒ O
-   | S m ⇒ S (aux m)
-   ]
- in
-  aux
-: (∃n. 2 ≤ n) → ∃n. 1 ≤ n);
-
-qed.
-
-(*
-theorem test5: nat → ∃n. 0 ≤ n.
- apply (λn:nat.?);
- apply
-  (match n return λ_.∃n.0 ≤ n with [O ⇒ (0 : ∃n.0 ≤ n) | S n' ⇒ ex_intro ? ? n' ?]
-  : ∃n. 0 ≤ n);
- autobatch.
-qed.
-*)
-*)
\ No newline at end of file