restored the good factorization file

diff --git a/matita/library/nat/factorization.ma b/matita/library/nat/factorization.ma
index 6241244f39a2c24e5776a3caea7492ad616ef190..4c8de0f51ff3e112205dda4c97d26ae1b9939bca 100644 (file)
--- a/matita/library/nat/factorization.ma
+++ b/matita/library/nat/factorization.ma
@@ -18,133 +18,6 @@ include "nat/ord.ma".
 include "nat/gcd.ma".
 include "nat/nth_prime.ma".
 
-
-theorem prova :
-  \forall n,m:nat.
-  \forall P:nat \to Prop.
-  \forall H:P (S (S O)).
-  \forall H:P (S (S (S O))).
-  \forall H1: \forall x.P x \to O = x.
-   O = S (S (S (S (S O)))).
-   intros.
-   auto paramodulation.
- qed.
- 
-theorem example2:
-\forall x: nat. (x+S O)*(x-S O) = x*x - S O.
-intro;
-apply (nat_case x);
- [ auto paramodulation.|intro.auto paramodulation.]
-qed.
-
-theorem prova3:
-  \forall A:Set.
-  \forall m:A \to A \to A.
-  \forall divides: A \to A \to Prop.
-  \forall o,a,b,two:A.
-  \forall H1:\forall x.m o x = x.
-  \forall H1:\forall x.m x o = x.
-  \forall H1:\forall x,y,z.m x (m y z) = m (m x y) z.
-  \forall H1:\forall x.m x o = x.
-  \forall H2:\forall x,y.m x y = m y x.
-  \forall H3:\forall x,y,z. m x y = m x z \to y = z. 
-  (* \forall H4:\forall x,y.(\exists z.m x z = y) \to divides x y. *)
-  \forall H4:\forall x,y.(divides x y \to (\exists z.m x z = y)). 
-  \forall H4:\forall x,y,z.m x z = y \to divides x y.
-  \forall H4:\forall x,y.divides two (m x y) \to divides two x ∨ divides two y.
-  \forall H5:m a a = m two (m b b).
-  \forall H6:\forall x.divides x a \to divides x b \to x = o.
-  two = o.
-  intros.
-  cut (divides two a);
-    [2:elim (H8 a a);[assumption.|assumption|rewrite > H9.auto.]
-    |elim (H6 ? ? Hcut).
-     cut (divides two b);
-       [ apply (H10 ? Hcut Hcut1).
-       | elim (H8 b b);[assumption.|assumption|
-         apply (H7 ? ? (m a1 a1));
-         apply (H5 two ? ?);rewrite < H9.
-         rewrite < H11.rewrite < H2.
-         apply eq_f.rewrite > H2.rewrite > H4.reflexivity.
-         ]
-         ]
-         ]
-         qed.
-         
-theorem prova31:
-  \forall A:Set.
-  \forall m,f:A \to A \to A.
-  \forall divides: A \to A \to Prop.
-  \forall o,a,b,two:A.
-  \forall H1:\forall x.m o x = x.
-  \forall H1:\forall x.m x o = x.
-  \forall H1:\forall x,y,z.m x (m y z) = m (m x y) z.
-  \forall H1:\forall x.m x o = x.
-  \forall H2:\forall x,y.m x y = m y x.
-  \forall H3:\forall x,y,z. m x y = m x z \to y = z. 
-  (* \forall H4:\forall x,y.(\exists z.m x z = y) \to divides x y. *)
-  \forall H4:\forall x,y.(divides x y \to m x (f x y) = y). 
-  \forall H4:\forall x,y,z.m x z = y \to divides x y.
-  \forall H4:\forall x,y.divides two (m x y) \to divides two x ∨ divides two y.
-  \forall H5:m a a = m two (m b b).
-  \forall H6:\forall x.divides x a \to divides x b \to x = o.
-  two = o.
-  intros.
-  cut (divides two a);
-    [2:elim (H8 a a);[assumption.|assumption|rewrite > H9.auto.]
-    |(*elim (H6 ? ? Hcut). *)
-     cut (divides two b);
-       [ apply (H10 ? Hcut Hcut1).
-       | elim (H8 b b);[assumption.|assumption|
-       
-         apply (H7 ? ? (m (f two a) (f two a)));
-         apply (H5 two ? ?);
-         rewrite < H9.
-         rewrite < (H6 two a Hcut) in \vdash (? ? ? %).
-         rewrite < H2.apply eq_f.
-         rewrite < H4 in \vdash (? ? ? %).
-         rewrite > H2.reflexivity.
-         ]
-         ]
-         ]
-         qed.  
-           
-theorem prova32:
-  \forall A:Set.
-  \forall m,f:A \to A \to A.
-  \forall divides: A \to A \to Prop.
-  \forall o,a,b,two:A.
-  \forall H1:\forall x.m o x = x.
-  \forall H1:\forall x.m x o = x.
-  \forall H1:\forall x,y,z.m x (m y z) = m (m x y) z.
-  \forall H1:\forall x.m x o = x.
-  \forall H2:\forall x,y.m x y = m y x.
-  \forall H3:\forall x,y,z. m x y = m x z \to y = z. 
-  (* \forall H4:\forall x,y.(\exists z.m x z = y) \to divides x y. *)
-  \forall H4:\forall x,y.(divides x y \to m x (f x y) = y). 
-  \forall H4:\forall x,y,z.m x z = y \to divides x y.
-  \forall H4:\forall x.divides two (m x x) \to divides two x.
-  \forall H5:m a a = m two (m b b).
-  \forall H6:\forall x.divides x a \to divides x b \to x = o.
-  two = o.
-  intros.
-  cut (divides two a);[|apply H8;rewrite > H9.auto].
-  apply H10;
-  [ assumption.
-  | apply (H8 b);       
-         apply (H7 ? ? (m (f two a) (f two a)));
-         apply (H5 two ? ?);
-         auto paramodulation.
-         (*
-         rewrite < H9.
-         rewrite < (H6 two a Hcut) in \vdash (? ? ? %).
-         rewrite < H2.apply eq_f.
-         rewrite < H4 in \vdash (? ? ? %).
-         rewrite > H2.reflexivity.
-         *)
-  ]
-qed.
-             
 (* the following factorization algorithm looks for the largest prime
    factor. *)
 definition max_prime_factor \def \lambda n:nat.
@@ -769,4 +642,3 @@ intros.
 apply injective_defactorize.
 apply defactorize_factorize.
 qed.
-