(* *)
(**************************************************************************)
-set "baseuri" "cic:/matita/Z/times".
-
include "nat/lt_arith.ma".
include "Z/plus.ma".
| (pos n) \Rightarrow (neg (pred ((S m) * (S n))))
| (neg n) \Rightarrow (pos (pred ((S m) * (S n))))]].
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "integer times" 'times x y = (cic:/matita/Z/times/Ztimes.con x y).
+interpretation "integer times" 'times x y = (Ztimes x y).
theorem Ztimes_z_OZ: \forall z:Z. z*OZ = OZ.
intro.elim z.
variant distr_Ztimes_Zplus: \forall x,y,z.
x * (y + z) = x*y + x*z \def
distributive_Ztimes_Zplus.
-
-theorem eq_plus_Zplus: \forall n,m:nat. Z_of_nat (n+m) =
-Z_of_nat n + Z_of_nat m.
-intro.cases n;intro
- [reflexivity
- |cases m
- [simplify.rewrite < plus_n_O.reflexivity
- |simplify.reflexivity.
- ]]
-qed.