(* ArithCompl.v *)
(**********************************)
(* Some complements of arithmetic *)
(**********************************)
Require Export Wf_nat.
Require Export ZArith.
Require Export Znumtheory.
Require Export Reals.
Open Scope Z_scope.
Unset Standard Proposition Elimination Names.
(***************)
(* Regarding Z *)
(***************)
Definition is_sqr (n : Z) : Prop :=
0 <= n /\ exists i : Z, i * i = n /\ 0 <= i.

Lemma neq_1 : forall u v m n : Z,
m <> 0 -> n <> 0 -> u * u = m * m + n * n -> v * v = n * n - m * m ->
u <> 1 /\ v <> 1.