(* 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.
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(* Regarding Z *)
(***************)
Definition is_sqr (n : Z) : Prop :=
0 <= n /\ exists i : Z, i * i = n /\ 0 <= i.

Lemma sqr_lt : forall a : Z, a <> 0 -> a <> 1 -> a < a * a.