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(* Regarding Z *)
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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.