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  1. Require Import Reals Lra.
  2. Open Scope R_scope.
  3.  
  4. Lemma sqrt2: 1414213562370951 / 1000000000000000 <> sqrt 2.
  5. Proof.
  6. intros contra.
  7. symmetry in contra.
  8. apply sqrt_lem_0 with 2 (1414213562370951 / 1000000000000000) in contra;
  9. lra.
  10. Qed.
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