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(* Micromega: A reflexive tactic using the Positivstellensatz           *)
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(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
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Open Scope Z_scope.
(* From Laurent Théry *)
Goal forall (x y : Z), x = 0 -> x * y = 0.
Goal forall (x y : Z), x = 0 -> x * y = 0.
Goal forall (x y : Z), 2*x = 0 -> x * y = 0.
Goal forall (x y: Z), - x*x >= 0 -> x * y = 0.

Lemma pol3: forall x y, 0 <= x + y ->
x^3 + 3*x^2*y + 3*x* y^2 + y^3 >= 0.