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Require Export Gappa_tactic.
Require Export Reals.
Open Scope Z_scope.
Open Scope R_scope.
Ltac gappa := gappa_prepare; gappa_internal.
Lemma test1 :
forall x y:R,
0 <= x <= 1 ->
0 <= -y <= 1 ->
0 <= x * (-y) <= 1.
Proof.
gappa.
Qed.
Lemma test2 :
forall x y:R,
0 <= x <= 3 ->
0 <= sqrt x <= 1775 * (powerRZ 2 (-10)).
Proof.
gappa.
Qed.
Lemma test3 :
forall x y z:R,
0 <= x - y <= 3 ->
-2 <= y - z <= 4 ->
-2 <= x - z <= 7.
Proof.
gappa.
Qed.
Lemma test4 :
forall x1 x2 y1 y2 : R,
1 <= Rabs y1 <= 1000 ->
1 <= Rabs y2 <= 1000 ->
- powerRZ 2 (-53) <= (x1 - y1) / y1 <= powerRZ 2 (-53) ->
- powerRZ 2 (-53) <= (x2 - y2) / y2 <= powerRZ 2 (-53) ->
- powerRZ 2 (-51) <= (x1 * x2 - y1 * y2) / (y1 * y2) <= powerRZ 2 (-51).
Proof.
gappa.
Qed.
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