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-rw-r--r--test-suite/micromega/qexample.v17
1 files changed, 9 insertions, 8 deletions
diff --git a/test-suite/micromega/qexample.v b/test-suite/micromega/qexample.v
index 47e6005b9..d001e8f7f 100644
--- a/test-suite/micromega/qexample.v
+++ b/test-suite/micromega/qexample.v
@@ -6,32 +6,29 @@
(* *)
(************************************************************************)
-Require Import Psatz.
+Require Import Lqa.
Require Import QArith.
Lemma plus_minus : forall x y,
0 == x + y -> 0 == x -y -> 0 == x /\ 0 == y.
Proof.
intros.
- psatzl Q.
+ lra.
Qed.
-
-
-
(* Other (simple) examples *)
Open Scope Q_scope.
Lemma binomial : forall x y:Q, ((x+y)^2 == x^2 + (2 # 1) *x*y + y^2).
Proof.
intros.
- psatzl Q.
+ lra.
Qed.
Lemma hol_light19 : forall m n, (2 # 1) * m + n == (n + m) + m.
Proof.
- intros ; psatzl Q.
+ intros ; lra.
Qed.
Open Scope Z_scope.
Open Scope Q_scope.
@@ -60,7 +57,11 @@ Lemma vcgen_25 : forall
(( 1# 1) == (-2 # 1) * i + it).
Proof.
intros.
- psatzl Q.
+ lra.
+Qed.
+
+Goal forall x : Q, x * x >= 0.
+ intro; nra.
Qed.
Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False.