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authorGravatar Enrico Tassi <gareuselesinge@debian.org>2016-12-27 16:53:30 +0100
committerGravatar Enrico Tassi <gareuselesinge@debian.org>2016-12-27 16:53:30 +0100
commita4c7f8bd98be2a200489325ff7c5061cf80ab4f3 (patch)
tree26dd9c4aa142597ee09c887ef161d5f0fa5077b6 /test-suite/micromega/qexample.v
parent164c6861860e6b52818c031f901ffeff91fca16a (diff)
Imported Upstream version 8.6upstream/8.6
Diffstat (limited to 'test-suite/micromega/qexample.v')
-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 47e6005b..d001e8f7 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.