diff options
Diffstat (limited to 'test-suite/micromega/qexample.v')
| -rw-r--r-- | test-suite/micromega/qexample.v | 17 |
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. |