diff options
Diffstat (limited to 'test-suite/micromega')
| -rw-r--r-- | test-suite/micromega/bertot.v | 2 | ||||
| -rw-r--r-- | test-suite/micromega/qexample.v | 17 | ||||
| -rw-r--r-- | test-suite/micromega/rexample.v | 26 | ||||
| -rw-r--r-- | test-suite/micromega/square.v | 3 | ||||
| -rw-r--r-- | test-suite/micromega/zomicron.v | 60 |
5 files changed, 89 insertions, 19 deletions
diff --git a/test-suite/micromega/bertot.v b/test-suite/micromega/bertot.v index bcf222f9..29171aed 100644 --- a/test-suite/micromega/bertot.v +++ b/test-suite/micromega/bertot.v @@ -11,6 +11,8 @@ Require Import Psatz. Open Scope Z_scope. + + Goal (forall x y n, ( ~ x < n /\ x <= n /\ 2 * y = x*(x+1) -> 2 * y = n*(n+1)) /\ 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. diff --git a/test-suite/micromega/rexample.v b/test-suite/micromega/rexample.v index 2eed7e95..bd522701 100644 --- a/test-suite/micromega/rexample.v +++ b/test-suite/micromega/rexample.v @@ -6,16 +6,22 @@ (* *) (************************************************************************) -Require Import Psatz. +Require Import Lra. Require Import Reals. Open Scope R_scope. + +Lemma cst_test : 5^5 = 5 * 5 * 5 *5 *5. +Proof. + lra. +Qed. + Lemma yplus_minus : forall x y, 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y. Proof. intros. - psatzl R. + lra. Qed. (* Other (simple) examples *) @@ -23,13 +29,13 @@ Qed. Lemma binomial : forall x y, ((x+y)^2 = x^2 + 2 *x*y + y^2). Proof. intros. - psatzl R. + lra. Qed. Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m. Proof. - intros ; psatzl R. + intros ; lra. Qed. @@ -57,7 +63,7 @@ Lemma vcgen_25 : forall (( 1 ) = (-2 ) * i + it). Proof. intros. - psatzl R. + lra. Qed. Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False. @@ -72,5 +78,11 @@ Proof. Qed. Lemma l1 : forall x y z : R, Rabs (x - z) <= Rabs (x - y) + Rabs (y - z). -intros; split_Rabs; psatzl R. -Qed.
\ No newline at end of file +intros; split_Rabs; lra. +Qed. + +(* Bug 5073 *) +Lemma opp_eq_0_iff a : -a = 0 <-> a = 0. +Proof. + lra. +Qed. diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v index 8767f687..abf8be72 100644 --- a/test-suite/micromega/square.v +++ b/test-suite/micromega/square.v @@ -53,8 +53,7 @@ Qed. Theorem sqrt2_not_rational : ~exists x:Q, x^2==2#1. Proof. - unfold Qeq; intros [x]; simpl (Qden (2#1)); rewrite Z.mul_1_r. - intros HQeq. + unfold Qeq; intros (x,HQeq); simpl (Qden (2#1)) in HQeq; rewrite Z.mul_1_r in HQeq. assert (Heq : (Qnum x ^ 2 = 2 * ' Qden x ^ 2%Q)%Z) by (rewrite QnumZpower in HQeq ; rewrite QdenZpower in HQeq ; auto). assert (Hnx : (Qnum x <> 0)%Z) diff --git a/test-suite/micromega/zomicron.v b/test-suite/micromega/zomicron.v index 0ec1dbfb..239bc693 100644 --- a/test-suite/micromega/zomicron.v +++ b/test-suite/micromega/zomicron.v @@ -8,9 +8,10 @@ Proof. lia. Qed. + Lemma two_x_y_eq_1 : forall x y, 2 * x + 2 * y = 1 -> False. Proof. - intros. + intros. lia. Qed. @@ -20,6 +21,12 @@ Proof. lia. Qed. +Lemma unused : forall x y, y >= 0 /\ x = 1 -> x = 1. +Proof. + intros x y. + lia. +Qed. + Lemma omega_nightmare : forall x y, 27 <= 11 * x + 13 * y <= 45 -> -10 <= 7 * x - 9 * y <= 4 -> False. Proof. intros ; intuition auto. @@ -33,4 +40,53 @@ Lemma compact_proof : forall z, Proof. intros. lia. -Qed.
\ No newline at end of file +Qed. + +Lemma dummy_ex : exists (x:Z), x = x. +Proof. + eexists. + lia. + Unshelve. + exact Z0. +Qed. + +Lemma unused_concl : forall x, + False -> x > 0 -> x < 0. +Proof. + intro. + lia. +Qed. + +Lemma unused_concl_match : forall (x:Z), + False -> match x with + | Z0 => True + | _ => x = x + end. +Proof. + intros. + lia. +Qed. + +Lemma fresh : forall (__arith : Prop), + __arith -> True. +Proof. + intros. + lia. +Qed. + +Class Foo {x : Z} := { T : Type ; dec : T -> Z }. +Goal forall bound {F : @Foo bound} (x y : T), 0 <= dec x < bound -> 0 <= dec y +< bound -> dec x + dec y >= bound -> dec x + dec y < 2 * bound. +Proof. + intros. + lia. +Qed. + +(* Bug 5073 *) +Lemma opp_eq_0_iff a : -a = 0 <-> a = 0. +Proof. + lia. +Qed. + + + |