diff options
Diffstat (limited to 'test-suite/micromega/rexample.v')
| -rw-r--r-- | test-suite/micromega/rexample.v | 62 |
1 files changed, 62 insertions, 0 deletions
diff --git a/test-suite/micromega/rexample.v b/test-suite/micromega/rexample.v new file mode 100644 index 00000000..5132dc4e --- /dev/null +++ b/test-suite/micromega/rexample.v @@ -0,0 +1,62 @@ +(************************************************************************) +(* *) +(* Micromega: A reflexive tactic using the Positivstellensatz *) +(* *) +(* Frédéric Besson (Irisa/Inria) 2006-2008 *) +(* *) +(************************************************************************) + +Require Import Micromegatac. +Require Import Reals. +Require Import Ring_normalize. + +Open Scope R_scope. + +Lemma plus_minus : forall x y, + 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y. +Proof. + intros. + omicron R. +Qed. + +(* Other (simple) examples *) + +Lemma binomial : forall x y, ((x+y)^2 = x^2 + 2 *x*y + y^2). +Proof. + intros. + omicron R. +Qed. + + +Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m. +Proof. + intros ; omicron R. +Qed. + + +Lemma vcgen_25 : forall + (n : R) + (m : R) + (jt : R) + (j : R) + (it : R) + (i : R) + (H0 : 1 * it + (-2%R ) * i + (-1%R ) = 0) + (H : 1 * jt + (-2 ) * j + (-1 ) = 0) + (H1 : 1 * n + (-10 ) = 0) + (H2 : 0 <= (-4028 ) * i + (6222 ) * j + (705 ) * m + (-16674 )) + (H3 : 0 <= (-418 ) * i + (651 ) * j + (94 ) * m + (-1866 )) + (H4 : 0 <= (-209 ) * i + (302 ) * j + (47 ) * m + (-839 )) + (H5 : 0 <= (-1 ) * i + 1 * j + (-1 )) + (H6 : 0 <= (-1 ) * j + 1 * m + (0 )) + (H7 : 0 <= (1 ) * j + (5 ) * m + (-27 )) + (H8 : 0 <= (2 ) * j + (-1 ) * m + (2 )) + (H9 : 0 <= (7 ) * j + (10 ) * m + (-74 )) + (H10 : 0 <= (18 ) * j + (-139 ) * m + (1188 )) + (H11 : 0 <= 1 * i + (0 )) + (H13 : 0 <= (121 ) * i + (810 ) * j + (-7465 ) * m + (64350 )), + (( 1 ) = (-2 ) * i + it). +Proof. + intros. + omicron R. +Qed. |