Ltac convert_to_algebra :=
try setoid_rewrite characterization_of_betweenness_F;
try setoid_rewrite characterization_of_congruence_F;
try setoid_rewrite characterization_of_midpoint_F;
try setoid_rewrite characterization_of_collinearity_F;
try setoid_rewrite characterization_of_right_triangle_F;
try setoid_rewrite characterization_of_perpendicularity_F;
try setoid_rewrite characterization_of_parallelism_F;
try setoid_rewrite characterization_of_equality_F;
try setoid_rewrite characterization_of_neq_F.
Ltac express_disj_as_a_single_poly := repeat rewrite <- mulF__eq0.

Lemma put_neg_in_goal : forall A B, A \/ B -> (~ A -> B).
Definition vect := (F * F)%type.