intros.
congruence.
Qed.
intros.
congruence.
Qed.
(* 15=0 /\ 10=0 /\ 6=0 -> 0=1 *)
intros.
congruence.
Qed.
(* Examples that fail due to dependencies *)
(* yields transitivity problem *)
intros;  dependent rewrite e; exact e0.
Qed.
(* yields congruence problem *)

Theorem dep2 :
forall (A B : Set)
(f : forall (A : Set) (b : bool), if b then unit else A -> unit)
(e : A = B), f A true = f B true.