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 *)
intros;  rewrite e; reflexivity.
Qed.
(* example that Congruence. can solve (dependent function applied to the same argument)*)
congruence.
Qed.
(* Examples with injection rule *)
intros.
split;  congruence.
Qed.

Theorem inj2 :
forall (A : Set) (a c d : A) (f : A -> A * A),
f = pair (B:=A) a -> Some (f c) = Some (f d) -> c = d.