(**********************************************************************)
 
Inductive congruent : nat -> nat -> Prop :=
    congruentDef :
      forall a b u v : nat, a + u * n = b + v * n -> congruent a b.(**********************************************************************)
 
Inductive congruent : nat -> nat -> Prop :=
    congruentDef :
      forall a b u v : nat, a + u * n = b + v * n -> congruent a b.

Lemma cong_trans : forall a b c : nat, congruent a b -> congruent b c -> congruent a c.