Inductive Eqpair : relation (T * U) :=
  | Eqpair_both : forall a b c d, rT a b -> rU c d -> Eqpair (a,c) (b,d).Inductive Eqpair : relation (T * U) :=
  | Eqpair_both : forall a b c d, rT a b -> rU c d -> Eqpair (a,c) (b,d).Global Instance Reflexive_Eqpair {RrT : Reflexive rT} {RrU : Reflexive rU}
  : Reflexive Eqpair.Global Instance Symmetric_Eqpair {RrT : Symmetric rT} {RrU : Symmetric rU}
  : Symmetric Eqpair.Global Instance Transitive_Eqpair {RrT : Transitive rT} {RrU : Transitive rU}
  : Transitive Eqpair.Global Instance Injective_Eqpair a b c d : Injective (Eqpair (a,b) (c,d)).Inductive R_pair : T * U -> T * U -> Prop :=
  | L : forall l l' r r',
    RT l l' -> R_pair (l,r) (l',r')
  | R : forall l r r',
    RU r r' -> R_pair (l,r) (l,r').Inductive R_pair : T * U -> T * U -> Prop :=
  | L : forall l l' r r',
    RT l l' -> R_pair (l,r) (l',r')
  | R : forall l r r',
    RU r r' -> R_pair (l,r) (l,r').Inductive R_pair : T * U -> T * U -> Prop :=
  | L : forall l l' r r',
    RT l l' -> R_pair (l,r) (l',r')
  | R : forall l r r',
    RU r r' -> R_pair (l,r) (l,r').

Theorem wf_R_pair : well_founded R_pair.