Section wf_strict_order_list.
Variable (X : Type) (R : X -> X -> Prop).
Hypothesis (Rirrefl : forall x, ~ R x x)
(Rtrans : forall x y z, R x y -> R y z -> R x z).
Implicit Type l : list X.
Fact chain_trans n x y : chain R n x y -> n = 0 /\ x = y \/ R x y.

Corollary chain_irrefl n x : n = 0 \/ ~ chain R n x x.