Section StrongNormalisation.
Variables (X A: Type).
Variables (R: X -> X -> Prop) (S: A -> A -> Prop).
Inductive SN {X} (R: X -> X -> Prop) : X -> Prop :=
| SNC x : (forall y, R x y -> SN R y) -> SN R x.

Lemma SN_ext Q x :
(forall x y, R x y <-> Q x y) ->
SN R x <-> SN Q x.