Section AllRel.
Variables (T S : Type) (r : T -> S -> bool).
Implicit Types (x : T) (y : S) (xs : seq T) (ys : seq S).
Definition allrel xs ys := all [pred x | all (r x) ys] xs.

Lemma eq_allrel {T S : Type} (r r' : T -> S -> bool) :
r =2 r' -> allrel r =2 allrel r'.