Has it sense to add to IsStrictPatialOrder this: _≮_ : Rel A _ x ≮ y = ¬ x < y <-antisym : {x y : A} → x < y → y ≮ x <-antisym x<y = irrefl ≈refl ∘ <-trans x<y (one definition and one lemma) ? These two items are often used. And it looks like the most natural place for them to appear. (?) Regards, ------ Sergei