I was surprised when unfolding rationals_le to see that it specifies that le x y if there is a fraction p/q made of nats such that y=x+p/q:
Instance rationals_le `{Rationals Q} : Le Q | 10 := λ x y,
∃ num, ∃ den, y = x + naturals_to_semiring nat Q num / naturals_to_semiring nat Q den.Why not use any type that is an instance of Naturals?
I was surprised when unfolding
rationals_leto see that it specifies thatle x yif there is a fractionp/qmade ofnats such thaty=x+p/q:Instance rationals_le `{Rationals Q} : Le Q | 10 := λ x y, ∃ num, ∃ den, y = x + naturals_to_semiring nat Q num / naturals_to_semiring nat Q den.Why not use any type that is an instance of
Naturals?