Theorem
Doubly distributive hyperfields are stringent
Double distributivity forces every nonopposite binary hypersum to be a singleton.
Statement
Every doubly distributive hyperfield is stringent.
In other words, if is doubly distributive and , then
The converse is false: stringency alone does not imply double distributivity.
References
Nathan Bowler and Ting Su, Classification of doubly distributive skew hyperfields and stringent hypergroups, Proposition 1.3.