Homotopy Type Theory order > history (Rev #3)

Definition

A partial order \leq over a type AA is an order (also called total order or linear order) if it comes with a family of dependent terms

a:A,b:Aτ(a,b):R(a,b)+R(b,a)a:A, b:A \vdash \tau(a, b): \Vert R(a, b) + R(b, a) \Vert

representing the totality condition for the partial order. AA is called an ordered type, totally ordered type, or linearly ordered type.

See also

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