Extend a partial order to a linear order #

This file constructs a linear order which is an extension of the given partial order, using Zorn's lemma.

theorem extend_partialOrder {α : Type u} (r : ααProp) [IsPartialOrder α r] :
s x, r s

Any partial order can be extended to a linear order.

def LinearExtension (α : Type u) :

A type alias for α, intended to extend a partial order on α to a linear order.

Instances For
    def toLinearExtension {α : Type u} [PartialOrder α] :
    (fun x x_1 => x x_1) →r fun x x_1 => x x_1

    The embedding of α into LinearExtension α as a relation homomorphism.

    Instances For