order.extension

# 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_partial_order {α : Type u} (r : α → α → Prop) [ r] :
∃ (s : α → α → Prop) (_x : s), r s

Any partial order can be extended to a linear order.

def linear_extension (α : Type u) :
Type u

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

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@[instance]
def linear_extension.linear_order {α : Type u}  :
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def to_linear_extension {α : Type u}  :

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

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@[instance]
def linear_extension.inhabited {α : Type u} [inhabited α] :
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