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Theorems · Definition · order theory

IsSimpleOrder.linearOrder

{α : Type u_2} →
  [inst : PartialOrder α] → [inst_1 : BoundedOrder α] → [IsSimpleOrder α] → [DecidableEq α] → LinearOrder α

A simple partial ordered BoundedOrder induces a linear order. This is not an instance to prevent loops.

Defined in
Mathlib.Order.Atoms
Cited by
0 results in Mathlib
Foundations
Depth 11 from the axioms · uses propext
Assumes
PartialOrderBoundedOrderIsSimpleOrderDecidableEq

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