Theorems · Definition · order theory

Function.Injective.partialOrder

{α : Type u_2} →
  {β : Type u_3} →
    [inst : PartialOrder β] →
      [inst_1 : LE α] →
        [inst_2 : LT α] →
          (f : α → β) →
            Function.Injective f → (∀ {x y : α}, f x ≤ f y ↔ x ≤ y) → (∀ {x y : α}, f x < f y ↔ x < y) → PartialOrder α

Pull back a PartialOrder instance along an injective function. See note [reducible non-instances].

Defined in

Mathlib.Order.Basic

Cited by

0 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext

Assumes

PartialOrderLELT