Theorems · Definition · order theory

Function.Injective.semilatticeSup

{α : Type u} →
  {β : Type v} →
    [inst : Max α] →
      [inst_1 : LE α] →
        [inst_2 : LT α] →
          [inst_3 : SemilatticeSup β] →
            (f : α → β) →
              Function.Injective f →
                (∀ {x y : α}, f x ≤ f y ↔ x ≤ y) →
                  (∀ {x y : α}, f x < f y ↔ x < y) → (∀ (a b : α), f (a ⊔ b) = f a ⊔ f b) → SemilatticeSup α

A type endowed with ⊔ is a SemilatticeSup, if it admits an injective map that preserves ⊔ to a SemilatticeSup. See note [reducible non-instances].

Defined in

Mathlib.Order.Lattice

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext

Assumes

MaxLELTSemilatticeSup