Theorems · Definition · order theory

Function.Injective.generalizedBooleanAlgebra

{α : Type u} →
  {β : Type u_1} →
    [inst : Max α] →
      [inst_1 : Min α] →
        [inst_2 : LE α] →
          [inst_3 : LT α] →
            [inst_4 : Bot α] →
              [inst_5 : SDiff α] →
                [inst_6 : GeneralizedBooleanAlgebra 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) →
                            (∀ (a b : α), f (a ⊓ b) = f a ⊓ f b) →
                              f ⊥ = ⊥ → (∀ (a b : α), f (a \ b) = f a \ f b) → GeneralizedBooleanAlgebra α

Pullback a GeneralizedBooleanAlgebra along an injection.

Defined in

Mathlib.Order.BooleanAlgebra.Basic

Cited by

0 results in Mathlib

Foundations

Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MaxMinLELTBotSDiffGeneralizedBooleanAlgebra