Theorems · Theorem · order theory
compl_eq_bot
∀ {α : Type u} {x : α} [inst : BooleanAlgebra α], xᶜ = ⊥ ↔ x = ⊤- Defined in
- Mathlib.Order.BooleanAlgebra.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- BooleanAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Bot.botstatement · cited by 4,720
- Compl.complstatement · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- isCompl_top_botproof · cited by 5
- IsCompl.compl_eq_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Set.compl_empty_iffproof · cited by 11
- Finset.compl_eq_empty_iffproof · cited by 1
- bihimp_eq_botproof · cited by 0
- Equiv.Perm.exists_fixed_point_of_primeproof · cited by 0