Theorems · Theorem · order theory
IsAtom.compl
∀ {α : Type u_2} [inst : BooleanAlgebra α] {a : α}, IsAtom a → IsCoatom aᶜAlias of the reverse direction of isCoatom_compl.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Compl.complstatement · cited by 2,925
- BooleanAlgebrastatement and proof · cited by 300
- IsAtomstatement · cited by 130
- IsCoatomstatement · cited by 114
- isCoatom_complproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Finset.isCoatom_compl_singletonproof · cited by 0