Theorems · Theorem · order theory
isStronglyAtomic_dual_iff_is_stronglyCoatomic
∀ {α : Type u_4} [inst : Preorder α], IsStronglyAtomic αᵒᵈ ↔ IsStronglyCoatomic α- Defined in
- Mathlib.Order.Atoms
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement and proof · cited by 927
- OrderDual.toDualproof · cited by 481
- CovByproof · cited by 290
- IsStronglyAtomicstatement · cited by 17
- IsStronglyCoatomicstatement · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- ComplementedLattice.isStronglyCoatomicproof · cited by 1
- Set.OrdConnected.isStronglyCoatomicproof · cited by 0
- Lattice.isStronglyCoatomicproof · cited by 0
- isStronglyCoatomic_dual_iff_is_stronglyAtomicproof · cited by 0
- IsStronglyCoatomic.of_wellFounded_gtproof · cited by 0