Theorems · Theorem · order theory
IsCoatom.dual
∀ {α : Type u_2} [inst : Preorder α] [inst_1 : OrderTop α] {a : α}, IsCoatom a → IsAtom (OrderDual.toDual a)Alias of the reverse direction of isAtom_dual_iff_isCoatom.
- Defined in
- Mathlib.Order.Atoms
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- OrderDualstatement · cited by 927
- OrderTopstatement and proof · cited by 493
- OrderDual.toDualstatement · cited by 481
- IsAtomstatement · cited by 130
- IsCoatomstatement · cited by 114
- isAtom_dual_iff_isCoatomproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- IsCoatom.le_iffproof · cited by 4
- IsCoatom.le_iff_eqproof · cited by 4
- IsCoatom.lt_iffproof · cited by 1
- IsCoatom.Iciproof · cited by 0
- IsCoatom.Ici_eqproof · cited by 0
- GaloisCoinsertion.isCoatom_of_l_topproof · cited by 0