Theorems · Theorem · order theory
supPrime_ofDual
∀ {α : Type u_2} [inst : SemilatticeSup α] {a : αᵒᵈ}, SupPrime (OrderDual.ofDual a) ↔ InfPrime a- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
- Assumes
- SemilatticeSup
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.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- OrderDualstatement and proof · cited by 927
- SemilatticeSupstatement and proof · cited by 785
- OrderDual.ofDualstatement · cited by 400
- InfPrimestatement · cited by 26
- SupPrimestatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- InfPrime.ofDualproof · cited by 0