Theorems · Theorem · order theory
IsAntichain.to_dual
∀ {α : Type u_1} {s : Set α} [inst : LE α], IsAntichain (fun x1 x2 => x1 ≤ x2) s → IsAntichain (fun x1 x2 => x1 ≤ x2) s- Defined in
- Mathlib.Order.Antichain
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- OrderDualstatement and proof · cited by 927
- IsAntichainstatement and proof · cited by 105
Cited by5
Results whose statement or proof uses this declaration.
- IsAntichain.eq_setOfPred_minimalproof · cited by 1
- IsAntichain.maximal_mem_iffproof · cited by 0
- IsAntichain.maximal_mem_lowerClosure_iff_memproof · cited by 0
- IsAntichain.to_dual_iffproof · cited by 0
- IsAntichain.interior_eq_empty'proof · cited by 0