Theorems · Theorem · order theory
setOfPred_minimal_antichain
∀ {α : Type u_1} [inst : PartialOrder α] (P : α → Prop), IsAntichain (fun x1 x2 => x1 ≤ x2) {x | Minimal P x}- Defined in
- Mathlib.Order.Antichain
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement · cited by 6,101
- Minimalstatement · cited by 150
- IsAntichainstatement · cited by 105
- setOfPred_maximal_antichainproof · cited by 2
- IsAntichain.swapproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_of_subtractiveproof · cited by 2
- Submonoid.fg_of_divisiveproof · cited by 2
- AddSemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- SemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- setOf_minimal_antichainproof · cited by 0