Theorems · Theorem · order theory
setOfPred_minimal_subset
∀ {α : Type u_2} [inst : Preorder α] (s : Set α), {x | Minimal (fun x => x ∈ s) x} ⊆ s- Defined in
- Mathlib.Order.Minimal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Preorderstatement and proof · cited by 7,952
- Set.ofPredstatement · cited by 6,101
- Minimalstatement · cited by 150
- Set.sep_subsetproof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- AddSubmonoid.fg_of_subtractiveproof · cited by 2
- Submonoid.fg_of_divisiveproof · cited by 2
- setOf_minimal_subsetproof · cited by 0
- AddSemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- SemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0