Theorems · Theorem · order theory
maximal_subset_iff
∀ {α : Type u_2} {P : Set α → Prop} {s : Set α}, Maximal P s ↔ P s ∧ ∀ ⦃t : Set α⦄, P t → s ⊆ t → s = t- Defined in
- Mathlib.Order.Minimal
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Maximalstatement · cited by 211
- maximal_iffproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Matroid.dual_isBase_iffproof · cited by 9
- Matroid.map_isBase_iffproof · cited by 5
- Matroid.isBase_iff_maximal_indepproof · cited by 5
- Matroid.Indep.isBase_of_maximalproof · cited by 4
- Matroid.isBasis_iff'proof · cited by 2