Theorems · Theorem · order theory
Maximal.prop
∀ {α : Type u_1} [inst : LE α] {P : α → Prop} {x : α}, Maximal P x → P x- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Maximalstatement and proof · cited by 211
Cited by34
Results whose statement or proof uses this declaration.
- Ideal.radical_eq_sInfproof · cited by 21
- Ideal.exists_minimalPrimes_leproof · cited by 14
- exists_linearIndepOn_extensionproof · cited by 5
- Matroid.map_isBase_iffproof · cited by 5
- maximal_iff_eqproof · cited by 4
- image_monotone_setOfPred_maximalproof · cited by 4
- Vitali.exists_disjoint_subfamily_covering_enlargementproof · cited by 3
- maximal_mem_image_monotoneproof · cited by 3
- IsPGroup.exists_le_sylowproof · cited by 2
- Ideal.IsOka.forall_of_forall_primeproof · cited by 2
- maximal_and_iff_right_of_impproof · cited by 2
- Function.Embedding.min_injectiveproof · cited by 2