Theorems · Theorem · order theory
maximal_and_iff_right_of_imp
∀ {α : Type u_2} {P Q : α → Prop} {x : α} [inst : LE α],
(∀ ⦃x : α⦄, P x → Q x) → (Maximal (fun x => P x ∧ Q x) x ↔ Maximal P x ∧ Q x)- Defined in
- Mathlib.Order.Minimal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext, Quot.sound
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Maximalstatement and proof · cited by 211
- Maximal.propproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- Matroid.isBasis_ground_iffproof · cited by 10
- maximal_and_iff_left_of_impproof · cited by 1