Theorems · Theorem · number theory
Northcott.exists_min_image
∀ {α : Type u_1} {β : Type u_2} (h : α → β) [inst : LinearOrder β] [Northcott h] (s : Set α),
s.Nonempty → ∃ a ∈ s, ∀ a' ∈ s, h a ≤ h a'- Defined in
- Mathlib.Order.Northcott
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderNorthcott
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Set.Nonemptystatement and proof · cited by 2,627
- le_rflproof · cited by 1,558
- Set.Finite.inter_of_leftproof · cited by 31
- Northcottstatement and proof · cited by 19
- Northcott.finite_leproof · cited by 8
- Set.exists_min_imageproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Group.fg_of_descentproof · cited by 1
- AddGroup.fg_of_descentproof · cited by 1