Theorems · Theorem · order theory
List.minimum_eq_coe_iff
∀ {α : Type u_1} [inst : LinearOrder α] {l : List α} {m : α}, l.minimum = ↑m ↔ m ∈ l ∧ ∀ a ∈ l, m ≤ a- Defined in
- Mathlib.Data.List.MinMax
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
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.
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement and proof · cited by 3,754
- le_reflproof · cited by 2,061
- WithTop.somestatement and proof · cited by 1,128
- ge_antisymmproof · cited by 51
- List.minimumstatement · cited by 24
- List.argminproof · cited by 13
- WithTop.some_eq_coeproof · cited by 1
- List.argmin_eq_some_iffproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- List.getD_min?_eq_untopD_minimumproof · cited by 0