Theorems · Theorem · order theory
List.le_minimum_of_forall_le
∀ {α : Type u_1} [inst : LinearOrder α] {l : List α} {b : WithTop α}, (∀ a ∈ l, b ≤ ↑a) → b ≤ l.minimum- Defined in
- Mathlib.Data.List.MinMax
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- WithTop.somestatement and proof · cited by 1,128
- le_topproof · cited by 411
- List.minimumstatement and proof · cited by 24
- le_min_iffproof · cited by 9
- List.minimum_consproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- List.minimum_antiproof · cited by 0