Theorems · Theorem · order theory
List.minimum_le_coe_iff
∀ {α : Type u_1} [inst : LinearOrder α] {l : List α} {a : α}, l.minimum ≤ ↑a ↔ ∃ b ∈ l, b ≤ a- Defined in
- Mathlib.Data.List.MinMax
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 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
- WithTop.somestatement and proof · cited by 1,128
- top_le_iffproof · cited by 175
- WithTop.coe_le_coeproof · cited by 65
- WithTop.coe_ne_topproof · cited by 43
- List.minimumstatement and proof · cited by 24
- List.minimum_consproof · cited by 7
- inf_le_iffproof · cited by 6
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