Theorems · Theorem · order theory
Finset.min_le
∀ {α : Type u_2} [inst : LinearOrder α] {a : α} {s : Finset α}, a ∈ s → s.min ≤ ↑a- Defined in
- Mathlib.Data.Finset.Max
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 56 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- LinearOrderstatement and proof · cited by 8,572
- WithTopstatement · cited by 3,754
- WithTop.somestatement · cited by 1,128
- Finset.minstatement · cited by 36
- Finset.inf_leproof · cited by 23
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.minDegree_le_degreeproof · cited by 6
- Polynomial.trailingDegree_le_of_ne_zeroproof · cited by 5
- Polynomial.le_trailingDegree_mulproof · cited by 2
- Finset.min_le_of_eqproof · cited by 1
- Finset.notMem_of_coe_lt_minproof · cited by 1
- Finset.card_le_of_interleavedproof · cited by 1