Theorems · Theorem · order theory
Finset.le_sup_iff
∀ {α : Type u_2} {ι : Type u_5} [inst : LinearOrder α] [inst_1 : OrderBot α] {s : Finset ι} {f : ι → α} {a : α},
⊥ < a → (a ≤ s.sup f ↔ ∃ b ∈ s, a ≤ f b)- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- le_transproof · cited by 985
- Finset.supstatement and proof · cited by 530
- Finset.consproof · cited by 221
- Finset.le_supproof · cited by 112
- not_le_of_gtproof · cited by 97
- Finset.cons_inductionproof · cited by 85
- Finset.mem_consproof · cited by 35
- Finset.sup_consproof · cited by 30
Cited by4
Results whose statement or proof uses this declaration.
- Finset.le_sup'_iffproof · cited by 5
- MvPolynomial.le_degreeOf_of_mem_supportproof · cited by 2
- Finset.sup_eq_top_iffproof · cited by 2
- MvPolynomial.degreeOf_add_eq_of_degreeOf_ltproof · cited by 1