Theorems · Theorem · order theory
Finset.lt_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 < s.sup f ↔ ∃ b ∈ s, a < f b- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 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.
Cites12
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
- OrderBotstatement and proof · cited by 1,055
- Finset.supstatement and proof · cited by 530
- lt_of_lt_of_leproof · cited by 438
- Finset.consproof · cited by 221
- Finset.le_supproof · cited by 112
- Finset.cons_inductionproof · cited by 85
- Finset.mem_consproof · cited by 35
- Finset.sup_consproof · cited by 30
- not_lt_botproof · cited by 19
- lt_sup_iffproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Finset.lt_sup'_iffproof · cited by 0