Theorems · Theorem · order theory
Finset.sup_eq_zero
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeSup α] [inst_1 : OrderBot α] {s : Finset β} {f : β → α}
[inst_2 : Zero α] [IsBotZeroClass α], s.sup f = 0 ↔ ∀ i ∈ s, f i = 0- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Bot.botproof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement and proof · cited by 530
- IsBotZeroClassstatement and proof · cited by 71
- bot_eq_zeroproof · cited by 31
- Finset.sup_eq_bot_iffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sup'_eq_zeroproof · cited by 0