Theorems · Theorem · order theory
SupPrime.le_finset_sup
∀ {ι : Type u_1} {α : Type u_2} [inst : SemilatticeSup α] {a : α} [inst_1 : OrderBot α] {s : Finset ι} {f : ι → α},
SupPrime a → (a ≤ s.sup f ↔ ∃ i ∈ s, a ≤ f i)- Defined in
- Mathlib.Order.Irreducible
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemilatticeSupOrderBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- Finset.supstatement and proof · cited by 530
- Finset.inductionproof · cited by 108
- Finset.sup_emptyproof · cited by 72
- Finset.sup_insertproof · cited by 35
- SupPrimestatement and proof · cited by 19
- SupPrime.le_supproof · cited by 1
- SupPrime.ne_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- InfPrime.finset_inf_leproof · cited by 0