Theorems · Theorem · order theory
Order.Ideal.coe_sInf
∀ {P : Type u_1} [inst : SemilatticeSup P] [inst_1 : OrderBot P] {S : Set (Order.Ideal P)}, ↑(sInf S) = ⋂ s ∈ S, ↑s- Defined in
- Mathlib.Order.Ideal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Set.iInterstatement · cited by 1,084
- OrderBotstatement and proof · cited by 1,055
- InfSet.sInfstatement · cited by 935
- SemilatticeSupstatement and proof · cited by 785
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.toLowerSetproof · cited by 9
- LowerSet.coe_iInf₂proof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Order.Ideal.mem_sInfproof · cited by 0