Theorems · Theorem · order theory
sInf_sup_eq
∀ {α : Type u} [inst : Order.Coframe α] {s : Set α} {b : α}, sInf s ⊔ b = ⨅ a ∈ s, a ⊔ b- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- iInfstatement and proof · cited by 1,690
- InfSet.sInfstatement and proof · cited by 935
- iInf_congr_Propproof · cited by 218
- sup_commproof · cited by 165
- Order.Coframestatement and proof · cited by 38
- sup_sInf_eqproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- iInf_sup_eqproof · cited by 7
- Filter.limsup_sup_filterproof · cited by 1
- sInf_codisjoint_iffproof · cited by 1