Theorems · Theorem · order theory
sSup_inf_eq
∀ {α : Type u} [inst : Order.Frame α] {s : Set α} {b : α}, sSup 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.Frame
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
- iSupstatement and proof · cited by 2,415
- SupSet.sSupstatement and proof · cited by 954
- iSup_congr_Propproof · cited by 247
- inf_commproof · cited by 139
- Order.Framestatement and proof · cited by 88
- inf_sSup_eqproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- iSup_inf_eqproof · cited by 7
- sSup_disjoint_iffproof · cited by 2
- scottContinuous_inf_leftproof · cited by 1