Theorems · Theorem · order theory
sup_sInf_eq
∀ {α : Type u} [inst : Order.Coframe α] {s : Set α} {a : α}, a ⊔ sInf s = ⨅ b ∈ s, a ⊔ b⊔ distributes over ⨅.
- Defined in
- Mathlib.Order.CompleteBooleanAlgebra
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- Order.Coframe
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 · cited by 1,690
- InfSet.sInfstatement · cited by 935
- Order.Coframestatement and proof · cited by 38
- GaloisConnection.u_sInfproof · cited by 11
- gc_sdiff_supproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- sInf_sup_eqproof · cited by 3
- Filter.limsup_sup_filterproof · cited by 1
- Order.Coframe.MinimalAxioms.ofproof · cited by 0
- CompleteDistribLattice.MinimalAxioms.ofproof · cited by 0