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Theorems · Theorem · order theory

inf_sSup_eq

∀ {α : Type u} [inst : Order.Frame α] {s : Set α} {a : α}, a ⊓ sSup 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.Frame
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sSup_inf_eq · cited by 3sSup_inf_eqscottContinuous_inf_right · cited by 1scottContinuous_inf_rightOrder.Frame.MinimalAxioms.of · cited by 0MinimalAxioms.ofCompleteDistribLattice.MinimalAxioms.of · cited by 0MinimalAxioms.ofSet · cited by 53352SetiSup · cited by 2415iSupSupSet.sSup · cited by 954SupSet.sSupOrder.Frame · cited by 88Order.FrameGaloisConnection.l_sSup · cited by 19GaloisConnection.l_sSupgc_inf_himp · cited by 1gc_inf_himpinf_sSup_eqCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.