Theorems · Theorem · order theory
iInf_option
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] (f : Option β → α), ⨅ o, f o = f none ⊓ ⨅ b, f (some b)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- eq_of_forall_le_iffproof · cited by 65
- le_inf_iffproof · cited by 48
- le_iInf_iffproof · cited by 30
Cited by7
Results whose statement or proof uses this declaration.
- iInf_iSup_eq_of_finiteproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.emultiplicity_iSupproof · cited by 1
- ENNReal.iInf_ennrealproof · cited by 1
- Subspace.dualAnnihilator_iInf_eqproof · cited by 1
- TopologicalSpace.Opens.coe_iInfproof · cited by 1
- Set.iInter_optionproof · cited by 1
- iInf_option_elimproof · cited by 0