Theorems · Theorem · order theory
iInf_univ
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α}, ⨅ x ∈ Set.univ, f x = ⨅ x, f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 8 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.univstatement · cited by 3,945
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- Set.mem_univproof · cited by 416
- iInf_congr_Propproof · cited by 218
- iInf_posproof · cited by 31
Cited by8
Results whose statement or proof uses this declaration.
- IsArtinianRing.nilradical_pow_eq_iInfproof · cited by 3
- iSup_iInf_of_monotoneproof · cited by 3
- PrimeSpectrum.vanishingIdeal_univproof · cited by 2
- inf_iInf_nat_succproof · cited by 1
- LinearGrowth.linearGrowthInf_iInfproof · cited by 0
- Set.map_finite_iInfproof · cited by 0
- ExpGrowth.expGrowthInf_iInfproof · cited by 0
- Set.biInter_univproof · cited by 0