Theorems · Theorem · order theory
iInf_congr
∀ {α : Type u_1} {ι : Sort u_4} [inst : InfSet α] {f g : ι → α}, (∀ (i : ι), f i = g i) → ⨅ i, f i = ⨅ i, g i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses Quot.sound
- Assumes
- InfSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by15
Results whose statement or proof uses this declaration.
- Set.iInter_congrproof · cited by 9
- Ideal.height_eq_inf_minimalPrimesproof · cited by 7
- IsLocalization.height_underproof · cited by 6
- LinearMap.withSeminorms_inducedproof · cited by 5
- biInf_prodproof · cited by 4
- withSeminorms_iInfproof · cited by 3
- biInf_congrproof · cited by 2
- EquicontinuousOn.comap_uniformOnFun_eqproof · cited by 2
- UniformOnFun.iInf_eqproof · cited by 1
- AlgebraicGeometry.isNoetherianRing_of_awayproof · cited by 1
- MeasureTheory.measure_iInter_of_ae_monotoneproof · cited by 1
- Filter.lift'_infproof · cited by 1