Theorems · Theorem · order theory
iInf_const
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {a : α} [Nonempty ι], ⨅ x, a = a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeNonempty
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.
- Setproof · cited by 53,352
- iInfstatement · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfproof · cited by 935
- Set.range_constproof · cited by 25
- sInf_singletonproof · cited by 8
Cited by9
Results whose statement or proof uses this declaration.
- norm_withSeminormsproof · cited by 12
- Filter.limsup_eq_iInf_iSup_of_natproof · cited by 5
- Set.iInter_constproof · cited by 4
- iInf_infproof · cited by 3
- biInf_constproof · cited by 3
- inf_iInfproof · cited by 3
- Set.Finite.iInf_biSup_of_monotoneproof · cited by 2
- iInf_uniqueproof · cited by 1
- Filter.lift_constproof · cited by 0