Theorems · Theorem · order theory
inf_iInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] [Nonempty ι] {f : ι → α} {a : α}, a ⊓ ⨅ x, f x = ⨅ x, a ⊓ f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLatticeNonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_inf_eqproof · cited by 12
- iInf_constproof · cited by 9
Cited by3
Results whose statement or proof uses this declaration.
- Set.inter_iInterproof · cited by 6
- Filter.prod_iInf_rightproof · cited by 1
- Submodule.inf_iInf_maxGenEigenspace_of_forall_mapsToproof · cited by 1