Theorems · Theorem · order theory
iInf_inf
∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] [Nonempty ι] {f : ι → α} {a : α},
(⨅ x, f x) ⊓ a = ⨅ x, f x ⊓ a- 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.
- biInf_infproof · cited by 4
- Set.iInter_interproof · cited by 2
- Filter.prod_iInf_leftproof · cited by 1