Theorems · Theorem · order theory
iInf_insert
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α} {s : Set β} {b : β},
⨅ x ∈ insert b s, f x = f b ⊓ ⨅ x ∈ s, f x- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- iInf_congr_Propproof · cited by 218
- Set.mem_insert_iffproof · cited by 39
- iInf_iInf_eq_leftproof · cited by 12
- iInf_inf_eqproof · cited by 12
- iInf_orproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Finset.iInf_insertproof · cited by 5
- iInf_pairproof · cited by 2
- Set.Finite.iSup_biInf_of_monotoneproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.ideal_biInfproof · cited by 1
- Set.einfsep_tripleproof · cited by 1