Theorems · Theorem · order theory
sInf_image
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {s : Set β} {f : β → α}, sInf (f '' s) = ⨅ a ∈ s, f a- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 25 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
- Set.Elemproof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- InfSet.sInfstatement and proof · cited by 935
- iInf_subtype''proof · cited by 11
- sInf_image'proof · cited by 9
Cited by25
Results whose statement or proof uses this declaration.
- Set.sInter_imageproof · cited by 26
- OrderIso.map_sInf_eq_sInf_symm_preimageproof · cited by 18
- iInf_imageproof · cited by 14
- Algebra.coe_sInfproof · cited by 7
- NonUnitalAlgebra.coe_sInfproof · cited by 5
- StarSubalgebra.coe_sInfproof · cited by 3
- NonUnitalStarAlgebra.coe_sInfproof · cited by 3
- InfClosed.biInf_memproof · cited by 2
- WithTop.coe_sInfproof · cited by 2
- Function.coframeMinimalAxiomsproof · cited by 2
- CompleteSublattice.coe_sInf'proof · cited by 1
- InfClosed.biInf_mem_of_nonemptyproof · cited by 1