Theorems · Theorem · order theory
directed_comp
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {ι : Sort u_5} {f : ι → β} {g : β → α},
Directed r (g ∘ f) ↔ Directed (g ⁻¹'o r) f- Defined in
- Mathlib.Order.Directed
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Directedstatement · cited by 213
- Order.Preimagestatement · cited by 42
Cited by8
Results whose statement or proof uses this declaration.
- Directed.mono_compproof · cited by 12
- Filter.hasBasis_biInf_principalproof · cited by 5
- DirectedOn.exists_mem_subset_of_finset_subset_biUnionproof · cited by 3
- AddSubsemigroup.mem_biSup_of_directedOnproof · cited by 0
- Submonoid.mem_biSup_of_directedOnproof · cited by 0
- AddSubmonoid.mem_biSup_of_directedOnproof · cited by 0
- Subsemigroup.mem_biSup_of_directedOnproof · cited by 0
- linearIndepOn_biUnion_of_directedproof · cited by 0