Theorems · Theorem · order theory
Directed.mono_comp
∀ {α : Type u_1} {β : Type u_2} (r : α → α → Prop) {ι : Sort u_5} {rb : β → β → Prop} {g : α → β} {f : ι → α},
(∀ ⦃x y : α⦄, r x y → rb (g x) (g y)) → Directed r f → Directed rb (g ∘ f)- Defined in
- Mathlib.Order.Directed
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Directedstatement and proof · cited by 213
- directed_compproof · cited by 8
- Directed.monoproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- directed_of_isDirected_leproof · cited by 8
- LowerSemicontinuousOn.exists_isMinOnproof · cited by 6
- Filter.hasBasis_biInf_principalproof · cited by 5
- IsCompact.elim_directed_family_closedproof · cited by 3
- directed_of_isDirected_geproof · cited by 3
- MeasureTheory.Measure.restrict_iUnion_apply_eq_iSupproof · cited by 3
- LocalSubring.exists_le_valuationSubringproof · cited by 2
- Directed.measure_iInterproof · cited by 1
- exists_compact_surjective_zorn_subsetproof · cited by 1
- MeasureTheory.biSup_measure_Iicproof · cited by 1
- Filter.hasBasis_iInf_principalproof · cited by 1
- RelHomClass.directedproof · cited by 0