Theorems · Theorem · order theory
Monotone.directed_le
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [IsDirectedOrder α] [inst_2 : Preorder β] {f : α → β},
Monotone f → Directed (fun x1 x2 => x1 ≤ x2) f- Defined in
- Mathlib.Order.Directed
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- IsDirectedOrderstatement and proof · cited by 316
- Directedstatement · cited by 213
- directed_of_isDirected_leproof · cited by 8
Cited by25
Results whose statement or proof uses this declaration.
- tendsto_atTop_ciSupproof · cited by 13
- Monotone.measure_iUnionproof · cited by 10
- Module.End.mem_genEigenspaceproof · cited by 4
- ProbabilityTheory.Kernel.indep_limsup_atTop_selfproof · cited by 3
- isPiSystem_iUnion_of_monotoneproof · cited by 2
- CompactExhaustion.exists_superset_of_isCompactproof · cited by 2
- ProbabilityTheory.setLIntegral_toKernel_univproof · cited by 2
- UniformOnFun.hasAntitoneBasis_uniformityproof · cited by 2
- ProbabilityTheory.Kernel.indep_iSup_of_monotoneproof · cited by 2
- MeasureTheory.Measure.ext_of_Iicproof · cited by 2
- Besicovitch.exists_disjoint_closedBall_covering_ae_of_finiteMeasure_auxproof · cited by 1
- Module.End.genEigenspace_directedproof · cited by 1