Theorems · Theorem · order theory
StrictMono.monotone
∀ {α : Type u} {β : Type v} [inst : PartialOrder α] [inst_1 : Preorder β] {f : α → β}, StrictMono f → Monotone f- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 118 results in Mathlib
- Foundations
- Depth 16 from the axioms, rests on 60 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- Monotonestatement · cited by 1,397
- StrictMonostatement and proof · cited by 706
- monotone_iff_forall_ltproof · cited by 9
Cited by120
Results whose statement or proof uses this declaration.
- Real.exp_monotoneproof · cited by 30
- ENNReal.log_monotoneproof · cited by 14
- Order.IsNormal.monotoneproof · cited by 11
- IsAdicComplete.StrictMono.liftstatement · cited by 6
- StieltjesFunction.measure_singletonproof · cited by 6
- Rat.cast_monoproof · cited by 6
- ack_mono_leftproof · cited by 5
- ack_mono_rightproof · cited by 5
- LTSeries.monotoneproof · cited by 5
- Valuation.subgroups_basisproof · cited by 5
- IsAdicComplete.StrictMono.liftRingHomstatement · cited by 4
- Cardinal.lift_monotoneproof · cited by 4