Theorems · Theorem · order theory
Monotone.dual
∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → Monotone (⇑OrderDual.toDual ∘ f ∘ ⇑OrderDual.ofDual)Alias of the reverse direction of monotone_dual_iff.
- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 39 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- Equivstatement · cited by 8,337
- Preorderstatement and proof · cited by 7,952
- Monotonestatement · cited by 1,397
- OrderDualstatement · cited by 927
- OrderDual.toDualstatement · cited by 481
- OrderDual.ofDualstatement · cited by 400
- monotone_dual_iffproof · cited by 2
Cited by39
Results whose statement or proof uses this declaration.
- Monotone.map_limsInf_of_continuousAtproof · cited by 5
- Monotone.le_of_tendstoproof · cited by 4
- Monotone.le_rightLimproof · cited by 4
- Monotone.rightLim_leproof · cited by 3
- Monotone.tendsto_nhdsGTproof · cited by 3
- Monotone.continuousWithinAt_Ioi_iff_rightLim_eqproof · cited by 3
- ContinuousAt.comp_upperSemicontinuousAtproof · cited by 2
- ContinuousAt.comp_upperSemicontinuousWithinAtproof · cited by 2
- Monotone.seq_pos_lt_seq_of_le_of_ltproof · cited by 2
- QuasiconcaveOn.monotone_compproof · cited by 2
- Monotone.map_csInf_of_continuousAtproof · cited by 2
- Function.Commute.iterate_pos_lt_of_map_lt'proof · cited by 1