Theorems · Theorem · order theory
WithTop.monotone_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : WithTop α → β},
Monotone f ↔ (Monotone fun a => f ↑a) ∧ ∀ (x : α), f ↑x ≤ f ⊤- Defined in
- Mathlib.Order.WithBot
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- WithTopstatement and proof · cited by 3,754
- le_rflproof · cited by 1,558
- Monotonestatement and proof · cited by 1,397
- WithTop.somestatement and proof · cited by 1,128
- le_topproof · cited by 411
- Monotone.compproof · cited by 67
- WithTop.coe_le_coeproof · cited by 65
- WithTop.forallproof · cited by 8
- WithTop.coe_monoproof · cited by 6
- WithTop.not_top_le_coeproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- WithTop.monotone_map_iffproof · cited by 2