Theorems · Theorem · order theory
WithTop.strictMono_iff
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder α] [inst_1 : Preorder β] {f : WithTop α → β},
StrictMono f ↔ (StrictMono fun a => f ↑a) ∧ ∀ (x : α), f ↑x < f ⊤- Defined in
- Mathlib.Order.WithBot
- Cited by
- 4 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
- WithTop.somestatement and proof · cited by 1,128
- StrictMonostatement and proof · cited by 706
- lt_irreflproof · cited by 190
- WithTop.coe_lt_coeproof · cited by 47
- WithTop.coe_lt_topproof · cited by 44
- StrictMono.compproof · cited by 36
- not_top_ltproof · cited by 17
- WithTop.forallproof · cited by 8
- WithTop.coe_strictMonoproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- EReal.coe_ennreal_strictMonoproof · cited by 4
- Cardinal.ofENat_strictMonoproof · cited by 4
- WithTop.strictMono_map_iffproof · cited by 2
- WithTop.strictAnti_iffproof · cited by 1