Theorems · Theorem · order theory
StrictMono.le_iff_le
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β},
StrictMono f → ∀ {a b : α}, f a ≤ f b ↔ a ≤ b- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 104 results in Mathlib
- Foundations
- Depth 13 from the axioms, rests on 38 definitions · uses no axioms
- Assumes
- LinearOrderPreorder
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.
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- Set.univproof · cited by 3,945
- StrictMonostatement and proof · cited by 706
- StrictMono.strictMonoOnproof · cited by 24
- StrictMonoOn.le_iff_leproof · cited by 17
Cited by106
Results whose statement or proof uses this declaration.
- Nat.cast_leproof · cited by 159
- Real.exp_le_expproof · cited by 16
- OrderEmbedding.ofStrictMonoproof · cited by 15
- EReal.coe_le_coe_iffproof · cited by 10
- rank_span_leproof · cited by 9
- ENNReal.rpow_le_rpow_iffproof · cited by 7
- zpow_le_zpow_iff_right₀proof · cited by 7
- EReal.le_div_iff_mul_leproof · cited by 6
- EReal.div_le_iff_le_mulproof · cited by 6
- Real.sinh_le_sinhproof · cited by 5
- ENNReal.mul_le_mul_iff_rightproof · cited by 5
- MulArchimedean.comapproof · cited by 5