Theorems · Theorem · order theory
Order.IsNormal.monotone
∀ {α : Type u_1} {β : Type u_2} [inst : LinearOrder α] [inst_1 : LinearOrder β] {f : α → β},
Order.IsNormal f → Monotone f- Defined in
- Mathlib.Order.IsNormal
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrderLinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Monotonestatement · cited by 1,397
- StrictMono.monotoneproof · cited by 118
- Order.IsNormalstatement and proof · cited by 118
- Order.IsNormal.strictMonoproof · cited by 44
Cited by11
Results whose statement or proof uses this declaration.
- Ordinal.veblenWith_posproof · cited by 2
- Ordinal.add_eq_right_iff_mul_omega0_leproof · cited by 2
- Ordinal.le_iff_derivFamilyproof · cited by 2
- Ordinal.nfp_mul_opow_omega0_addproof · cited by 1
- Ordinal.eq_zero_or_opow_omega0_le_of_mul_eq_rightproof · cited by 1
- Ordinal.IsFundamentalSeq.comp_isNormalproof · cited by 0
- Ordinal.nfp_mul_eq_opow_omega0proof · cited by 0
- Ordinal.apply_le_nfpproof · cited by 0
- Ordinal.apply_le_nfpFamilyproof · cited by 0
- Ordinal.nfp_add_eq_mul_omega0proof · cited by 0
- Ordinal.monotone_gammaproof · cited by 0