Theorems · Theorem · order theory
NeZero.of_gt
∀ {α : Type u_1} {a b : α} [inst : Zero α] [inst_1 : Preorder α] [IsBotZeroClass α], a < b → NeZero b- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ZeroPreorderIsBotZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- IsBotZeroClassstatement and proof · cited by 71
- LT.lt.ne_zeroproof · cited by 34
Cited by8
Results whose statement or proof uses this declaration.
- Nat.totient_evenproof · cited by 4
- IsCyclotomicExtension.Rat.adjoin_singleton_eq_topproof · cited by 3
- CommGroup.monoidHom_mulEquiv_of_hasEnoughRootsOfUnityproof · cited by 2
- IsPrimitiveRoot.finite_quotient_toInteger_sub_onestatement · cited by 1
- IsPrimitiveRoot.norm_toInteger_sub_one_eq_onestatement and proof · cited by 1
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- IsPrimitiveRoot.not_coprime_norm_of_mk_eq_onestatement · cited by 1
- IsPrimitiveRoot.prime_dvd_of_dvd_norm_sub_onestatement and proof · cited by 1