Theorems · Theorem · order theory
pos_of_gt
∀ {α : Type u_1} {a b : α} [inst : Preorder α] [inst_1 : Zero α] [IsBotZeroClass α], a < b → 0 < b- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PreorderZeroIsBotZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- LE.le.trans_ltproof · cited by 795
- zero_leproof · cited by 382
- IsBotZeroClassstatement and proof · cited by 71
Cited by24
Results whose statement or proof uses this declaration.
- LT.lt.posproof · cited by 30
- Polynomial.iterate_derivative_eq_zeroproof · cited by 3
- AddCircle.ergodic_zsmulproof · cited by 2
- ArithmeticFunction.vonMangoldt_sumproof · cited by 2
- padicNorm.padicNorm_pproof · cited by 2
- Polynomial.sub_one_pow_totient_lt_cyclotomic_evalproof · cited by 2
- Finset.sum_Ico_by_partsproof · cited by 2
- bernsteinPolynomial.iterate_derivative_at_0proof · cited by 2
- Nat.card_units_zmod_lt_sub_oneproof · cited by 1
- Nat.exists_infinite_pseudoprimesproof · cited by 1
- IsPrimePow.posproof · cited by 1
- Behrend.map_eq_iffproof · cited by 1