Theorems · Theorem · order theory
LT.lt.ne_zero
∀ {α : Type u_1} {a b : α} [inst : Preorder α] [inst_1 : Zero α] [IsBotZeroClass α], a < b → b ≠ 0Alias of ne_zero_of_lt.
- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- PreorderZeroIsBotZeroClass
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 · cited by 7,952
- IsBotZeroClassstatement · cited by 71
- ne_zero_of_ltproof · cited by 17
Cited by34
Results whose statement or proof uses this declaration.
- NeZero.of_gtproof · cited by 8
- CategoryTheory.SimplicialObject.δ_comp_σ_of_gt'statement and proof · cited by 6
- WithZeroMulInt.toNNReal_strictMonostatement and proof · cited by 4
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- Valued.isClosed_closedBallproof · cited by 4
- SimplexCategory.δ_comp_σ_of_gt'statement and proof · cited by 4
- Valuation.isClosed_closedBallproof · cited by 4
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroproof · cited by 3
- ContinuousLinearMap.exists_lt_apply_of_lt_opNNNormproof · cited by 3
- CategoryTheory.SimplicialObject.δ_comp_δ'statement and proof · cited by 2
- Ordinal.mul_add_div_mulproof · cited by 2
- SimplexCategory.δ_comp_δ'statement and proof · cited by 2