Theorems · Theorem · order theory
LT.lt.ne
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → a ≠ bAlias of ne_of_lt.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 872 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 14 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
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Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by872
Results whose statement or proof uses this declaration.
- ne_top_of_le_ne_topproof · cited by 68
- ne_top_of_ltproof · cited by 50
- abs_posproof · cited by 45
- MeasureTheory.dominatedFinMeasAdditive_cbmApplyMeasureproof · cited by 31
- Fin.castSucc_castPredproof · cited by 23
- Monotone.strictMono_of_injectiveproof · cited by 22
- Eq.not_ltproof · cited by 22
- MeasureTheory.Measure.rnDeriv_lt_topproof · cited by 21
- MeasureTheory.Lp.eLpNorm_ne_topproof · cited by 20
- edist_ne_topproof · cited by 17
- Set.VAddAntidiagonal.finite_of_isPWOproof · cited by 16
- MeasureTheory.MemLp.eLpNorm_ne_topproof · cited by 16
Showing the 200 most cited of 872.