Theorems · Theorem · order theory
ne_of_lt
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a < b → a ≠ b- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 203 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 14 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by203
Results whose statement or proof uses this declaration.
- LT.lt.neproof · cited by 872
- MeasureTheory.measure_ne_topproof · cited by 171
- lt_iff_le_and_neproof · cited by 47
- LE.le.lt_iff_neproof · cited by 34
- IsPrimitiveRoot.isIntegralproof · cited by 15
- hasSum_geometric_of_lt_oneproof · cited by 14
- ENNReal.top_rpow_of_negproof · cited by 12
- MeasureTheory.eLpNorm_lt_top_iff_lintegral_rpow_enorm_lt_topproof · cited by 9
- Multiset.lt_cons_selfproof · cited by 8
- nhdsLT_le_nhdsNEproof · cited by 8
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- Real.rpow_def_of_negproof · cited by 7
Showing the 200 most cited of 203.