Theorems · Theorem · order theory
Ne.lt_of_le
∀ {α : Type u_2} [inst : PartialOrder α] {a b : α}, a ≠ b → a ≤ b → a < b- Defined in
- Mathlib.Order.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- lt_of_le_of_neproof · cited by 230
Cited by27
Results whose statement or proof uses this declaration.
- OrdinalApprox.lfpApprox_ord_mem_fixedPointproof · cited by 3
- Real.sin_sq_lt_sqproof · cited by 3
- IsChain.lt_of_leproof · cited by 2
- Real.exists_int_int_abs_mul_sub_leproof · cited by 2
- AddOreLocalization.oreSub_zero_surjective_of_finite_leftproof · cited by 2
- AddOreLocalization.oreSub_zero_surjective_of_finite_rightproof · cited by 2
- LinearGrowth.linearGrowthSup_comp_leproof · cited by 2
- Monotone.le_linearGrowthSup_compproof · cited by 2
- Int.fract_eq_zero_or_add_one_sub_ceilproof · cited by 2
- Prod.fst_eq_or_snd_eq_of_wcovByproof · cited by 2
- OreLocalization.oreDiv_one_surjective_of_finite_leftproof · cited by 2
- Monotone.linearGrowthInf_compproof · cited by 2