Theorems · Theorem · order theory
le_of_forall_pos_le_add
∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : AddMonoid α] [ExistsAddOfLE α] [AddLeftReflectLT α]
{a b : α}, (∀ (ε : α), 0 < ε → a ≤ b + ε) → a ≤ b- Cited by
- 15 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- AddMonoidstatement and proof · cited by 2,864
- LT.lt.leproof · cited by 2,189
- DenselyOrderedstatement and proof · cited by 471
- ExistsAddOfLEstatement and proof · cited by 330
- ExistsAddOfLE.exists_add_of_leproof · cited by 42
- AddLeftReflectLTstatement and proof · cited by 33
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
- pos_of_lt_add_rightproof · cited by 4
Cited by15
Results whose statement or proof uses this declaration.
- le_iff_forall_pos_le_addproof · cited by 4
- HasFDerivAt.le_of_lip'proof · cited by 4
- rieszContentAux_sup_leproof · cited by 3
- Seminorm.gauge_ballproof · cited by 2
- ContinuousWithinAt.oscillationWithin_eq_zeroproof · cited by 2
- Asymptotics.IsBigO.continuousMultilinearMap_apply_eq_zeroproof · cited by 1
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_le_Icoproof · cited by 1
- GromovHausdorff.ghDist_le_of_approx_subsetsproof · cited by 1
- MeasureTheory.LevyProkhorov.continuous_toMeasure_probabilityMeasureproof · cited by 1
- le_of_forall_neg_add_leproof · cited by 1
- KuratowskiEmbedding.embeddingOfSubset_isometryproof · cited by 1