Theorems · Theorem · order theory
le_iff_forall_pos_le_add
∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : AddMonoid α] [ExistsAddOfLE α] [AddLeftReflectLT α]
{a b : α} [AddLeftStrictMono α], a ≤ b ↔ ∀ (ε : α), 0 < ε → a ≤ b + ε- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 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
- AddLeftStrictMonostatement and proof · cited by 203
- AddLeftReflectLTstatement and proof · cited by 33
- le_of_forall_pos_le_addproof · cited by 15
- lt_add_of_le_of_posproof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- contentRegular_rieszContentproof · cited by 3
- NNRealRMK.le_rieszMeasure_of_isCompact_tsupport_subsetproof · cited by 1
- RealRMK.le_rieszMeasure_tsupport_subsetproof · cited by 0
- le_iff_forall_neg_add_leproof · cited by 0