Theorems · Theorem · order theory
le_iff_forall_one_lt_le_mul
∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : Monoid α] [ExistsMulOfLE α] [MulLeftReflectLT α]
{a b : α} [MulLeftStrictMono α], a ≤ b ↔ ∀ (ε : α), 1 < ε → a ≤ b * ε- Cited by
- 1 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
- Monoidstatement and proof · cited by 3,887
- LT.lt.leproof · cited by 2,189
- DenselyOrderedstatement and proof · cited by 471
- MulLeftStrictMonostatement and proof · cited by 146
- MulLeftReflectLTstatement and proof · cited by 16
- ExistsMulOfLEstatement and proof · cited by 14
- lt_mul_of_le_of_one_ltproof · cited by 4
- le_of_forall_one_lt_le_mulproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- le_iff_forall_lt_one_mul_leproof · cited by 0