Theorems · Theorem · order theory
le_of_forall_one_lt_le_mul
∀ {α : Type u} [inst : LinearOrder α] [DenselyOrdered α] [inst_2 : Monoid α] [ExistsMulOfLE α] [MulLeftReflectLT α]
{a b : α}, (∀ (ε : α), 1 < ε → a ≤ b * ε) → a ≤ b- Cited by
- 3 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
- Monoidstatement and proof · cited by 3,887
- LT.lt.leproof · cited by 2,189
- DenselyOrderedstatement and proof · cited by 471
- le_of_forall_gt_imp_ge_of_denseproof · cited by 21
- MulLeftReflectLTstatement and proof · cited by 16
- ExistsMulOfLEstatement and proof · cited by 14
- ExistsMulOfLE.exists_mul_of_leproof · cited by 7
- one_lt_of_lt_mul_rightproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- le_of_forall_one_lt_lt_mul'proof · cited by 1
- le_iff_forall_one_lt_le_mulproof · cited by 1
- le_of_forall_lt_one_mul_leproof · cited by 1