Theorems · Theorem · order theory
le_mul_of_one_le_right
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [PosMulMono α],
0 ≤ a → 1 ≤ b → a ≤ a * b- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- mul_oneproof · cited by 3,885
- MulOneClassstatement and proof · cited by 1,018
- mul_le_mul_of_nonneg_leftproof · cited by 361
- PosMulMonostatement and proof · cited by 165
Cited by15
Results whose statement or proof uses this declaration.
- pow_right_mono₀proof · cited by 19
- one_le_mul_of_one_le_of_one_leproof · cited by 11
- zpow_right_mono₀proof · cited by 4
- Polynomial.finiteMultiplicity_of_degree_pos_of_monicproof · cited by 3
- one_lt_mul_of_lt_of_leproof · cited by 3
- UpperHalfPlane.dist_self_centerproof · cited by 2
- ContinuousOn.isBigOWith_rev_principalproof · cited by 1
- GaussianInt.norm_le_norm_mul_leftproof · cited by 1
- le_iff_forall_one_lt_le_mul₀proof · cited by 1
- WeakFEPair.hf_zero'proof · cited by 1
- Nat.prime_pow_pow_totient_ediv_prodproof · cited by 1
- LinearMap.bound_of_ball_boundproof · cited by 0