Theorems · Theorem · order theory
le_mul_iff_one_le_right
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [PosMulMono α]
[PosMulReflectLE α], 0 < a → (a ≤ a * b ↔ 1 ≤ b)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- PosMulMonostatement and proof · cited by 165
- mul_le_mul_iff_right₀proof · cited by 38
- PosMulReflectLEstatement and proof · cited by 16
Cited by5
Results whose statement or proof uses this declaration.
- separate_convex_open_setproof · cited by 2
- Real.exists_rat_abs_sub_lt_and_lt_of_irrationalproof · cited by 1
- seminormFromBounded_of_mul_leproof · cited by 0
- FixedDetMatrices.reps_entries_le_m'proof · cited by 0
- Function.Periodic.norm_qParam_le_of_one_half_le_improof · cited by 0