Theorems · Theorem · order theory
mul_lt_iff_lt_one_left
∀ {α : Type u_1} [inst : MulOneClass α] [inst_1 : Zero α] {a b : α} [inst_2 : Preorder α] [MulPosStrictMono α]
[MulPosReflectLT α], 0 < b → (a * b < b ↔ a < 1)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 7 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
- one_mulproof · cited by 2,841
- MulOneClassstatement and proof · cited by 1,018
- MulPosStrictMonostatement and proof · cited by 94
- MulPosReflectLTstatement and proof · cited by 93
- mul_lt_mul_iff_left₀proof · cited by 13
Cited by3
Results whose statement or proof uses this declaration.
- Int.fract_div_mul_self_mem_Icoproof · cited by 2
- Real.cos_eq_one_iff_of_lt_of_ltproof · cited by 1
- Asymptotics.IsLittleO.eventuallyLT_norm_of_eventually_posproof · cited by 1