Theorems · Theorem · order theory
div_lt_div_iff_of_pos_left
∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] [inst_1 : PartialOrder G₀] [PosMulReflectLT G₀] [MulPosReflectLT G₀]
{a b c : G₀}, 0 < a → 0 < b → 0 < c → (a / b < a / c ↔ c < b)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- GroupWithZerostatement and proof · cited by 691
- PosMulReflectLTstatement and proof · cited by 278
- MulPosReflectLTstatement and proof · cited by 93
- lt_iff_lt_of_le_iff_le'proof · cited by 26
- div_le_div_iff_of_pos_leftproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- one_div_lt_one_divproof · cited by 4
- div_lt_div_of_pos_leftproof · cited by 2
- FormalMultilinearSeries.lt_radius_of_isBigOproof · cited by 0