Theorems · Theorem · order theory
mabs_div_le_iff
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {a b c : G},
|a / b|ₘ ≤ c ↔ a / b ≤ c ∧ b / a ≤ c- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- mabsstatement · cited by 148
- div_le_iff_le_mul'proof · cited by 3
- mabs_leproof · cited by 3
- inv_le_div_iff_le_mulproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- div_le_of_mabs_div_le_leftproof · cited by 1
- mabs_div_le_of_le_of_leproof · cited by 0
- mabs_div_le_of_one_le_of_leproof · cited by 0
- mabs_mabs_div_mabs_le_mabs_divproof · cited by 0