Theorems · Theorem · order theory
eq_of_mabs_div_le_one
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {a b : G}, |a / b|ₘ ≤ 1 → a = b- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, 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
- le_antisymmproof · cited by 2,068
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- mabsstatement and proof · cited by 148
- one_le_mabsproof · cited by 11
- eq_of_mabs_div_eq_oneproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- mabs_div_le_oneproof · cited by 1
- eq_of_mabs_div_le_allproof · cited by 0
- eq_of_mabs_div_lt_allproof · cited by 0