Theorems · Theorem · order theory
mabs_eq_inv_self
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {a : G}, |a|ₘ = a⁻¹ ↔ a ≤ 1- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 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
- CommGroupstatement and proof · cited by 990
- IsOrderedMonoidstatement and proof · cited by 577
- mabsstatement · cited by 148
- max_eq_right_iffproof · cited by 5
- mabs_eq_max_invproof · cited by 2
- le_inv_self_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.lt_of_mk_lt_mk_of_le_oneproof · cited by 1
- MulArchimedeanClass.mk_monotoneOnproof · cited by 0