Theorems · Theorem · order theory
mabs_eq_self
∀ {G : Type u_1} [inst : CommGroup G] [inst_1 : LinearOrder G] [IsOrderedMonoid G] {a : G}, |a|ₘ = a ↔ 1 ≤ a- Defined in
- Mathlib.Algebra.Order.Group.Abs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 20 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_left_iffproof · cited by 4
- inv_le_self_iffproof · cited by 2
- mabs_eq_max_invproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.mk_antitoneOnproof · cited by 1
- MulArchimedeanClass.lt_of_mk_lt_mk_of_one_leproof · cited by 0
- MulArchimedeanClass.mulArchimedean_of_mk_eq_mkproof · cited by 0