Theorems · Theorem · order theory
one_lt_mabs
∀ {α : Type u_1} [inst : Group α] [inst_1 : LinearOrder α] [MulLeftMono α] {a : α}, 1 < |a|ₘ ↔ a ≠ 1- Cited by
- 6 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- GroupLinearOrderMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Groupstatement and proof · cited by 6,238
- LT.lt.ne'proof · cited by 1,417
- LT.lt.neproof · cited by 872
- MulLeftMonostatement and proof · cited by 410
- lt_trichotomyproof · cited by 178
- mabsstatement · cited by 148
- mabs_oneproof · cited by 5
- mabs_of_lt_oneproof · cited by 2
- mabs_of_one_ltproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Subgroup.exists_isLeast_one_ltproof · cited by 2
- mabs_ne_oneproof · cited by 1
- one_lt_mabs_of_lt_oneproof · cited by 0
- one_lt_mabs_pos_of_one_ltproof · cited by 0
- MulArchimedeanClass.mk_le_mk_iff_ltproof · cited by 0
- tendsto_mabs_nhdsNE_oneproof · cited by 0