Theorems · Theorem · order theory
mabs_of_le_one
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] {a : α} [MulLeftMono α], a ≤ 1 → |a|ₘ = a⁻¹- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- LatticeGroupMulLeftMono
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.
- Groupstatement and proof · cited by 6,238
- LE.le.transproof · cited by 3,151
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- mabsstatement · cited by 148
- sup_eq_rightproof · cited by 53
- one_le_inv'proof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- mabs_of_lt_oneproof · cited by 2
- max_div_min_eq_mabs'proof · cited by 1
- mabs_powproof · cited by 1
- inv_mabs_leproof · cited by 1
- mabs_div_le_max_divproof · cited by 0
- mabs_le_mabs_of_le_oneproof · cited by 0