Theorems · Theorem · order theory
mabs_of_one_le
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] {a : α} [MulLeftMono α], 1 ≤ a → |a|ₘ = a- Cited by
- 11 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_leftproof · cited by 71
- inv_le_one'proof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- mabs_oneproof · cited by 5
- mabs_mabsproof · cited by 2
- mabs_of_one_ltproof · cited by 1
- mabs_powproof · cited by 1
- max_div_min_eq_mabs'proof · cited by 1
- inv_mabs_leproof · cited by 1
- mabs_div_le_max_divproof · cited by 0
- MulArchimedeanClass.min_le_mk_of_le_of_leproof · cited by 0
- mabs_eqproof · cited by 0
- mabs_le_mabs_of_one_leproof · cited by 0
- multipliable_mabs_iffproof · cited by 0