Theorems · Theorem · order theory
mabs_mul_le
∀ {α : Type u_1} [inst : Lattice α] [inst_1 : CommGroup α] [MulLeftMono α] (a b : α), |a * b|ₘ ≤ |a|ₘ * |b|ₘThe absolute value satisfies the triangle inequality.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- LatticeCommGroupMulLeftMono
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommGroupstatement and proof · cited by 990
- Latticestatement and proof · cited by 916
- MulLeftMonostatement and proof · cited by 410
- mul_le_mul'proof · cited by 274
- sup_leproof · cited by 159
- mabsstatement and proof · cited by 148
- mul_invproof · cited by 50
- le_mabs_selfproof · cited by 5
- inv_le_mabsproof · cited by 4
Cited by7
Results whose statement or proof uses this declaration.
- MulArchimedeanClass.min_le_mk_mulproof · cited by 4
- mabs_div_mabs_le_mabs_divproof · cited by 2
- mabs_mul'proof · cited by 1
- mabs_mul_threeproof · cited by 0
- mabs_divproof · cited by 0
- mabs_mabs_div_mabs_leproof · cited by 0
- mabs_div_leproof · cited by 0