English
From a mul-invariant pseudodistance on a commutative group, one obtains a NormedCommGroup via a separations condition, with mul_comm included.
Русский
Из муль-инвариантного псеводистанцирования на комм-группе получается NormedCommGroup при условии разделения и добавляется mul_comm.
LaTeX
$$$\text{NormedCommGroup.ofMulDist } h$ yields a NormedCommGroup with mul_comm := mul_comm.$$
Lean4
/-- Construct a normed group from a multiplication-invariant pseudodistance. -/
@[to_additive /-- Construct a normed group from a translation-invariant pseudodistance. -/
]
abbrev ofMulDist [Norm E] [CommGroup E] [MetricSpace E] (h₁ : ∀ x : E, ‖x‖ = dist x 1)
(h₂ : ∀ x y z : E, dist x y ≤ dist (x * z) (y * z)) : NormedCommGroup E :=
{ NormedGroup.ofMulDist h₁ h₂ with mul_comm := mul_comm }
-- See note [reducible non-instances]
