unitsEquivIsUnitSubmonoid — Mathlib

English

There is a noncomputable equivalence between the units within S and the submonoid IsUnit.submonoid S.

Русский

Существует неконп computable эквивалентность между единицами внутри S и подмоном IsUnit.submonoid S.

LaTeX

$$$ S.units \simeq_* IsUnit.submonoid S $$$

Lean4

/-- The equivalence between the subgroup of units of `S` and the submonoid of unit
elements of `S`. -/
@[to_additive /-- The equivalence between the additive subgroup of additive units of
    `S` and the additive submonoid of additive unit elements of `S`. -/
    ]
noncomputable def unitsEquivIsUnitSubmonoid (S : Submonoid M) : S.units ≃* IsUnit.submonoid S :=
  S.unitsEquivUnitsType.trans unitsTypeEquivIsUnitSubmonoid

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