English
toWord maps a free group element to a representative word obtained by reducing a chosen representative list; it is defined as the quotient-lift of reduce equalities along equal representatives.
Русский
toWord переводит элемент свободной группы в представительное слово, полученное редукцией выбранного представителя; определён через переход по эквивалентностям в фактор-группе.
LaTeX
$$$$\mathrm{toWord}: \mathrm{FreeGroup}(\alpha) \to \mathrm{List}(\alpha \times \{0,1\})\quad\text{is the quotient-lift of }\operatorname{reduce}.$$$$
Lean4
/-- The function that sends an element of the free group to its maximal reduction. -/
@[to_additive /-- The function that sends an element of the additive free group to its maximal
reduction. -/
]
def toWord : FreeGroup α → List (α × Bool) :=
Quot.lift reduce fun _L₁ _L₂ H => reduce.Step.eq H
