English
Britton's lemma for HNN extensions: any reduced word representing an element of the base group G contains no occurrences of the stable letter t.
Русский
Лемма Британтона для HNN-расширений: любое редуцированное слово, представляющее элемент базовой группы, не содержит ни одной буквы t.
LaTeX
$$$w$ reduced word with $w.prod φ \\in G$ implies $w.toList = []$ (no t appearing).$$
Lean4
/-- The index of a subgroup as a natural number. Returns `0` if the index is infinite. -/
@[to_additive /-- The index of an additive subgroup as a natural number.
Returns 0 if the index is infinite. -/
]
noncomputable def index : ℕ :=
Nat.card (G ⧸ H)
