isTorsion — Mathlib

English

Torsion submonoids are torsion.

Русский

Торовые подмножества являются торовыми.

LaTeX

$$IsTorsion (torsion G)$$

Lean4

/-- Torsion submonoids are torsion. -/
@[to_additive /-- Additive torsion submonoids are additively torsion. -/
    ]
theorem isTorsion : IsTorsion <| torsion G := fun ⟨x, n, npos, hn⟩ =>
  ⟨n, npos,
    Subtype.ext <| by
      dsimp
      rw [mul_left_iterate]
      change _ * 1 = 1
      rw [_root_.mul_one, SubmonoidClass.coe_pow, Subtype.coe_mk, (isPeriodicPt_mul_iff_pow_eq_one _).mp hn]⟩

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