expand' — Mathlib

English

For any index i and g ∈ M(i), the order of Pi.mulSingle i g equals the order of g.

Русский

Для любого индекса i и элемента g ∈ M(i) порядок Pi.mulSingle i g равен порядку g.

LaTeX

$$orderOf (Pi.mulSingle i g) = orderOf g$$

Lean4

/-- A fraction is equal to its expansion by a factor from `S`. -/
@[to_additive /-- A difference is equal to its expansion by a summand from `S`. -/
    ]
protected theorem expand' (r : X) (s s' : S) : r /ₒ s = s' • r /ₒ (s' * s) :=
  OreLocalization.expand r s s' (by norm_cast; apply SetLike.coe_mem)

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