uniqueProds_iff — Mathlib

English

A multiplicative equivalence between G and H preserves the UniqueProds property: UniqueProds G iff UniqueProds H.

Русский

Умножительная эквивалентность между G и H сохраняет свойство UniqueProds: UniqueProds G эквивалентно UniqueProds H.

LaTeX

$$$ \\forall f:\\, G \\simeq^* H,\\; \\mathrm{UniqueProds}(G) \\iff \\mathrm{UniqueProds}(H). $$$

Lean4

/-- `UniqueProd` is preserved under multiplicative equivalences. -/
@[to_additive /-- `UniqueSums` is preserved under additive equivalences. -/
    ]
theorem _root_.MulEquiv.uniqueProds_iff (f : G ≃* H) : UniqueProds G ↔ UniqueProds H :=
  ⟨of_injective_mulHom f.symm f.symm.injective, of_injective_mulHom f f.injective⟩

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