twoUniqueProds_iff — Mathlib

English

A multiplicative equivalence f: G ≃* H preserves TwoUniqueProds in both directions.

Русский

Мультивероятная эквивалентность сохраняет TwoUniqueProds в обе стороны.

LaTeX

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

Lean4

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

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