Theorems · Theorem · group theory
MulHom.pi_injective
∀ {I : Type u} {f : I → Type v} [inst : (i : I) → Mul (f i)] {γ : Type w} [Nonempty I] [inst_2 : Mul γ]
(g : (i : I) → γ →ₙ* f i), (∀ (i : I), Function.Injective ⇑(g i)) → Function.Injective ⇑(MulHom.pi g)- Defined in
- Mathlib.Algebra.Group.Pi.Lemmas
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- MulHomstatement and proof · cited by 299
- MulHom.pistatement and proof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- MonoidHom.pi_injectiveproof · cited by 3
- NonUnitalRingHom.pi_injectiveproof · cited by 1
- MulHom.injective_piproof · cited by 0
- Pi.mulHom_injectiveproof · cited by 0