Theorems · Theorem · group theory
MonoidHom.pi_injective
∀ {I : Type u} {f : I → Type v} [inst : (i : I) → MulOneClass (f i)] {γ : Type w} [Nonempty I] [inst_2 : MulOneClass γ]
(g : (i : I) → γ →* f i), (∀ (i : I), Function.Injective ⇑(g i)) → Function.Injective ⇑(MonoidHom.pi g)- Defined in
- Mathlib.Algebra.Group.Pi.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- MonoidHomstatement and proof · cited by 3,629
- MulOneClassstatement and proof · cited by 1,018
- MonoidHom.pistatement · cited by 9
- MonoidHom.toMulHomproof · cited by 9
- MulHom.pi_injectiveproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.pi_injectiveproof · cited by 1
- MonoidHom.injective_piproof · cited by 0
- Pi.monoidHom_injectiveproof · cited by 0