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Theorems · Theorem · ring theory

RingHom.pi_injective

∀ {I : Type u} {f : I → Type u_1} {γ : Type u_2} [Nonempty I] [inst : (i : I) → NonAssocSemiring (f i)]
  [inst_1 : NonAssocSemiring γ] (g : (i : I) → γ →+* f i),
  (∀ (i : I), Function.Injective ⇑(g i)) → Function.Injective ⇑(RingHom.pi g)
Defined in
Mathlib.Algebra.Ring.Pi
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
NonemptyNonAssocSemiringNonAssocSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Pi.ringHom_injective · cited by 0Pi.ringHom_injectiveDFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomNonAssocSemiring · cited by 805NonAssocSemiringRingHom.toMonoidHom · cited by 132RingHom.toMonoidHomRingHom.pi · cited by 26RingHom.piMonoidHom.pi_injective · cited by 3MonoidHom.pi_injectiveRingHom.pi_injectiveCITED BYCITES

Cites6

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Cited by1

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