fintypeOfKerLeRange — Mathlib

English

The congruence applied to mk' x gives the corresponding mk' of the image.

Русский

При конгруэнции к mk' x даёт соответствующий mk' образа.

LaTeX

$$$\\text{congr } G' H' e he (mk' G' x) = mk' H'(e x)$$$

Lean4

/-- If `F` and `H` are finite such that `ker(G →* H) ≤ im(F →* G)`, then `G` is finite. -/
@[to_additive /-- If `F` and `H` are finite such that `ker(G →+ H) ≤ im(F →+ G)`, then `G` is finite. -/
    ]
noncomputable def fintypeOfKerLeRange (h : g.ker ≤ f.range) : Fintype G :=
  @Fintype.ofEquiv _ _
    (@instFintypeProd _ _ (Fintype.ofInjective _ <| kerLift_injective g) <|
      Fintype.ofInjective _ <| inclusion_injective h)
    groupEquivQuotientProdSubgroup.symm

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