toNonUnitalRingHomm_comp_symm_toNonUnitalRingHom

English

The composition of e.toNonUnitalRingHom with e.symm.toNonUnitalRingHom equals the identity on the target.

Русский

Состав e.toNonUnitalRingHom и e.symm.toNonUnitalRingHom равен единице на целевом кольце.

LaTeX

$$$$ e.toNonUnitalRingHom .\\circ e.symm.toNonUnitalRingHom = \\mathrm{id}_{S}. $$$$

Lean4

@[simp]
theorem toNonUnitalRingHomm_comp_symm_toNonUnitalRingHom (e : R ≃+* S) :
    e.toNonUnitalRingHom.comp e.symm.toNonUnitalRingHom = NonUnitalRingHom.id _ :=
  by
  ext
  simp

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