rangeRestrict — Mathlib

English

The product of the top subrings on both sides is equal to the top: (⊤ : NonUnitalSubring R).prod (⊤ : NonUnitalSubring S) = ⊤.

Русский

Произведение верхних подполь слева и справа равно верхнему: ⊤.prod ⊤ = ⊤.

LaTeX

$$$(\top : NonUnitalSubring R).prod (\top : NonUnitalSubring S) = \top$$$

Lean4

/-- Restriction of a ring homomorphism to its range interpreted as a `NonUnitalSubring`.

This is the bundled version of `Set.rangeFactorization`. -/
def rangeRestrict (f : R →ₙ+* S) : R →ₙ+* f.range :=
  NonUnitalRingHom.codRestrict f f.range fun x => ⟨x, rfl⟩

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