inr — Mathlib

English

Equality of inr after translating through inrₗ with units.

Русский

Равенство inr после перевода через inrℓ с единицами.

LaTeX

$$$inr = inr_ℓ$ на соответствующих типах.$$

Lean4

/-- Given linearly ordered groups with zero M, N, the natural inclusion ordered homomorphism from
N to `WithZero (Mˣ ×ₗ Nˣ)`, which is the linearly ordered group with zero that can be identified
as their product. -/
@[simps!]
nonrec def inr : β →*₀o WithZero (αˣ ×ₗ βˣ)
    where
  __ := (WithZero.map' (toLexMulEquiv ..).toMonoidHom).comp (inr α β)
  monotone' := by simpa using (WithZero.map'_mono (Prod.Lex.toLex_mono)).comp inr_mono

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