castHom — Mathlib

English

The universe of SignType is exactly {0, -1, 1} in finite type terms.

Русский

Область SignType состоит ровно из элементов 0, -1, 1 в конечном наборе.

LaTeX

$$$(\text{Finset.univ} : \text{Finset SignType}) = \{0, -1, 1\}$$$

Lean4

/-- `SignType.cast` as a `MulWithZeroHom`. -/
@[simps]
def castHom {α} [MulZeroOneClass α] [HasDistribNeg α] : SignType →*₀ α
    where
  toFun := cast
  map_zero' := rfl
  map_one' := rfl
  map_mul' x y := by cases x <;> cases y <;> simp [zero_eq_zero, pos_eq_one, neg_eq_neg_one]

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