invertibleAlgebraCoeNat — Mathlib

English

A natural number that is invertible in R remains invertible in any R-algebra via the scalar tower.

Русский

Единица, числo Nat, обратима в R, сохраняет обратимость при переходе в любой R-алгебра через башню скаляров.

LaTeX

$$$$ \text{invertibleAlgebraCoeNat}(n) : Invertible (n: A) $$$$

Lean4

/-- A natural number that is invertible when coerced to `R` is also invertible
when coerced to any `R`-algebra. -/
def invertibleAlgebraCoeNat (n : ℕ) [inv : Invertible (n : R)] : Invertible (n : A) :=
  haveI : Invertible (algebraMap ℕ R n) := inv
  Invertible.algebraTower ℕ R A n

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