isUnit_of_isUnit_ι — Mathlib

English

Equivalence between isUnit of ι_Q(m) and isUnit of Q(m), assuming 2 is invertible in the base ring.

Русский

Эквивалентность: IsUnit(ι_Q(m)) ⇔ IsUnit(Q(m)) при условии обратимости 2 в кольце базы.

LaTeX

$$isUnit_of_isUnit_ι(Q,m)$$

Lean4

theorem isUnit_of_isUnit_ι {m : M} (h : IsUnit (ι Q m)) : IsUnit (Q m) :=
  by
  cases h.nonempty_invertible
  letI := invertibleOfInvertibleι Q m
  exact isUnit_of_invertible (Q m)

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