isSolvableAdd — Mathlib

English

The equality of underlying sets of derived series holds consistently when passing from R to ℤ, i.e., the coefficients do not affect the set-theoretic realization of the derived series.

Русский

Эквивалентность множества производящих серий при переходе от кольца R к целым ℤ сохраняется на уровне множеств.

LaTeX

$$$(\mathrm{derivedSeries} \ R \ L \ k : Set L) = (\mathrm{derivedSeries} \ ℤ \ L \ k : Set L)$$$

Lean4

instance isSolvableAdd {I J : LieIdeal R L} [IsSolvable I] [IsSolvable J] : IsSolvable (I + J) :=
  by
  obtain ⟨k, hk⟩ := IsSolvable.solvable R I
  obtain ⟨l, hl⟩ := IsSolvable.solvable R J
  exact IsSolvable.mk (LieIdeal.derivedSeries_add_eq_bot hk hl)

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