English
If hv is iSupIndep for the family of submodules generated by {v_i} and each v_i has trivial torsion, then the family v is linearly independent over R.
Русский
Если hv задаёт iSupIndep для семейства подмодулей, порождённых v_i, и каждый v_i не имеет torsion, тогда семейство v линейно независимо над R.
LaTeX
$$linearIndependent' (hv) (h_ne_zero) : LinearIndependent_R v$$
Lean4
/-- A torsion module is a module where every element is `a`-torsion for some non-zero-divisor `a`.
-/
abbrev IsTorsion :=
∀ ⦃x : M⦄, ∃ a : R⁰, a • x = 0