of_right_le_one_of_flat — Mathlib

English

If N is basis of N and M is LI, M,N linearly disjoint, then the product-matrix basis yields independence.

Русский

Если N базис N и M линейно независим, то произведение базисов образует независимую систему.

LaTeX

$$M.LinearDisjoint N$$

Lean4

/-- If `M` is flat, `N` is contained in `i(R)`, where `i : R → S` is the structure map,
then `M` and `N` are linearly disjoint. -/
theorem of_right_le_one_of_flat (h : N ≤ 1) [Module.Flat R M] : M.LinearDisjoint N :=
  (one_right M).of_le_right_of_flat h

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