one_right — Mathlib

English

M is linearly disjoint with the image of R in S, i.e., 1-contributive submodule, under standard identifications.

Русский

M линейно несовместим с образом 1 в S, то есть с образной подмодулей.

LaTeX

$$M.LinearDisjoint (1 : Submodule R S)$$

Lean4

/-- The image of `R` in `S` is linearly disjoint with any other submodules. -/
theorem one_right : M.LinearDisjoint (1 : Submodule R S) :=
  by
  rw [linearDisjoint_iff, ← Algebra.toSubmodule_bot, mulMap_one_right_eq]
  exact M.injective_subtype.comp M.rTensorOne.injective

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