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acmepjz committed Oct 28, 2024
1 parent 8333def commit e3b75b0
Showing 1 changed file with 6 additions and 4 deletions.
10 changes: 6 additions & 4 deletions Mathlib/RingTheory/LinearDisjoint.lean
Original file line number Diff line number Diff line change
Expand Up @@ -126,12 +126,14 @@ namespace LinearDisjoint
variable (A B)

/-- The image of `R` in `S` is linearly disjoint with any other subalgebras. -/
theorem bot_left : (⊥ : Subalgebra R S).LinearDisjoint B :=
Submodule.LinearDisjoint.one_left _
theorem bot_left : (⊥ : Subalgebra R S).LinearDisjoint B := by
rw [Subalgebra.LinearDisjoint, Algebra.toSubmodule_bot]
exact Submodule.LinearDisjoint.one_left _

/-- The image of `R` in `S` is linearly disjoint with any other subalgebras. -/
theorem bot_right : A.LinearDisjoint ⊥ :=
Submodule.LinearDisjoint.one_right _
theorem bot_right : A.LinearDisjoint ⊥ := by
rw [Subalgebra.LinearDisjoint, Algebra.toSubmodule_bot]
exact Submodule.LinearDisjoint.one_right _

end LinearDisjoint

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