Zulip Chat Archive

Stream: mathlib4

Topic: potential simp lemmas


Johan Commelin (Jun 02 2025 at 17:02):

Should these type of lemmas be tagged @[simp]?

/-- See `inner_smul_left_eq_star_smul` for the case of a general algebra action. -/
theorem inner_smul_left (x y : E) (r : 𝕜) : r  x, y = r * x, y :=
  inner_smul_left_eq_star_smul ..

theorem real_inner_smul_left (x y : F) (r : ) : r  x, y⟫_ = r * x, y⟫_ :=
  inner_smul_left _ _ _

theorem inner_smul_real_left (x y : E) (r : ) : (r : 𝕜)  x, y = r  x, y := by
  rw [inner_smul_left, conj_ofReal, Algebra.smul_def]

/-- See `inner_smul_right_eq_smul` for the case of a general algebra action. -/
theorem inner_smul_right (x y : E) (r : 𝕜) : x, r  y = r * x, y :=
  inner_smul_right_eq_smul ..

theorem real_inner_smul_right (x y : F) (r : ) : x, r  y⟫_ = r * x, y⟫_ :=
  inner_smul_right _ _ _

theorem inner_smul_real_right (x y : E) (r : ) : x, (r : 𝕜)  y = r  x, y := by
  rw [inner_smul_right, Algebra.smul_def]

https://github.com/leanprover-community/mathlib4/blob/5a2eaa85c555c4263e15928cef249cbaad2eb2d2/Mathlib/Analysis/InnerProductSpace/Basic.lean#L109-L111

Jovan Gerbscheid (Jun 02 2025 at 17:17):

I agree. But real_inner_smul_right and real_inner_smul_left need not be tagged if you tag inner_smul_right and inner_smul_left


Last updated: Dec 20 2025 at 21:32 UTC