Theorem: ContinuousLinearMap.sum_comp_single_apply (ForML/ContinuousLinearMapCo.lean)

State before:
ι : Type u_1
R : Type u_2
inst✝¹⁰ : Fintype ι
inst✝⁹ : DecidableEq ι
inst✝⁸ : NontriviallyNormedField R
M₁ : Type u_3
M₂ : Type u_4
inst✝⁷ : NormedAddCommGroup M₁
inst✝⁶ : NormedSpace R M₁
inst✝⁵ : NormedAddCommGroup M₂
inst✝⁴ : NormedSpace R M₂
M : ι → Type u_5
inst✝³ : (i : ι) → NormedAddCommGroup (M i)
inst✝² : (i : ι) → NormedSpace R (M i)
F : Type u_6
inst✝¹ : NormedAddCommGroup F
inst✝ : NormedSpace R F
f : ((i : ι) → M i) →L[R] F
x : (i : ι) → M i
⊢ ∑ j : ι, (comp f (single j)) (x j) = f x
Tactic:
simp
State after:
no goals