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[Merged by Bors] - chore(LinearAlgebra/Finsupp/LinearCombination) : restore order of two lemmas #22713

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[Merged by Bors] - chore(LinearAlgebra/Finsupp/LinearCombination) : restore order of two lemmas #22713

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30 changes: 15 additions & 15 deletions Mathlib/LinearAlgebra/Finsupp/LinearCombination.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -67,6 +67,21 @@ theorem linearCombination_single (c : R) (a : α) :
theorem linearCombination_zero_apply (x : α →₀ R) : (linearCombination R (0 : α → M)) x = 0 := by
simp [linearCombination_apply]

variable (α M)

@[simp]
theorem linearCombination_zero : linearCombination R (0 : α → M) = 0 :=
LinearMap.ext (linearCombination_zero_apply R)

@[simp]
theorem linearCombination_single_index (c : M) (a : α) (f : α →₀ R) [DecidableEq α] :
linearCombination R (Pi.single a c) f = f a • c := by
rw [linearCombination_apply, sum_eq_single a, Pi.single_eq_same]
· exact fun i _ hi ↦ by rw [Pi.single_eq_of_ne hi, smul_zero]
· exact fun _ ↦ by simp only [single_eq_same, zero_smul]

variable {α M}

theorem linearCombination_linear_comp (f : M →ₗ[R] M') :
linearCombination R (f ∘ v) = f ∘ₗ linearCombination R v := by
ext
Expand Down Expand Up @@ -251,21 +266,6 @@ theorem linearCombination_onFinset {s : Finset α} {f : α → R} (g : α → M)
contrapose! h
simp [h]

variable (α M)

@[simp]
theorem linearCombination_zero : linearCombination R (0 : α → M) = 0 :=
LinearMap.ext (linearCombination_zero_apply R)

@[simp]
theorem linearCombination_single_index (c : M) (a : α) (f : α →₀ R) [DecidableEq α] :
linearCombination R (Pi.single a c) f = f a • c := by
rw [linearCombination_apply, sum_eq_single a, Pi.single_eq_same]
· exact fun i _ hi ↦ by rw [Pi.single_eq_of_ne hi, smul_zero]
· exact fun _ ↦ by simp only [single_eq_same, zero_smul]

variable {α M}

variable [Module S M] [SMulCommClass R S M]

variable (S) in
Expand Down
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