[Merged by Bors] - feat(Analysis/Calculus/{Iterated}Deriv/*): add lemmas on composition with negation #11173
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MichaelStollBayreuth
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For the new lemmas on iterated derivatives to work, the file they are in needs to import |
MichaelStollBayreuth
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LGTM maintainer merge |
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π Pull request has been placed on the maintainer queue by loefflerd. |
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β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
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Pull request successfully merged into master. Build succeeded: |
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kbuzzard
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β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
dagurtomas
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β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
utensil
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β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
Louddy
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Apr 15, 2024
β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
callesonne
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Apr 22, 2024
β¦with negation (#11173) This adds ```lean lemma deriv_comp_neg (f : π β F) (a : π) : deriv (fun x β¦ f (-x)) a = -deriv f (-a) /-- A variant of `deriv_const_smul` without differentiability assumption when the scalar multiplication is by field elements. -/ lemma deriv_const_smul' {f : π β F} {x : π} {R : Type*} [Field R] [Module R F] [SMulCommClass π R F] [ContinuousConstSMul R F] (c : R) : deriv (fun y β¦ c β’ f y) x = c β’ deriv f x lemma iteratedDeriv_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ -(f x)) a = -(iteratedDeriv n f a) lemma iteratedDeriv_comp_neg (n : β) (f : π β F) (a : π) : iteratedDeriv n (fun x β¦ f (-x)) a = (-1 : π) ^ n β’ iteratedDeriv n f (-a) ``` which will come in handy in some future PRs on L-series. See [here](https://leanprover.zulipchat.com/#narrow/stream/144837-PR-reviews/topic/L-series/near/424858837) on Zulip.
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This adds
which will come in handy in some future PRs on L-series.
See here on Zulip.