normal_prob cont./reproductive property#1955
Open
affeldt-aist wants to merge 2 commits into
Open
Conversation
affeldt-aist
added
the
enhancement ✨
Co-authored-by: IshiguroYoshihiro <jb.15r.1213@s.thers.ac.jp>
affeldt-aist
force-pushed
the
normal_20260426
branch
from
8d9f595 to
ccb6ba0
Compare
IshiguroYoshihiro
approved these changes
May 18, 2026
Collaborator
IshiguroYoshihiro
left a comment
IshiguroYoshihiro
left a comment
There was a problem hiding this comment.
It looks good for me.
I think there is some room for generalization on auxiliary lemmas, but I don't think it need to block this PR.
|
|
||
| End normal_probability. | ||
|
|
||
| Section ge0_integration_by_substitution_shift. |
Collaborator
There was a problem hiding this comment.
I think it's better to move this section to ftc.v.
Comment on lines
+87
to
+88
| Lemma normal_fun_shift m s x : | ||
| normal_fun (shift m x) s (shift m x) = normal_fun m s m. |
Collaborator
There was a problem hiding this comment.
this can be generalized.
Lemma normal_fun_shift m s x t :
normal_fun (shift m t) s (shift x t) = normal_fun m s x.
Proof. by rewrite [in LHS]/normal_fun/= (addrC t x) addrKA. Qed.
| Proof. by apply/funext => x/=; rewrite /normal_fun/= subr0. Qed. | ||
|
|
||
| Definition normal_peak s := (sqrtr (s ^+ 2 * pi *+ 2))^-1. | ||
| Lemma normal_funN m s : normal_fun (- m) s (- m) = normal_fun m s m. |
Collaborator
There was a problem hiding this comment.
This lemma can be generalized.
Lemma normal_funN m s x : normal_fun (- m) s (- x) = normal_fun m s x.
Proof. by rewrite /normal_fun -opprD sqrrN. Qed.
Comment on lines
+83
to
+84
| Lemma normal_fun_center_new m s x : | ||
| normal_fun (center m x) s (center m x) = normal_fun m s m. |
Collaborator
There was a problem hiding this comment.
this can be generalized and have simple proof using normal_fun_shift.
Lemma normal_fun_center_new m s x t:
normal_fun (center m t) s (center x t) = normal_fun m s x.
Proof. by rewrite normal_fun_shift normal_funN. Qed.
Comment on lines
+142
to
+148
| Lemma normal_pdf0_center m s x : | ||
| normal_pdf0 (center m x) s (center m x) = normal_pdf0 m s m. | ||
| Proof. by rewrite /normal_pdf0 normal_fun_center_new. Qed. | ||
|
|
||
| Lemma normal_pdf0_shift m s x : | ||
| normal_pdf0 (shift m x) s (shift m x) = normal_pdf0 m s m. | ||
| Proof. by rewrite /normal_pdf0 normal_fun_shift. Qed. |
Collaborator
There was a problem hiding this comment.
these lemmas also can be generalized.
Lemma normal_pdf0_center m s x t :
normal_pdf0 (center m t) s (center x t) = normal_pdf0 m s x.
Proof. by rewrite /normal_pdf0 normal_fun_center_new. Qed.
Lemma normal_pdf0_shift m s x t :
normal_pdf0 (shift m t) s (shift x t) = normal_pdf0 m s x.
Proof. by rewrite /normal_pdf0 normal_fun_shift. Qed.
|
|
||
| End normal_prob_lemmas. | ||
|
|
||
| Section emeasurable_bounded_integrable. |
Collaborator
There was a problem hiding this comment.
I think that this section have to be moved to lebesgue_integral_theory/lebesgue_integrable.v.
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
2 participants
Add this suggestion to a batch that can be applied as a single commit.This suggestion is invalid because no changes were made to the code.Suggestions cannot be applied while the pull request is closed.Suggestions cannot be applied while viewing a subset of changes.Only one suggestion per line can be applied in a batch.Add this suggestion to a batch that can be applied as a single commit.Applying suggestions on deleted lines is not supported.You must change the existing code in this line in order to create a valid suggestion.Outdated suggestions cannot be applied.This suggestion has been applied or marked resolved.Suggestions cannot be applied from pending reviews.Suggestions cannot be applied on multi-line comments.Suggestions cannot be applied while the pull request is queued to merge.Suggestion cannot be applied right now. Please check back later.
Motivation for this change
This PR provides a proof of the continuity of
normal_proband of the reproductiveproperty of normal distribution:
This is taken from the PR #1712
and it relies on the
fieldtactic (fyi: @proux01 )Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
Merge policy
As a rule of thumb:
all compile are preferentially merged into master.
Reminder to reviewers