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is_derive1_sqrt lemma #1679
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is_derive1_sqrt lemma #1679
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remove comments point missing
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the proof script can be compressed a lot (@affeldt-aist will be good at that) |
t6s
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looks good
CohenCyril
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I didn't have time to finish the review
Thanks for the contribution. I had a small remark.
| Lemma sqrK {K : rcfType} : {in Num.pos, cancel (@Num.sqrt K) (fun x => x ^+ 2)}. | ||
| Proof. by move=> r r0; rewrite sqr_sqrtr// ltW. Qed. |
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This looks redundant with sqr_sqrt, (and slightly weaker since Num.pos can be weakened to Num.nneg).
If kept, it should be generalized and renamed sqrtK (the prefix of a K lemma is the section / thing being cancelled)
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Sorry for having been too hasty, will fix asap in a new PR.
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(an in the long run, we should actually replace sqr_sqrt which has an equivalent statement written in an expanded way and which name is not as canonical as sqrtK)
Co-authored with @affeldt-aist
Motivation for this change
This PR introduces the lemma is_derive1_sqrt, establishing the derivability of the square root function at any strictly positive real number and provides its derivative formula.
This result is essential to prove of the derivability of the norm function and such calculations.
Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
Merge policy
As a rule of thumb:
all compile are preferentially merged into master.
Reminder to reviewers