[Merged by Bors] - feat(analysis/convex/specific_functions): log is concave #5508
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dupuisf
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Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
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hrmacbeth
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Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
…ncave' into dupuisf_log_is_concave
hrmacbeth
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hrmacbeth
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| { intros x hx, | ||
| rw [function.iterate_succ, function.iterate_one], | ||
| change (deriv (deriv log)) x ≤ 0, | ||
| rw [deriv_log', deriv_inv (show x ≠ 0, by {rintro rfl, exact lt_irrefl 0 hx})], | ||
| exact neg_nonpos.mpr (inv_nonneg.mpr (pow_two_nonneg x)) } |
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I just wrote a quick PR #5521, which will let this be simplified to
{ intros x hx,
simp [function.iterate_succ, function.iterate_one, pow_two_nonneg] }
Let's not hold your PR up for this though.
hrmacbeth
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Co-authored-by: hrmacbeth <25316162+hrmacbeth@users.noreply.github.com>
…ncave' into dupuisf_log_is_concave
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This PR proves that the real log is concave on `Ioi 0` and `Iio 0`, and adds lemmas about concavity of functions along the way. Co-authored-by: Frédéric Dupuis <31101893+dupuisf@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
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This PR proves that the real log is concave on
Ioi 0andIio 0, and adds lemmas about concavity of functions along the way.