[Merged by Bors] - feat(analysis/convex/specific_functions): elementary convexity proofs #19026
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RemyDegenne
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RemyDegenne
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RemyDegenne
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Maybe add some comments to the lemmas where you give an elementary proof instead of the second derivative test, explaining that we use an elementary proof for import reasons? |
eric-wieser
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| have hxy' : 0 < y - x := by linarith, | ||
| have hxz' : 0 < z - x := by linarith, |
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I assume you're deliberately avoiding
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| have hxy' : 0 < y - x := by linarith, | |
| have hxz' : 0 < z - x := by linarith, | |
| have hxy' : 0 < y - x := sub_pos_of_lt hxy, | |
| have hxz' : 0 < z - x := sub_pos_of_lt (hxy.trans hyz), |
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I prefer the automation, someday I will write a linear_combination_for_inequalities which is fast but avoids calling the lemmas by name ...
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bors merge |
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…#19026) Give elementary proofs for the convexity of `pow`, `zpow`, `exp`, `log` and `rpow`, avoiding the second derivative test. See [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Shortcut.20to.20integration)
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Split `analysis/convex/specific_function` into a part which doesn't require differentiation (as of #19026) and a part which does. This removes the dependence of `measure_theory/integral/bochner` on differentiation, and decreases by 11 the length of the longest path in mathlib. See [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Shortcut.20to.20integration)
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Split `analysis/convex/specific_function` into a part which doesn't require differentiation (as of #19026) and a part which does. This removes the dependence of `measure_theory/integral/bochner` on differentiation, and decreases by 11 the length of the longest path in mathlib. See [Zulip](https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Shortcut.20to.20integration) Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
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Fiddly, not done yet ... help welcome. Cross-reference: leanprover-community/mathlib#19026. Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>
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Fiddly, not done yet ... help welcome. Cross-reference: leanprover-community/mathlib#19026. Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>
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Give elementary proofs for the convexity of
pow,zpow,exp,logandrpow, avoiding the second derivative test.See Zulip