refactor(analysis/convex): simplify proofs, use implicit args and dot notation #1804
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… notation * Use dot notation. * Swap LHS and RHS of `image_Icc_zero_one_eq_segment`. * Introduce `finset.center_mass`, prove basic properties. * Deduce Jensen's inequality from the corresponding property of convex sets; rename corresponding lemmas.
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Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr>
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… notation (leanprover-community#1804) * feat(data/set/intervals): add `nonempty_Icc` etc, `image_(add/mul)_(left/right)_Icc` * refactor(analysis/convex): simplify proofs, use implicit args and dot notation * Use dot notation. * Swap LHS and RHS of `image_Icc_zero_one_eq_segment`. * Introduce `finset.center_mass`, prove basic properties. * Deduce Jensen's inequality from the corresponding property of convex sets; rename corresponding lemmas. * Fix a typo Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr> * Update src/analysis/convex.lean
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… notation (leanprover-community#1804) * feat(data/set/intervals): add `nonempty_Icc` etc, `image_(add/mul)_(left/right)_Icc` * refactor(analysis/convex): simplify proofs, use implicit args and dot notation * Use dot notation. * Swap LHS and RHS of `image_Icc_zero_one_eq_segment`. * Introduce `finset.center_mass`, prove basic properties. * Deduce Jensen's inequality from the corresponding property of convex sets; rename corresponding lemmas. * Fix a typo Co-Authored-By: sgouezel <sebastien.gouezel@univ-rennes1.fr> * Update src/analysis/convex.lean
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Depends on #1803
image_Icc_zero_one_eq_segment.finset.center_mass, prove basic properties.sets; rename corresponding lemmas.
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