Add massOn empty simp lemma#4
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Xinze-Li-Moqian merged 1 commit intoMay 13, 2026
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…d + vanishing + eq_at Five new lemmas mirroring the Z-slot machinery for the first slot of riemannCurvature. The X-slot scalar Leibniz has clean cancellation (no h_interior required, no curvature correction): the Y(f) boundary contributions from the inner-section Leibniz pair against the Lie-bracket smul-Leibniz with opposite sign. * `riemannCurvature_smul_first_scalar_field`: R(f•X, Y) Z x = f x • R(X, Y) Z x * `riemannCurvature_add_first`: R(X+X', Y) Z = R(X, Y) Z + R(X', Y) Z * `riemannCurvature_eq_of_X_eventuallyEq`: X =ᶠ X' near x ⇒ R(X, Y) Z x = R(X', Y) Z x * `riemannCurvature_eq_zero_of_X_eq_zero_field`: X x = 0 ⇒ R(X, Y) Z x = 0 * `riemannCurvature_eq_of_X_eq_at`: X x = X' x ⇒ R(X, Y) Z x = R(X', Y) Z x Same chart-frame + bump + induction template as Z-slot vanishing, using `mlieBracket_smul_left` and `mlieBracket_add_left` for the direction-slot Leibniz rules. Item #4 in the Bochner closure plan (Z-slot chain #1-#3 already landed).
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Summary
Adds a small localized-mass API lemma for varifolds:
@[simp] theorem Varifold.massOn_emptyVarifold.massOn_univtheorem as@[simp]This is a small follow-up to the zero-varifold API and makes
massOnnormalize on the two basic sets.Validation
lake build OpenGALib.GeometricMeasureTheory.Varifoldlake build