Part of umbrella #9. Sub-task 9e — consumer migration.
Scope
Files (3):
OpenGALib/Comparison/BishopGromov/VolumeComparison.lean
OpenGALib/Riemannian/Volume/VolumeForm.lean
OpenGALib/GeometricMeasureTheory/Variation/SecondVariation.lean
After 9a–9d, the entire Riemannian-side stack has explicit `g`. The final consumer-facing surfaces still depend on `[HasMetric I M]` typeclass — this sub-issue migrates them.
Changes
For each consumer file:
- Drop `[HasMetric I M]` from section variables.
- Add `(g : RiemannianMetric I M)` as explicit theorem parameter (or section parameter, depending on convention).
- Replace `dV_g[(HasMetric.metric : RiemannianMetric I M)]` style with `dV_g[g]` (clean once `g` is explicit).
- Bishop–Gromov signature becomes:
theorem bishopGromov_volume_comparison
(g : RiemannianMetric I M) (hRic : ...)
(p : M) ... :
dV_g[g].real B(p, R) / V_K^n_M(R) ≤ dV_g[g].real B(p, r) / V_K^n_M(r)
— `g` is finally a first-class term in the most important Comparison theorem.
Acceptance
- Build clean.
- Sorry count unchanged.
- BG / VolumeForm / SecondVariation signatures show `g` as explicit parameter.
- No verbose
(HasMetric.metric : RiemannianMetric I M)\ workaround anywhere in the three files.
Dependencies
Requires #17 (9d) merged first.
See also
#9 umbrella · prev: 9d (#17) · next: 9f (notation infrastructure removal)
Part of umbrella #9. Sub-task 9e — consumer migration.
Scope
Files (3):
OpenGALib/Comparison/BishopGromov/VolumeComparison.leanOpenGALib/Riemannian/Volume/VolumeForm.leanOpenGALib/GeometricMeasureTheory/Variation/SecondVariation.leanAfter 9a–9d, the entire Riemannian-side stack has explicit `g`. The final consumer-facing surfaces still depend on `[HasMetric I M]` typeclass — this sub-issue migrates them.
Changes
For each consumer file:
Acceptance
(HasMetric.metric : RiemannianMetric I M)\workaround anywhere in the three files.Dependencies
Requires #17 (9d) merged first.
See also
#9 umbrella · prev: 9d (#17) · next: 9f (notation infrastructure removal)