9h (part 1): lift remaining RiemannCurvature theorems to explicit g#42
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…re(At) / _symmetric to explicit g
…eep proof cascade)
…ure) to explicit g - IsKilling predicate now takes (g : RiemannianMetric I M) - IsKilling.second_covDeriv_inner_skew lifted; local scalar var g renamed to kw_g to avoid shadowing the section g - second_covDeriv_commutator lifted - IsKilling.second_covDeriv_eq_curvature lifted All HasMetric.metric body refs replaced with g; metricInner abbrev calls with g.metricInner; metricInner_X lemma calls with g.metricInner_X. Internal callers within RiemannCurvature.lean updated to pass g.
The proof routes through ⟪·,·⟫_ℝ = hm.metric.inner via the InnerProductSpace instance derived from [HasMetric I M], so ricci_symm cannot be lifted for arbitrary g without InnerProductSpace restructure. Use subst hg pattern: caller passes g and proof of g = hm.metric, body works in hm.metric form. BochnerExpansion caller updated to pass (HasMetric.metric, rfl). RiemannCurvature.lean is now fully explicit-g for all theorems with at most this trivial hg sidecar.
This was referenced May 19, 2026
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Summary
9h — lift
Curvature/RiemannCurvature.leanfrom typeclass-boundHasMetric.metricto explicit(g : RiemannianMetric I M)parameters.Lifted theorems / defs
riemannCurvature_metric_skewriemannCurvature_inner_self_zeroriemannCurvature_pair_symmbianchi_first,_antisymm,_metric_skewsectionalCurvature(def)sectionalCurvatureAt(def)sectionalCurvature_symmetricIsFlat(predicate)IsKilling(predicate)IsKilling.second_covDeriv_inner_skewg : M → ℝrenamed tokw_gto avoid section-var shadowsecond_covDeriv_commutatorIsKilling.second_covDeriv_eq_curvaturericci_symmhg : g = hm.metric)LinearMap.trace_eq_sum_innerover⟪·,·⟫_ℝ = hm.metric.innerties tohm.metric; lift usessubst hgto bridge to typeclass formAfter this PR
RiemannCurvature.leanis fully explicit-g (5 residualHasMetric.metricoccurrences are in docstrings / cross-references, not in theorem bodies).Bochner caller update
Operators/Bochner/BochnerExpansion.leanline 421 caller updated fromricci_symm WV GV x h_interiortoricci_symm HasMetric.metric rfl WV GV x h_interior.Deferred
Bochner stack body lifts (
BochnerExpansion.lean179 sites,PerSummand.lean183 sites,Bochner.lean77 sites) — depend on lifting SmoothOrthoFrame wrappers (also have InnerProductSpace tie). Separate effort.Test plan
lake buildclean per commit