def
definition
def or abbrev
volume
show as:
view Lean formalization →
formal statement (Lean)
178def volume {V : Type*} (S : Finset V) : ℕ := S.card
proof body
Definition body.
179
180/-- In any cache, every boundary node determines the global field.
181 Therefore, the number of independent "information channels" to the
182 global state equals the surface area (boundary node count), not
183 the volume (total node count).
184
185 This theorem proves information scales with boundary size. -/
used by (40)
-
actionJ_convex_on_interp -
F_threshold -
aestronglyMeasurable_galerkinForcing_mode_of_continuous -
DuhamelKernelDominatedConvergenceAt -
duhamelKernelDominatedConvergenceAt_of_forcing -
duhamelRemainderOfGalerkin_integratingFactor -
duhamelRemainderOfGalerkin_kernel -
ForcingDominatedConvergenceAt -
ForcingDominatedConvergenceAt -
galerkin_duhamelKernel_identity -
GalerkinForcingDominatedConvergenceHypothesis -
nsDuhamelCoeffBound_galerkinKernel -
nsDuhamelCoeffBound_galerkinKernel_of_forcing -
nsDuhamelCoeffBound_galerkinKernel_of_forcingHyp -
of_convectionNormBound -
tendsto_duhamelKernelIntegral_of_dominated_convergence -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcing -
rs_implies_global_regularity_2d_nsDuhamelCoeffBound_galerkinKernel_of_forcingHyp -
CARuntime -
caTimeBound -
ca_to_tm_simulation_prop -
config_space_complete -
seam_ratio_from_topology -
total_angular_is_pi5 -
cosmologicalConstant -
costDensity -
dark_energy_dominates -
entryDensity -
isBalanced