Assouad's lower bound. For a finite-VC class, ⌊log₂ VCDim⌋ ≤ VCDim(dualClass): the exponential blow-up under dualization is necessary, not merely permitted. Together with the proven upper bound vcDim_dualClass_le (VCDim(dual) ≤ 2^(VCDim+1) − 1) this sandwiches the dual VC dimension between ⌊log₂ d⌋ and 2^(d+1) − 1.

Stated with d := VCDim C extracted as a natural number (finite by hypothesis). The proof picks a shattered set T with 2^(log₂ d) ≤ |T| (which exists because 2^(log₂ d) ≤ d ≤ |T| for the supremal shattered set) and applies pow_le_vcDim_imp_le_vcDim_dualClass.