theorem J_mediated_activation_linearity
{beta_n sigma_n J_n Fbar_n sigma_prev alpha : ℝ}
(hsp : sigma_prev ≠ 0) :
ngmEntryReal beta_n sigma_n (alpha * J_n) Fbar_n sigma_prev =
alpha * ngmEntryReal beta_n sigma_n J_n Fbar_n sigma_prev :=
ngmEntryReal_linear_in_J hspPaper 3c, Section 6: Hierarchical Implications