Entropic BSG on finite weighted spaces: restrict to support for a.s. identities

When proving Tao's entropic BSG (sum_z P[Z=z] d(A|z;B|z) <= 3I[A:B]+2H[Z]-H[A]-H[B]) with conditionally independent trials glued along Z=A+B, the key identity A1-B2 = A2-B1 only holds on the support of the glued weight, so plain submodularity (which needs C = f(A) pointwise) does not apply. Fix: prove once that entropy is unchanged by restricting to the subtype {w // mu w != 0} (push-forward along Subtype.val), then derive almost-sure versions of submodularity and congruence for free. The conditional-law identity is easiest via the auxiliary weight mu'(w1,w2) = [Z w1 = z][Z w2 = z] mu w1 mu w2 / p_Z(z)^2: the product of conditional laws is its push-forward along (A w1, B w2), and the glued joint law is p_Z(z) times it; with x/0 = 0 no case split on p_Z(z) = 0 is needed except at the very end.