SatisfiesCompositionLaw is the predicate asserting that a cost functional F satisfies the Recognition Composition Law. In the canon it is equivalent to CoshAddIdentity via the theorem composition_law_equiv_coshAdd. For Jcost the property holds because Jcost_cosh_add_identity establishes the cosh-add identity and the equivalence is applied in the opposite direction.
Explicitly: let F = Jcost. Then (composition_law_equiv_coshAdd Jcost).2 Jcost_cosh_add_identity yields SatisfiesCompositionLaw Jcost. This is the hypothesis hComp in unique_cost_on_pos_from_rcl, which together with reciprocal symmetry, normalization, calibration and continuity forces F = Jcost on (0, ∞) by reducing to the d'Alembert equation whose unique continuous solution with the given second derivative at zero is cosh, hence Jcost after the log reparametrization G and H.