proposition: Lemma Advantage_triangle_chain : ∀ P (l : seq raw_package) Q A, AdvantageE P Q A <= advantage_sum P l Q A.
proof: Proof. intros P l Q A. induction l as [| R l ih] in P, Q |- *. - simpl. auto. - simpl. eapply order.Order.POrderTheory.le_trans. + eapply Advantage_triangle. + eapply ler_add. * auto. * eapply ih. Qed.
imports: Coq(Utf8) Relational(OrderEnrichedCategory OrderEnrichedRelativeMonadExamples) mathcomp(ssrnat ssreflect ssrfun ssrbool ssrnum eqtype choice reals distr seq all_algebra fintype realsum) extructures(ord fset fmap) Mon(SPropBase) Crypt(Prelude Axioms ChoiceAsOrd SubDistr Couplings RulesStateProb UniformStateProb UniformDistrLemmas StateTransfThetaDens StateTransformingLaxMorph choice_type pkg_core_definition pkg_notation pkg_tactics pkg_composition pkg_heap pkg_semantics pkg_lookup) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)