proposition: Lemma ReductionLem : ∀ L₀ L₁ E M (G : GamePair) `{ValidPackage L₀ Game_import E (M ∘ G false)} `{ValidPackage L₁ Game_import E (M ∘ G true)}, (M ∘ (G false)) ≈[ λ A, Advantage G (A ∘ M) ] (M ∘ (G true)).
proof: Proof. intros L₀ L₁ E M G v₀ v₁. unfold adv_equiv. intros LA A vA hd₀ hd₁. rewrite Advantage_E. unfold AdvantageE. rewrite !link_assoc. reflexivity. 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)