proposition: Lemma rrewrite_eqDistrR : ∀ {A₀ A₁ : ord_choiceType} {P Q} (c₀ : raw_code A₀) (c₁ c₁' : raw_code A₁), ⊢ ⦃ P ⦄ c₀ ≈ c₁ ⦃ Q ⦄ → (∀ s, θ_dens (θ0 (repr c₁) s) = θ_dens (θ0 (repr c₁') s)) → ⊢ ⦃ P ⦄ c₀ ≈ c₁' ⦃ Q ⦄.
proof: Proof. intros A₀ A₁ P Q c₀ c₁ c₁' h hθ. eapply to_sem_jdg in h. eapply from_sem_jdg. eapply rewrite_eqDistrR. all: eauto. 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 pkg_advantage pkg_invariants pkg_distr) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)