proposition: Lemma rcoupling_eq : ∀ {A : ord_choiceType} (K₀ K₁ : raw_code A) (ψ : precond), ⊢ ⦃ ψ ⦄ K₀ ≈ K₁ ⦃ eq ⦄ → ∀ s₀ s₁, ψ (s₀, s₁) → θ_dens (θ0 (repr K₀) s₀) = θ_dens (θ0 (repr K₁) s₁).
proof: Proof. intros A K₀ K₁ ψ h s₀ s₁ hψ. eapply to_sem_jdg in h. eapply coupling_eq. 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)