proposition: Lemma rsamplerC_sym' : ∀ {A : ord_choiceType} (o : Op) (c : raw_code A), ⊢ ⦃ λ '(h₀, h₁), h₀ = h₁ ⦄ a ← c ;; r ← (r ← sample o ;; ret r) ;; (ret (r, a)) ≈ r ← (r ← sample o ;; ret r) ;; a ← c ;; (ret (r, a)) ⦃ eq ⦄.
proof: Proof. intros A o c. unshelve eapply rswap_ruleR. - auto. - intros a r. apply rsym_pre. 1: auto. apply rreflexivity_rule. - apply rsamplerC. 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)