proposition: Lemma rsamplerC'_cmd : ∀ {A : ord_choiceType} (o : Op) (c : command A), ⊢ ⦃ λ '(h₀, h₁), h₀ = h₁ ⦄ r ← sample o ;; a ← cmd c ;; ret (r, a) ≈ a ← cmd c ;; r ← sample o ;; ret (r, a) ⦃ eq ⦄.
proof: Proof. intros A o c. eapply rsymmetry. eapply rsym_pre. 1: auto. eapply rpost_weaken_rule. - apply rsamplerC_sym'_cmd. - intros [? ?] [? ?] e. inversion e. intuition auto. 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)