proposition: Lemma rsymmetry : ∀ {A₀ A₁ : ord_choiceType} {pre : precond} {post} {c₀ : raw_code A₀} {c₁ : raw_code A₁}, ⊢ ⦃ λ '(h₁, h₀), pre (h₀, h₁) ⦄ c₁ ≈ c₀ ⦃ λ '(a₁, h₁) '(a₀, h₀), post (a₀, h₀) (a₁, h₁) ⦄ → ⊢ ⦃ pre ⦄ c₀ ≈ c₁ ⦃ post ⦄.
proof: Proof. intros A₀ A₁ pre post c₀ c₁ h. eapply from_sem_jdg. eapply symmetry_rule. eapply to_sem_jdg. 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)