proposition: Lemma r_ret : ∀ {A₀ A₁ : ord_choiceType} u₀ u₁ (pre : precond) (post : postcond A₀ A₁), (∀ s₀ s₁, pre (s₀, s₁) → post (u₀, s₀) (u₁, s₁)) → ⊢ ⦃ pre ⦄ ret u₀ ≈ ret u₁ ⦃ post ⦄.
proof: Proof. intros A₀ A₁ u₀ u₁ pre post h. eapply from_sem_jdg. simpl. eapply weaken_rule. 1: eapply ret_rule. intros [s₀ s₁] P [hpre hpost]. simpl. eapply hpost. eapply h. apply hpre. 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)