proposition: Lemma r_bind_assertD_sym : ∀ (A B : choice_type) b k1 (k2 : _ → raw_code B), ⊢ ⦃ λ '(h₀, h₁), h₀ = h₁ ⦄ @assertD B b (λ z, x ← k1 z ;; k2 x) ≈ x ← (@assertD A b (λ z, k1 z)) ;; k2 x ⦃ eq ⦄.
proof: Proof. intros A B b k1 k2. eapply rsymmetry. eapply rsym_pre. 1: auto. eapply rpost_weaken_rule. - eapply r_bind_assertD. - intros [] []. 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)