proposition: Lemma preserve_update_filter_couple_rhs : ∀ ℓ ℓ' R l m, preserve_update_mem (filter is_hpv_r l) m (couple_rhs ℓ ℓ' R) → preserve_update_mem l m (couple_rhs ℓ ℓ' R).
proof: Proof. intros ℓ ℓ' R l m h. intros s₀ s₁ hh. eapply h in hh. destruct update_heaps eqn:e1. destruct (update_heaps l s₀ s₁) eqn:e2. apply (f_equal (λ x, x.2)) in e1. rewrite update_heaps_filter_r in e1. rewrite e2 in e1. simpl in e1. subst. 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) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)