proposition: Lemma update_heaps_filter_r : ∀ l s₀ s₁, (update_heaps (filter is_hpv_r l) s₀ s₁).2 = (update_heaps l s₀ s₁).2.
proof: Proof. intros l s₀ s₁. induction l as [| [] l ih] in s₀, s₁ |- *. - reflexivity. - simpl. destruct update_heaps eqn:e1. destruct (update_heaps l s₀ s₁) eqn:e2. simpl. specialize (ih s₀ s₁). rewrite e2 e1 in ih. simpl in ih. auto. - simpl. destruct update_heaps eqn:e1. destruct (update_heaps l s₀ s₁) eqn:e2. simpl. specialize (ih s₀ s₁). rewrite e2 e1 in ih. simpl in ih. subst. reflexivity. 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)