proposition: Lemma preserve_update_cons_sym_heap_ignore : ∀ L ℓ v l m, preserve_update_mem l m (heap_ignore L) → preserve_update_mem (hpv_r ℓ v :: hpv_l ℓ v :: l) m (heap_ignore L).
proof: Proof. intros L ℓ v l m h. intros s₀ s₁ hh. simpl. destruct update_heaps eqn:e. intros ℓ₀ hℓ₀. destruct (ℓ₀ != ℓ) eqn:e1. - rewrite !get_set_heap_neq. 2,3: auto. eapply h in hh. rewrite e in hh. apply hh. auto. - move: e1 => /eqP e1. subst. rewrite !get_set_heap_eq. 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)