proposition: Lemma preserve_update_cons_sym_eq : ∀ ℓ v l m, preserve_update_mem l m (λ '(h₀, h₁), h₀ = h₁) → preserve_update_mem (hpv_r ℓ v :: hpv_l ℓ v :: l) m (λ '(h₀, h₁), h₀ = h₁).
proof: Proof. intros ℓ v l m h. intros s₀ s₁ e. simpl. destruct update_heaps eqn:e'. eapply h in e as h'. rewrite e' in h'. 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)