proposition: Lemma restore_update_mem : ∀ l m pre s₀ s₁, update_pre l (remember_pre m pre) (s₀, s₁) → preserve_update_mem l m pre → pre (s₀, s₁).
proof: Proof. intros l m pre s₀ s₁ hu hp. eapply update_pre_spec in hu. destruct hu as [s₀' [s₁' [hpre e]]]. rewrite e. eapply hp. 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)