proposition: Lemma lookup_hpv_r_None_spec : ∀ ℓ l s₀ s₁ h₀ h₁, lookup_hpv_r ℓ l = None → update_heaps l s₀ s₁ = (h₀, h₁) → get_heap h₁ ℓ = get_heap s₁ ℓ.
proof: Proof. intros ℓ l s₀ s₁ h₀ h₁ hl e. funelim (lookup_hpv_r ℓ l). - simpl in e. noconf e. reflexivity. - simpl in *. destruct update_heaps eqn:e1. noconf e. eauto. - rewrite -Heqcall in hl. noconf hl. - simpl in e0. destruct update_heaps eqn:e1. noconf e0. rewrite get_set_heap_neq. 2:{ rewrite -e. auto. } rewrite -Heqcall in hl. eauto. 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)