proposition: Lemma preserve_update_couple_lhs_lookup : ∀ ℓ ℓ' (R : _ → _ → Prop) v v' (l : seq heap_val) m, lookup_hpv_l ℓ l = Some v → lookup_hpv_l ℓ' l = Some v' → R v v' → preserve_update_mem l m (couple_lhs ℓ ℓ' R).
proof: Proof. intros ℓ ℓ' R v v' l m hl hr h. intros s₀ s₁ hh. unfold couple_lhs in *. destruct update_heaps eqn:e. erewrite lookup_hpv_l_spec. 2,3: eauto. erewrite lookup_hpv_l_spec. 2,3: eauto. 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)