proposition: Lemma lookup_op_spec_inv : ∀ (p : raw_package) id S T f, p id = Some (S ; T ; f) → lookup_op p (id, (S, T)) = Some f.
proof: Proof. intros p id S T f e. unfold lookup_op. destruct (p id) as [[S' [T' g]]|] eqn:e1. 2: discriminate. destruct choice_type_eqP. 2:{ noconf e. contradiction. } destruct choice_type_eqP. 2:{ noconf e. contradiction. } subst. noconf e. 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) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)