proposition: Lemma remember_pre_pre : ∀ m pre s₀ s₁, remember_pre m pre (s₀, s₁) → pre (s₀, s₁).
proof: Proof. intros m pre s₀ s₁ h. induction m as [| [] m ih] in pre, s₀, s₁, h |- *. - auto. - simpl in h. destruct h as [h _]. eapply ih. auto. - simpl in h. destruct h as [h _]. eapply ih. 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)