proposition: Lemma r_transL : ∀ {A₀ A₁ : ord_choiceType} {P Q} (c₀ c₀' : raw_code A₀) (c₁ : raw_code A₁), ⊢ ⦃ λ '(s₀, s₁), s₀ = s₁ ⦄ c₀ ≈ c₀' ⦃ eq ⦄ → ⊢ ⦃ P ⦄ c₀ ≈ c₁ ⦃ Q ⦄ → ⊢ ⦃ P ⦄ c₀' ≈ c₁ ⦃ Q ⦄.
proof: Proof. intros A₀ A₁ P Q c₀ c₀' c₁ he h. eapply rrewrite_eqDistrL. 1: exact h. intro s. eapply rcoupling_eq. 1: exact he. cbn. 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 pkg_lookup pkg_advantage pkg_invariants pkg_distr) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)