proposition: Lemma r_assertD_same : ∀ (A : choice_type) b (pre : precond) (post : postcond A A) k₀ k₁, (∀ e, ⊢ ⦃ pre ⦄ k₀ e ≈ k₁ e ⦃ post ⦄) → ⊢ ⦃ pre ⦄ #assert b as x ;; k₀ x ≈ #assert b as x ;; k₁ x ⦃ post ⦄.
proof: Proof. intros A b pre post k₀ k₁ h. eapply r_assertD. - reflexivity. - intros e₀ e₁. assert (e₀ = e₁) by eapply eq_irrelevance. subst. eapply h. 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)