proposition: Theorem rpre_hypothesis_rule : ∀ {A₀ A₁ : ord_choiceType} {p₀ : raw_code A₀} {p₁ : raw_code A₁} (pre : precond) post, (∀ s₀ s₁, pre (s₀, s₁) → ⊢ ⦃ λ s, s.1 = s₀ ∧ s.2 = s₁ ⦄ p₀ ≈ p₁ ⦃ post ⦄ ) → ⊢ ⦃ pre ⦄ p₀ ≈ p₁ ⦃ post ⦄.
proof: Proof. intros A₀ A₁ p₀ p₁ pre post h. eapply from_sem_jdg. eapply pre_hypothesis_rule. intros. eapply to_sem_jdg. apply h. 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 pkg_invariants pkg_distr) Equations.Prop.DepElim Equations(Equations) Crypt(FreeProbProg)