proposition: Lemma Pr_eq_empty : ∀ {X Y : ord_choiceType} {A : pred (X * heap_choiceType)} {B : pred (Y * heap_choiceType)} Ψ ϕ (c1 : @FrStP heap_choiceType X) (c2 : @FrStP heap_choiceType Y), ⊨ ⦃ Ψ ⦄ c1 ≈ c2 ⦃ ϕ ⦄ → Ψ (empty_heap, empty_heap) → (∀ x y, ϕ x y → (A x) ↔ (B y)) → \P_[ θ_dens (θ0 c1 empty_heap) ] A = \P_[ θ_dens (θ0 c2 empty_heap) ] B.
proof: Proof. intros X Y A B Ψ Φ c1 c2 ? ? ?. apply (Pr_eq Ψ Φ). all: assumption. 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)