proposition: Lemma destruct_pair_eq {R : ringType} {A B : eqType} {a b : A} {c d : B} : ((a, c) == (b, d))%:R = (a == b)%:R * (c == d)%:R :> R.
proof: Proof. destruct (a == b) eqn:ab, (c == d) eqn:cd. all: cbn; rewrite ab cd /=; try rewrite GRing.mulr1; try rewrite GRing.mulr0; 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)