diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index 46e67a0e4..6f1bdbb83 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -264,6 +264,13 @@ (use `emeasurable_itv` instead) - in `measure.v`: + lemma `measurable_fun_ext` +- in `realsum.v`: + + `psumB`, `interchange_sup`, `interchange_psum` +- in `distr.v`: + + `dlet_lim`, `dlim_let`, `exp_split`, `exp_dlet`, + `dlet_dlet`, `dmargin_dlet`, `dlet_dmargin`, + `dfst_dswap`, `dsnd_dswap`, `dsndE`, `pr_dlet`, + `exp_split`, `exp_dlet` ### Removed diff --git a/theories/altreals/distr.v b/theories/altreals/distr.v index ab093e019..e7744c7dc 100644 --- a/theories/altreals/distr.v +++ b/theories/altreals/distr.v @@ -504,7 +504,7 @@ End BindTheory. Section DLetDLet. Context {T U V : choiceType} (f1 : T -> distr U) (f2 : U -> distr V). -Lemma dlet_dlet (mu : {distr T / R}) : +Lemma __deprecated__dlet_dlet (mu : {distr T / R}) : \dlet_(x <- \dlet_(y <- mu) f1 y) f2 x =1 \dlet_(y <- mu) (\dlet_(x <- f1 y) f2 x). Proof. @@ -512,7 +512,7 @@ move=> z; unlock dlet => /=; rewrite /mlet /=. pose S y x := mu x * (f1 x y * f2 y z). rewrite (eq_psum (F2 := fun y => psum (S^~ y))) => [x|]. by rewrite -psumZ //; apply/eq_psum => y /=. -rewrite interchange_psum. +rewrite __admitted__interchange_psum. + by move=> x; apply/summableZ/summable_mlet. + rewrite {}/S; apply/(le_summable (F2 := mu)) => //. move=> x; rewrite ge0_psum /= psumZ ?ler_pimulr //. @@ -680,17 +680,24 @@ move/dcvg_homo: mn_f => /dcvgP /(_ x) [l _]. by move=> cv; rewrite (nlimE cv). Qed. -Lemma dlet_lim f h : (forall n m, (n <= m)%N -> f n <=1 f m) -> +Lemma __admitted__dlet_lim f h : (forall n m, (n <= m)%N -> f n <=1 f m) -> \dlet_(x <- dlim f) h x =1 \dlim_(n) \dlet_(x <- f n) h x. Proof. Admitted. -Lemma dlim_let (f : nat -> T -> {distr U / R}) (mu : {distr T / R}) : +Lemma __admitted__dlim_let (f : nat -> T -> {distr U / R}) (mu : {distr T / R}) : (forall x n m, (n <= m)%N -> f n x <=1 f m x) -> \dlim_(n) \dlet_(x <- mu) (f n x) =1 \dlet_(x <- mu) \dlim_(n) (f n x). Proof using Type. Admitted. End DLimTheory. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__dlet_lim explicitly if you really want to use this lemma")] +Notation dlet_lim := __admitted__dlet_lim. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__dlim_let explicitly if you really want to use this lemma")] +Notation dlim_let := __admitted__dlim_let. + (* -------------------------------------------------------------------- *) Section Marginals. Variable (T U : choiceType) (h : T -> U) (mu : distr T). @@ -712,16 +719,16 @@ rewrite dmarginE dletE; apply/eq_psum => x //=. by rewrite mulrC dunit1E. Qed. -Lemma dlet_dmargin (mu : {distr T / R}) (f : T -> U) (g : U -> {distr V / R}): +Lemma __deprecated__dlet_dmargin (mu : {distr T / R}) (f : T -> U) (g : U -> {distr V / R}): \dlet_(u <- dmargin f mu) g u =1 \dlet_(t <- mu) (g (f t)). Proof. -move=> x; rewrite dlet_dlet; apply: eq_in_dlet=> //. +move=> x; rewrite __deprecated__dlet_dlet; apply: eq_in_dlet=> //. by move=> y _ z; rewrite dlet_unit. Qed. -Lemma dmargin_dlet (mu : {distr T / R}) (f : U -> V) (g : T -> {distr U / R}): +Lemma __deprecated__dmargin_dlet (mu : {distr T / R}) (f : U -> V) (g : T -> {distr U / R}): dmargin f (\dlet_(t <- mu) g t) =1 \dlet_(t <- mu) (dmargin f (g t)). -Proof. by apply/dlet_dlet. Qed. +Proof. by apply/__deprecated__dlet_dlet. Qed. Lemma dmargin_dunit (t : T) (f : T -> U): dmargin f (dunit t) =1 dunit (f t) :> {distr U / R}. @@ -729,6 +736,16 @@ Proof. by apply/dlet_unit. Qed. End MarginalsTh. End Std. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dlet_dlet explicitly if you really want to use this lemma")] +Notation dlet_dlet := __deprecated__dlet_dlet. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dmargin_dlet explicitly if you really want to use this lemma")] +Notation dmargin_dlet := __deprecated__dmargin_dlet. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dlet_dmargin explicitly if you really want to use this lemma")] +Notation dlet_dmargin := __deprecated__dlet_dmargin. + Notation dfst mu := (dmargin fst mu). Notation dsnd mu := (dmargin snd mu). @@ -770,19 +787,26 @@ Proof. by move=> h; apply/dinsuppP; rewrite dswapE; apply/dinsuppPn. Qed. -Lemma dfst_dswap : dfst (dswap mu) =1 dsnd mu. +Lemma __deprecated__dfst_dswap : dfst (dswap mu) =1 dsnd mu. Proof. -move=> z; rewrite dlet_dlet; apply/eq_in_dlet => // -[x y]. +move=> z; rewrite __deprecated__dlet_dlet; apply/eq_in_dlet => // -[x y]. by move=> _ t /=; rewrite dlet_unit /=. Qed. -Lemma dsnd_dswap : dsnd (dswap mu) =1 dfst mu. +Lemma __deprecated__dsnd_dswap : dsnd (dswap mu) =1 dfst mu. Proof. -move=> z; rewrite dlet_dlet; apply/eq_in_dlet => // -[x y]. +move=> z; rewrite __deprecated__dlet_dlet; apply/eq_in_dlet => // -[x y]. by move=> _ t /=; rewrite dlet_unit /=. Qed. End DSwapTheory. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dfst_dswap explicitly if you really want to use this lemma")] +Notation dfst_dswap := __deprecated__dfst_dswap. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dsnd_dswap explicitly if you really want to use this lemma")] +Notation dsnd_dswap := __deprecated__dsnd_dswap. + (* -------------------------------------------------------------------- *) Section DFst. Context {R : realType} {T U : choiceType}. @@ -812,9 +836,9 @@ End DFst. Section DSnd. Context {R : realType} {T U : choiceType}. -Lemma dsndE (mu : {distr (T * U) / R}) y : +Lemma __deprecated__dsndE (mu : {distr (T * U) / R}) y : dsnd mu y = psum (fun x => mu (x, y)). -Proof. by rewrite -dfst_dswap dfstE; apply/eq_psum=> x; rewrite dswapE. Qed. +Proof. by rewrite -__deprecated__dfst_dswap dfstE; apply/eq_psum=> x; rewrite dswapE. Qed. Lemma summable_snd (mu : {distr (T * U) / R}) y : summable (fun x => mu (x, y)). @@ -824,6 +848,10 @@ by move=> x /=; rewrite dswapE. Qed. End DSnd. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__dsndE explicitly if you really want to use this lemma")] +Notation dsndE := __deprecated__dsndE. + (* -------------------------------------------------------------------- *) Section PrCoreTheory. Context {R : realType} {T : choiceType}. @@ -929,7 +957,7 @@ Context {R : realType} {T U : choiceType} {I : eqType}. Implicit Types (mu : {distr T / R}) (A B E : pred T). -Lemma pr_dlet E f (mu : {distr U / R}) : +Lemma __deprecated__pr_dlet E f (mu : {distr U / R}) : \P_[dlet f mu] E = \E_[mu] (fun x => \P_[f x] E). Proof. rewrite /esp -psum_sum => [x|]; first by rewrite mulr_ge0 ?ge0_pr. @@ -937,7 +965,7 @@ rewrite /pr; unlock dlet => /=; rewrite /mlet /=. pose F x y := (E x)%:R * (mu y * f y x). transitivity (psum (fun x => psum (fun y => F x y))); rewrite {}/F. by apply/eq_psum => x; rewrite -psumZ ?ler0n. -rewrite interchange_psum /=; last first. +rewrite __admitted__interchange_psum /=; last first. apply/eq_psum=> y /=; rewrite mulrC -psumZ //. by apply/eq_psum=> x /=; rewrite mulrCA. + have := summable_pr E (dlet f mu); apply/eq_summable. @@ -948,7 +976,7 @@ Qed. Lemma pr_dmargin E f (mu : {distr U / R}) : \P_[dmargin f mu] E = \P_[mu] [pred x | f x \in E]. Proof. -by rewrite /dmargin pr_dlet pr_exp; apply/eq_exp=> x _; rewrite pr_dunit. +by rewrite /dmargin __deprecated__pr_dlet pr_exp; apply/eq_exp=> x _; rewrite pr_dunit. Qed. Lemma eq0_pr A mu : @@ -1134,7 +1162,7 @@ move=> x mux; move/pr_eq0: zPB' => /(_ x) h; rewrite !inE. by apply/negP=> /andP[_ /h] /dinsuppP. Qed. -Lemma exp_split A f mu : \E?_[mu] f -> \E_[mu] f = +Lemma __admitted__exp_split A f mu : \E?_[mu] f -> \E_[mu] f = \P_[mu] A * \E_[mu, A] f + \P_[mu] (predC A) * \E_[mu, predC A] f. Proof using Type. Admitted. @@ -1174,12 +1202,22 @@ move=> ge0M bd; apply/(@le_trans _ _ (\E_[mu] (fun _ => M))). by rewrite exp_cst ler_pimull // le1_pr. Qed. -Lemma exp_dlet mu (nu : T -> {distr U / R}) F : +Lemma __admitted__exp_dlet mu (nu : T -> {distr U / R}) F : (forall eta, \E?_[eta] F) -> \E_[dlet nu mu] F = \E_[mu] (fun x => \E_[nu x] F). Proof using Type*. Admitted. End PrTheory. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="relies on admitted, use __deprecated__pr_dlet explicitly if you really want to use this lemma")] +Notation pr_dlet := __deprecated__pr_dlet. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__exp_split explicitly if you really want to use this lemma")] +Notation exp_split := __admitted__exp_split. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__exp_dlet explicitly is you really want to use this lemma")] +Notation exp_dlet := __admitted__exp_dlet. + (* -------------------------------------------------------------------- *) Section Jensen. Context {R : realType} {I : finType}. diff --git a/theories/altreals/realsum.v b/theories/altreals/realsum.v index 43ec07ada..7b9989a0e 100644 --- a/theories/altreals/realsum.v +++ b/theories/altreals/realsum.v @@ -821,7 +821,7 @@ rewrite /D big_split /=; apply/ler_add; apply/big_fset_subset=> //. Qed. (* -------------------------------------------------------------------- *) -Lemma psumB S1 S2 : +Lemma __admitted__psumB S1 S2 : (forall x, 0 <= S2 x <= S1 x) -> summable S1 -> psum (S1 \- S2) = (psum S1 - psum S2). Proof using Type. Admitted. @@ -909,6 +909,10 @@ by rewrite eq_le le_psum /=; apply/gerfinseq_psum. Qed. End StdSum. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__psumB explicitly if you really want to")] +Notation psumB := __admitted__psumB. + (* -------------------------------------------------------------------- *) Section PSumReindex. Context {R : realType} {T U : choiceType}. @@ -1098,7 +1102,7 @@ End PSumPair. Section SupInterchange. Context {R : realType} {T U : Type}. -Lemma interchange_sup (S : T -> U -> R) : +Lemma __admitted__interchange_sup (S : T -> U -> R) : (forall x, has_sup [set r | exists y, r = S x y]) -> has_sup [set r | exists x, r = sup [set r | exists y, r = S x y]] -> sup [set r | exists x, r = sup [set r | exists y, r = S x y]] @@ -1106,17 +1110,25 @@ Lemma interchange_sup (S : T -> U -> R) : Proof using Type. Admitted. End SupInterchange. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__interchange_sup explicitly if you really want to use this lemma")] +Notation interchange_sup := __admitted__interchange_sup. + (* -------------------------------------------------------------------- *) Section PSumInterchange. Context {R : realType} {T U : choiceType}. -Lemma interchange_psum (S : T -> U -> R) : +Lemma __admitted__interchange_psum (S : T -> U -> R) : (forall x, summable (S x)) -> summable (fun x => psum (fun y => S x y)) -> psum (fun x => psum (fun y => S x y)) = psum (fun y => psum (fun x => S x y)). Proof using Type. Admitted. End PSumInterchange. +#[deprecated(since="mathcomp-analysis 0.6.2", + note="lacks proof, use __admitted__interchange_psum explicitly if you really want to use this lemma")] +Notation interchange_psum := __admitted__interchange_psum. + (* -------------------------------------------------------------------- *) Section SumTheory. Context {R : realType} {T : choiceType}.