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Fix compilation #927

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May 15, 2023
Merged

Fix compilation #927

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13 changes: 5 additions & 8 deletions theories/kernel.v
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Original file line number Diff line number Diff line change
Expand Up @@ -501,7 +501,8 @@ rewrite [X in measurable_fun _ X](_ : _ = (fun x => \sum_(r \in range (k_ n))
apply/funext => x; rewrite -ge0_integral_fsum//.
- by apply: eq_integral => y _; rewrite -fsumEFin.
- move=> r.
apply/EFin_measurable_fun/measurable_funrM/measurable_fun_prod1 => /=.
apply/EFin_measurable_fun/measurable_funT_comp => [//|].
apply/measurable_fun_prod1 => /=.
rewrite (_ : \1_ _ = mindic R (measurable_sfunP (k_ n) (measurable_set1 r)))//.
exact/measurable_funP.
- by move=> m y _; rewrite nnfun_muleindic_ge0.
Expand Down Expand Up @@ -779,7 +780,6 @@ apply: measurable_fun_if => //.
[set t | k t setT == +oo]); last first.
by apply/seteqP; split=> x /= /orP//.
by apply: measurableU; exact: kernel_measurable_eq_cst.
- exact: measurable_fun_cst.
- apply/emeasurable_funM; first exact/measurable_funTS/measurable_kernel.
apply/EFin_measurable_fun; rewrite setTI.
apply: (@measurable_fun_comp _ _ _ _ _ _ [set r : R | r != 0%R]).
Expand Down Expand Up @@ -809,15 +809,13 @@ rewrite (_ : (fun _ => _) = (fun x =>
else f x U * (fine (f x setT))^-1%:E)); last first.
apply/funext => x; case: ifPn => [/orP[->//|->]|]; first by case: ifPn.
by rewrite negb_or=> /andP[/negbTE -> /negbTE ->].
apply: measurable_fun_if => //;
[exact: kernel_measurable_fun_eq_cst|exact: measurable_fun_cst|].
apply: measurable_fun_if => //; [exact: kernel_measurable_fun_eq_cst|].
apply: measurable_fun_if => //.
- rewrite setTI [X in measurable X](_ : _ = [set t | f t setT != 0]).
exact: kernel_measurable_neq_cst.
by apply/seteqP; split => [x /negbT//|x /negbTE].
- apply: (@measurable_funS _ _ _ _ setT) => //.
exact: kernel_measurable_fun_eq_cst.
- exact: measurable_fun_cst.
- apply: emeasurable_funM.
by have := measurable_kernel f U mU; exact: measurable_funS.
apply/EFin_measurable_fun.
Expand Down Expand Up @@ -931,7 +929,6 @@ apply: (@le_lt_trans _ _ (\int[l x]__ r%:num%:E)).
apply: ge0_le_integral => //.
- have /measurable_fun_prod1 := measurable_kernel k _ measurableT.
exact.
- exact/measurable_fun_cst.
- by move=> y _; exact/ltW/hr.
by rewrite integral_cst//= EFinM lte_pmul2l.
Qed.
Expand Down Expand Up @@ -1081,7 +1078,7 @@ Let integral_kcomp_nnsfun x (f : {nnsfun Z >-> R}) :
Proof.
under [in LHS]eq_integral do rewrite fimfunE -fsumEFin//.
rewrite ge0_integral_fsum//; last 2 first.
- move=> r; apply/EFin_measurable_fun/measurable_funrM.
- move=> r; apply/EFin_measurable_fun/measurable_funT_comp => [//|].
have fr : measurable (f @^-1` [set r]) by exact/measurable_sfunP.
by rewrite (_ : \1__ = mindic R fr).
- by move=> r z _; rewrite EFinM nnfun_muleindic_ge0.
Expand All @@ -1090,7 +1087,7 @@ under [in RHS]eq_integral.
under eq_integral.
by move=> z _; rewrite fimfunE -fsumEFin//; over.
rewrite /= ge0_integral_fsum//; last 2 first.
- move=> r; apply/EFin_measurable_fun/measurable_funrM.
- move=> r; apply/EFin_measurable_fun/measurable_funT_comp => [//|].
have fr : measurable (f @^-1` [set r]) by exact/measurable_sfunP.
by rewrite (_ : \1__ = mindic R fr).
- by move=> r z _; rewrite EFinM nnfun_muleindic_ge0.
Expand Down
4 changes: 2 additions & 2 deletions theories/lebesgue_integral.v
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Expand Up @@ -4071,7 +4071,7 @@ Let integral_measure_lt (D : set T) (mD : measurable D) (g f : T -> \bar R) :
Proof.
move=> mf mg fg; pose E j := D `&` [set x | f x - g x >= j.+1%:R^-1%:E].
have mE j : measurable (E j).
rewrite /E; apply: emeasurable_fun_le => //; first exact: measurable_fun_cst.
rewrite /E; apply: emeasurable_fun_le => //.
by apply/(emeasurable_funD mf.1)/emeasurable_funN; case: mg.
have muE j : mu (E j) = 0.
apply/eqP; rewrite eq_le measure_ge0// andbT.
Expand All @@ -4088,7 +4088,7 @@ have muE j : mu (E j) = 0.
apply: (@le_trans _ _ (j.+1%:R%:E * \int[mu]_(x in E j) j.+1%:R^-1%:E)).
by rewrite integral_cst// muleA -EFinM divrr ?unitfE// mul1e.
rewrite lee_pmul//; first exact: integral_ge0.
apply: ge0_le_integral => //; [exact: measurable_fun_cst| | |by move=> x []].
apply: ge0_le_integral => //; [| |by move=> x []].
- by move=> x [_/=]; exact: le_trans.
- apply: emeasurable_funB.
+ by apply: measurable_funS mf.1 => //; exact: subIsetl.
Expand Down