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various fixes #1409

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17 changes: 17 additions & 0 deletions CHANGELOG_UNRELEASED.md
Original file line number Diff line number Diff line change
Expand Up @@ -38,6 +38,18 @@
+ `emeasurable_fun_fsum` -> `emeasurable_fsum`
+ `ge0_emeasurable_fun_sum` -> `ge0_emeasurable_sum`

- in `classical_sets.v`:
+ `preimage_itv_o_infty` -> `preimage_itvoy`
+ `preimage_itv_c_infty` -> `preimage_itvcy`
+ `preimage_itv_infty_o` -> `preimage_itvNyo`
+ `preimage_itv_infty_c` -> `preimage_itvNyc`

- in `constructive_ereal.v`:
+ `maxeMr` -> `maxe_pMr`
+ `maxeMl` -> `maxe_pMl`
+ `mineMr` -> `mine_pMr`
+ `mineMl` -> `mine_pMl`

### Generalized

### Deprecated
Expand All @@ -50,6 +62,11 @@
- in `lebesgue_integral.v`:
+ lemma `measurable_indic` (was uselessly specializing `measurable_fun_indic` (now `measurable_indic`) from `lebesgue_measure.v`)
+ notation `measurable_fun_indic` (deprecation since 0.6.3)
- in `constructive_ereal.v`
+ notation `lee_opp` (deprecated since 0.6.5)
+ notation `lte_opp` (deprecated since 0.6.5)
- in `measure.v`:
+ `dynkin_setI_bigsetI` (use `big_ind` instead)

### Infrastructure

Expand Down
16 changes: 12 additions & 4 deletions classical/classical_sets.v
Original file line number Diff line number Diff line change
Expand Up @@ -469,25 +469,33 @@ Lemma preimage_itv T d (rT : porderType d) (f : T -> rT) (i : interval rT) (x :
((f @^-1` [set` i]) x) = (f x \in i).
Proof. by rewrite inE. Qed.

Lemma preimage_itv_o_infty T d (rT : porderType d) (f : T -> rT) y :
Lemma preimage_itvoy T d (rT : porderType d) (f : T -> rT) y :
f @^-1` `]y, +oo[%classic = [set x | (y < f x)%O].
Proof.
by rewrite predeqE => t; split => [|?]; rewrite /= in_itv/= andbT.
Qed.
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to preimage_itvoy")]
Notation preimage_itv_o_infty := preimage_itvoy (only parsing).

Lemma preimage_itv_c_infty T d (rT : porderType d) (f : T -> rT) y :
Lemma preimage_itvcy T d (rT : porderType d) (f : T -> rT) y :
f @^-1` `[y, +oo[%classic = [set x | (y <= f x)%O].
Proof.
by rewrite predeqE => t; split => [|?]; rewrite /= in_itv/= andbT.
Qed.
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to preimage_itvcy")]
Notation preimage_itv_c_infty := preimage_itvcy (only parsing).

Lemma preimage_itv_infty_o T d (rT : orderType d) (f : T -> rT) y :
Lemma preimage_itvNyo T d (rT : orderType d) (f : T -> rT) y :
f @^-1` `]-oo, y[%classic = [set x | (f x < y)%O].
Proof. by rewrite predeqE => t; split => [|?]; rewrite /= in_itv. Qed.
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to preimage_itvNyo")]
Notation preimage_itv_infty_o := preimage_itvNyo (only parsing).

Lemma preimage_itv_infty_c T d (rT : orderType d) (f : T -> rT) y :
Lemma preimage_itvNyc T d (rT : orderType d) (f : T -> rT) y :
f @^-1` `]-oo, y]%classic = [set x | (f x <= y)%O].
Proof. by rewrite predeqE => t; split => [|?]; rewrite /= in_itv. Qed.
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to preimage_itvNyc")]
Notation preimage_itv_infty_c := preimage_itvNyc (only parsing).

Lemma eq_set T (P Q : T -> Prop) : (forall x : T, P x = Q x) ->
[set x | P x] = [set x | Q x].
Expand Down
26 changes: 15 additions & 11 deletions reals/constructive_ereal.v
Original file line number Diff line number Diff line change
Expand Up @@ -2468,7 +2468,7 @@ Qed.
Lemma oppe_min : {morph -%E : x y / mine x y >-> maxe x y : \bar R}.
Proof. by move=> x y; rewrite -[RHS]oppeK oppe_max !oppeK. Qed.

Lemma maxeMr z x y : z \is a fin_num -> 0 <= z ->
Lemma maxe_pMr z x y : z \is a fin_num -> 0 <= z ->
z * maxe x y = maxe (z * x) (z * y).
Proof.
move=> /[swap]; rewrite le_eqVlt => /predU1P[<- _|z0].
Expand All @@ -2478,20 +2478,20 @@ have [xy|yx|->] := ltgtP x y; last by rewrite maxxx.
- by move=> zfin; rewrite maxC /maxe lte_pmul2l// yx.
Qed.

Lemma maxeMl z x y : z \is a fin_num -> 0 <= z ->
Lemma maxe_pMl z x y : z \is a fin_num -> 0 <= z ->
maxe x y * z = maxe (x * z) (y * z).
Proof. by move=> zfin z0; rewrite muleC maxeMr// !(muleC z). Qed.
Proof. by move=> zfin z0; rewrite muleC maxe_pMr// !(muleC z). Qed.

Lemma mineMr z x y : z \is a fin_num -> 0 <= z ->
Lemma mine_pMr z x y : z \is a fin_num -> 0 <= z ->
z * mine x y = mine (z * x) (z * y).
Proof.
move=> fz zge0.
by rewrite -eqe_oppP -muleN [in LHS]oppe_min maxeMr// !muleN -oppe_min.
by rewrite -eqe_oppP -muleN [in LHS]oppe_min maxe_pMr// !muleN -oppe_min.
Qed.

Lemma mineMl z x y : z \is a fin_num -> 0 <= z ->
Lemma mine_pMl z x y : z \is a fin_num -> 0 <= z ->
mine x y * z = mine (x * z) (y * z).
Proof. by move=> zfin z0; rewrite muleC mineMr// !(muleC z). Qed.
Proof. by move=> zfin z0; rewrite muleC mine_pMr// !(muleC z). Qed.

Lemma bigmaxe_fin_num (s : seq R) r : r \in s ->
\big[maxe/-oo%E]_(i <- s) i%:E \is a fin_num.
Expand Down Expand Up @@ -2660,10 +2660,6 @@ Arguments lee_sum_nneg_natl {R}.
Arguments lee_sum_npos_natl {R}.
#[global] Hint Extern 0 (is_true (0 <= `| _ |)%E) => solve [apply: abse_ge0] : core.

#[deprecated(since="mathcomp-analysis 0.6.5", note="Use leeN2 instead.")]
Notation lee_opp := leeN2 (only parsing).
#[deprecated(since="mathcomp-analysis 0.6.5", note="Use lteN2 instead.")]
Notation lte_opp := lteN2 (only parsing).
#[deprecated(since="mathcomp-analysis 1.1.0", note="Use leeDl instead.")]
Notation lee_addl := leeDl (only parsing).
#[deprecated(since="mathcomp-analysis 1.1.0", note="Use leeDr instead.")]
Expand Down Expand Up @@ -2730,6 +2726,14 @@ Notation lte_le_sub := lte_leB (only parsing).
Notation lee_opp2 := leeN2 (only parsing).
#[deprecated(since="mathcomp-analysis 1.3.0", note="Use lteN2 instead.")]
Notation lte_opp2 := lteN2 (only parsing).
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to maxe_pMr")]
Notation maxeMr := maxe_pMr (only parsing).
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to maxe_pMl")]
Notation maxeMl := maxe_pMl (only parsing).
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to mine_pMr")]
Notation mineMr := mine_pMr (only parsing).
#[deprecated(since="mathcomp-analysis 1.8.0", note="renamed to mine_pMl")]
Notation mineMl := mine_pMl (only parsing).

Module DualAddTheoryRealDomain.

Expand Down
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