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Merged
affeldt-aist merged 1 commit into from
Jan 27, 2023
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expeS, fin_numX #829

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4 changes: 4 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -49,6 +49,10 @@
- in `lebesgue_integral.v`:
+ notations `\x`, `\x^` for `product_measure1` and `product_measure2`

- in `constructive_ereal.v`:
+ lemmas `expeS`, `fin_numX`


### Changed

- in `fsbigop.v`:
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6 changes: 6 additions & 0 deletions theories/constructive_ereal.v
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Expand Up @@ -717,6 +717,9 @@ Proof. by move: x => [r| |]/=; rewrite /mule/= ?mul0r// eqxx. Qed.

Canonical mule_mulmonoid := @Monoid.MulLaw _ _ mule mul0e mule0.

Lemma expeS x n : x ^+ n.+1 = x * x ^+ n.
Proof. by case: n => //=; rewrite mule1. Qed.

Definition mule_def x y :=
~~ (((x == 0) && (`| y | == +oo)) || ((y == 0) && (`| x | == +oo))).

Expand Down Expand Up @@ -814,6 +817,9 @@ Lemma fin_numM x y : x \is a fin_num -> y \is a fin_num ->
x * y \is a fin_num.
Proof. by move: x y => [x| |] [y| |]. Qed.

Lemma fin_numX x n : x \is a fin_num -> x ^+ n \is a fin_num.
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@zstone1 zstone1 Jan 26, 2023

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Maybe fin_num_expe?

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@affeldt-aist affeldt-aist Jan 26, 2023

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I think that fin_numX is appropriate because the suffix X is used in most lemmas involving ^+.
Of course, here we are indeed talking about expe and not the operator coming from MathComp
but since this is a lemma about fun_num the user can infer this difference from the context.

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@zstone1 zstone1 Jan 26, 2023

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Ah, makes sense. I'm happy with it's current state then.

Proof. by elim: n x => // n ih x finx; rewrite expeS fin_numM// ih. Qed.

Lemma fineD : {in @fin_num R &, {morph fine : x y / x + y >-> (x + y)%R}}.
Proof. by move=> [r| |] [s| |]. Qed.

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