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fixes #1094 (renaming of expRMm) #1200

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Merged
affeldt-aist merged 2 commits into from
Mar 31, 2024
Merged

fixes #1094 (renaming of expRMm) #1200

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639c724
fixes #1094
affeldt-aist Mar 29, 2024
e528752
more conservative version
affeldt-aist Mar 31, 2024
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6 changes: 6 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Original file line number Diff line number Diff line change
Expand Up @@ -65,6 +65,9 @@
+ definition `notP`
+ hint view for `move/` and `apply/` for `Internals.equivT_LR`, `Internals.equivT_RL`

- in `exp.v`:
+ lemma `expRM_natr`

### Changed
- moved from `topology.v` to `function_spaces.v`: `prod_topology`,
`product_topology_def`, `proj_continuous`, `dfwith_continuous`,
Expand Down Expand Up @@ -143,6 +146,9 @@
+ `SigmaFinite_isFinite` -> `isFinite`
+ `FiniteMeasure_isSubProbability` -> `isSubProbability`

- in `exp.v`:
+ `expRMm` -> `expRM_natl`

### Generalized

- in `realfun.v`
Expand Down
10 changes: 8 additions & 2 deletions theories/exp.v
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Expand Up @@ -416,12 +416,15 @@ rewrite expRxDyMexpx expRN [_ * expR y]mulrC mulfK //.
by case: ltrgt0P (expR_gt0 x).
Qed.

Lemma expRMm n x : expR (n%:R * x) = expR x ^+ n.
Lemma expRM_natl n x : expR (n%:R * x) = expR x ^+ n.
Proof.
elim: n x => [x|n IH x] /=; first by rewrite mul0r expr0 expR0.
by rewrite exprS -nat1r mulrDl mul1r expRD IH.
Qed.

Lemma expRM_natr n x : expR (x * n%:R) = expR x ^+ n.
Proof. by rewrite mulrC expRM_natl. Qed.

Lemma expR_gt1 x : (1 < expR x) = (0 < x).
Proof.
case: ltrgt0P => [x_gt0| xN|->]; last by rewrite expR0.
Expand Down Expand Up @@ -506,6 +509,9 @@ Local Close Scope convex_scope.

End expR.

#[deprecated(since="mathcomp-analysis 1.1.0", note="renamed `expRM_natl`")]
Notation expRMm := expRM_natl (only parsing).

Section expeR.
Context {R : realType}.
Implicit Types (x y : \bar R) (r s : R).
Expand Down Expand Up @@ -895,7 +901,7 @@ rewrite le_eqVlt => /predU1P[<-|a0].
by rewrite powR0 ?invr_eq0 ?pnatr_eq0// sqrtr0.
have /eqP : (a `^ (2^-1)) ^+ 2 = (Num.sqrt a) ^+ 2.
rewrite sqr_sqrtr; last exact: ltW.
by rewrite /powR gt_eqF// -expRMm mulrA divrr ?mul1r ?unitfE// lnK.
by rewrite /powR gt_eqF// -expRM_natl mulrA divrr ?mul1r ?unitfE// lnK.
rewrite eqf_sqr => /predU1P[//|/eqP h].
have : 0 < a `^ 2^-1 by exact: powR_gt0.
by rewrite h oppr_gt0 ltNge sqrtr_ge0.
Expand Down