diff --git a/CHANGELOG_UNRELEASED.md b/CHANGELOG_UNRELEASED.md index e334580f12..e67d620275 100644 --- a/CHANGELOG_UNRELEASED.md +++ b/CHANGELOG_UNRELEASED.md @@ -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`, @@ -143,6 +146,9 @@ + `SigmaFinite_isFinite` -> `isFinite` + `FiniteMeasure_isSubProbability` -> `isSubProbability` +- in `exp.v`: + + `expRMm` -> `expRM_natl` + ### Generalized - in `realfun.v` diff --git a/theories/exp.v b/theories/exp.v index 73a4f32002..de5bbfc1c3 100644 --- a/theories/exp.v +++ b/theories/exp.v @@ -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. @@ -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). @@ -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.