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Added lemma to swap mathcomp natural log with Rocqs natural log #1831

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Merged
proux01 merged 2 commits into from
Jan 28, 2026
Merged

Added lemma to swap mathcomp natural log with Rocqs natural log #1831

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b96fbf3
Added lemma to swap mathcomp natural log with Rocqs natural log
lstrsrmn Jan 23, 2026
ff70107
Generalised Lemma and shortened
lstrsrmn Jan 28, 2026
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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -6,6 +6,9 @@
- in set_interval.v
+ definitions `itv_is_closed_unbounded`, `itv_is_cc`, `itv_closed_ends`

- in `Rstruct_topology.v`:
+ lemma `RlnE`

### Changed
- in set_interval.v
+ `itv_is_open_unbounded`, `itv_is_oo`, `itv_open_ends` (Prop to bool)
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11 changes: 11 additions & 0 deletions analysis_stdlib/Rstruct_topology.v
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Expand Up @@ -14,6 +14,8 @@ From mathcomp Require Export Rstruct.
From mathcomp Require Import topology.
(* The following line is for RexpE. *)
From mathcomp Require normedtype sequences.
(* The following line is for RlnE. *)
From mathcomp Require exp.

Set Implicit Arguments.
Unset Strict Implicit.
Expand Down Expand Up @@ -107,3 +109,12 @@ Unshelve. all: by end_near. Qed.
End RexpE.

Definition RexpE := RexpE.RexpE.

Lemma RlnE (x : R) : Rpower.ln x = exp.ln x.
Proof.
rewrite /Rpower.ln /Rln.
have [xle0|xgt0] := leP x 0.
by case: Rlt_dec => //= /[dup] /RltP + ?; rewrite exp.ln0// ltNge xle0.
case: (Rlt_dec 0 x) => [/= ? | /RltP/[!xgt0]//].
by case: ln_exists => y ->; rewrite RexpE exp.expRK.
Qed.