natural logarithm for extended real numbers #1649
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Note that the last commit changes the definition of Lemma lne_div : {in `]0, +oo] &, {morph lne : x y / x / y >-> x - y}}.instead of Lemma lne_div x y :
0 < x -> 0 < y -> lne (x * (fine y)^-1%:E) = lne x - lne y.(fyi: @CohenCyril) @jmmarulang It looks a bit better but is it as useful to you? |
2 tasks
affeldt-aist
changed the title
hoheinzollern
approved these changes
Jul 8, 2025
| @@ -21,7 +21,8 @@ From mathcomp Require Import realfun interval_inference convex. | |||
| (* pseries_diffs f i == (i + 1) * f (i + 1) *) | |||
| (* *) | |||
| (* expeR x == extended real number-valued exponential function *) | |||
| (* ln x == the natural logarithm *) | |||
| (* ln x == the natural logarithm, in ring_scope *) | |||
| (* lne x == the natural logarithm, in ereal_scope *) | |||
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I'd rather align the == than the function names
CohenCyril
reviewed
Jul 8, 2025
| by rewrite in_itv //= leey andbT addrC -(oppeK 1) sube_ge0. | ||
| Qed. | ||
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| Lemma lne_sublinear x : 0 < x < +oo -> lne x < x. |
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This is probably true for all finite x?
CohenCyril
reviewed
Jul 8, 2025
| by rewrite lne_EFin// lte_fin ln_sublinear. | ||
| Qed. | ||
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| Lemma lne_ge0 x : 1 <= x -> 0 <= lne x. |
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This is probably an equivalence?
CohenCyril
reviewed
Jul 8, 2025
| by rewrite lne_EFin// ?(lt_le_trans _ r1)// lee_fin ln_ge0. | ||
| Qed. | ||
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| Lemma lne_lt0 x : 0 < x < 1 -> lne x < 0. |
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This is probably a consequence of the following equivalence:
Suggested change
| Lemma lne_lt0 x : 0 < x < 1 -> lne x < 0. | |
| Lemma lne_lt0 x : (lne x < 0) = (x < 1). |
CohenCyril
reviewed
Jul 8, 2025
| by move=> /andP[? ?]; rewrite -lte_expeR expeR0 lneK ?in_itv//= leey andbT ?ltW. | ||
| Qed. | ||
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| Lemma lne_gt0 x : 1 < x -> 0 < lne x. |
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This is probably an equivalence
CohenCyril
reviewed
Jul 8, 2025
| by rewrite (le_trans _ (ltW x1)). | ||
| Qed. | ||
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| Fact le1_lne_le0 x : x <= 1 -> lne x <= 0. |
CohenCyril
reviewed
Jul 8, 2025
| by rewrite expeS lneM ?ih ?muleS// in_itv/= ?expe_gt0// ?x0/= leey. | ||
| Qed. | ||
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| Lemma le_lne1Dx x : - 1%E <= x -> lne (1 + x) <= x. |
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equivalence too? (and why %E?)
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Motivation for this change
closes draft PR #1613
@jmmarulang : I have duplicated your PR to avoid pushing on your master
Checklist
CHANGELOG_UNRELEASED.mdReference: How to document
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all compile are preferentially merged into master.
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