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rat_in_itvoo need not be restricted to realTypes #1286

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Aug 7, 2024
Merged

rat_in_itvoo need not be restricted to realTypes #1286

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rat_in_itvoo need not be restricted to realTypes
t6s Aug 7, 2024
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changelog
t6s Aug 7, 2024
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2 changes: 2 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -9,6 +9,8 @@
### Renamed

### Generalized
- in `reals.v`:
+ lemma `rat_in_itvoo`

### Deprecated

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2 changes: 1 addition & 1 deletion theories/reals.v
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Expand Up @@ -677,7 +677,7 @@ rewrite /bound_div (ltNge y 0) y0/= -mulr_natl -ltr_pdivrMr//.
by rewrite archi_boundP// (divr_ge0 _(ltW _)).
Qed.

Lemma rat_in_itvoo (R : realType) (x y : R) :
Lemma rat_in_itvoo (R : archiFieldType) (x y : R) :
x < y -> exists q, ratr q \in `]x, y[.
Proof.
move=> xy; move: (xy); rewrite -subr_gt0.
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