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fixes #1586 #1587

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Merged
affeldt-aist merged 1 commit into from
Apr 23, 2025
Merged

fixes #1586 #1587

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3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Original file line number Diff line number Diff line change
Expand Up @@ -6,6 +6,9 @@

### Changed

- in `pi_irrational`:
+ definition `rational`

### Renamed

- in `kernel.v`:
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6 changes: 5 additions & 1 deletion theories/pi_irrational.v
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Expand Up @@ -29,7 +29,7 @@ exact/continuous_horner.
Qed.

(* TODO: move somewhere to classical *)
Definition rational {R : realType} (x : R) := exists m n, x = (m%:R / n%:R)%R.
Definition rational {R : realType} (x : R) := exists m n, x = (m%:~R / n%:R)%R.

Module pi_irrational.
Local Open Scope ring_scope.
Expand Down Expand Up @@ -411,6 +411,10 @@ Lemma pi_irrationnal {R : realType} : ~ rational (pi : R).
Proof.
move=> [a [b]]; have [->|b0 piratE] := eqVneq b O.
by rewrite invr0 mulr0; apply/eqP; rewrite gt_eqF// pi_gt0.
have [na ana] : exists na, (a%:~R = na %:R :> R)%R.
exists `|a|; rewrite natr_absz gtr0_norm//.
by have := @pi_gt0 R; rewrite piratE pmulr_lgt0 ?invr_gt0 ?ltr0n ?lt0n// ltr0z.
rewrite {}ana in piratE.
have [N _] := pi_irrational.intfsin_small b0 (esym piratE) (@ltr01 R).
near \oo%classic => n.
have Nn : (N <= n)%N by near: n; exists N.
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