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tentative removal of Rint #1937

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73e1d82
tentative removal of Rint
affeldt-aist Apr 16, 2026
0db0b8d
fix
affeldt-aist Apr 16, 2026
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24 changes: 12 additions & 12 deletions reals/reals.v
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Original file line number Diff line number Diff line change
Expand Up @@ -149,7 +149,7 @@ Proof. exact: sup_adherent_subdef. Qed.
Section IsInt.
Context {R : realFieldType}.

Definition Rint_pred := fun x : R => `[< exists z, x == z%:~R >].
(*Definition Rint_pred := fun x : R => `[< exists z, x == z%:~R >].
Arguments Rint_pred _ /.
Definition Rint := [qualify a x | Rint_pred x].

Expand Down Expand Up @@ -193,18 +193,18 @@ Lemma Rint_ltr_addr1 (x y : R) : x \is a Rint -> y \is a Rint ->
Proof.
move=> /RintP[xi ->] /RintP[yi ->]; rewrite -{3}[1]mulr1z.
by rewrite -intrD !(ltr_int, ler_int) ltzD1.
Qed.
Qed.*)

End IsInt.
Arguments Rint_pred _ _ /.
(*Arguments Rint_pred _ _ /.*)

(* -------------------------------------------------------------------- *)
Section ToInt.
Context {R : realType}.

Implicit Types x y : R.

Definition Rtoint (x : R) : int :=
(*Definition Rtoint (x : R) : int :=
if insub x : {? x | x \is a Rint} is Some Px then
xchoose (asboolP _ (tagged Px))
else 0.
Expand All @@ -228,7 +228,7 @@ Lemma RtointN x : x \is a Rint -> Rtoint (- x) = - Rtoint x.
Proof.
move=> Ir; apply/eqP.
by rewrite -(@eqr_int R) RtointK // ?rpredN // mulrNz RtointK.
Qed.
Qed.*)

End ToInt.

Expand All @@ -238,7 +238,7 @@ Section RealDerivedOps.
Variable R : realType.

Implicit Types x y : R.
Definition floor_set x := [set y : R | (y \is a Rint) && (y <= x)].
Definition floor_set x := [set y : R | (y \is a Num.int) && (y <= x)].

Definition Rfloor x : R := (Num.floor x)%:~R.

Expand Down Expand Up @@ -456,15 +456,15 @@ move/sup_adherent=> -/(_ e) []; first by rewrite subr_gt0.
move=> z Fz; rewrite /= subKr => lt_yz.
have /sup_upper_bound /ubP /(_ _ Fz) := has_sup_floor_set x.
rewrite -(lerD2r (-y)) => /le_lt_trans /(_ lt1_FxBy).
case/andP: Fy Fz lt_yz=> /RintP[yi -> _].
case/andP=> /RintP[zi -> _]; rewrite -rmorphB /= ltrz1 ltr_int.
case/andP: Fy Fz lt_yz => /intrP[yi -> _].
case/andP => /intrP[zi -> _]; rewrite -rmorphB /= ltrz1 ltr_int.
rewrite lt_neqAle => /andP[ne_yz le_yz].
rewrite -[_-_]gez0_abs ?subr_ge0 // ltz_nat ltnS leqn0.
by rewrite absz_eq0 subr_eq0 eq_sym (negbTE ne_yz).
Qed.

Lemma isint_Rfloor x : Rfloor x \is a Rint.
Proof. by rewrite inE; exists (Num.floor x). Qed.
Lemma isint_Rfloor x : Rfloor x \is a Num.int.
Proof. by apply/intrP; exists (Num.floor x). Qed.

Lemma RfloorE x : Rfloor x = (Num.floor x)%:~R.
Proof. by []. Qed.
Expand Down Expand Up @@ -534,8 +534,8 @@ Variable R : realType.

Implicit Types x y : R.

Lemma isint_Rceil x : Rceil x \is a Rint.
Proof. by rewrite /Rceil RintC. Qed.
Lemma isint_Rceil x : Rceil x \is a Num.int.
Proof. by rewrite /Rceil intr_int. Qed.

Lemma Rceil0 : Rceil 0 = 0 :> R.
Proof. by rewrite /Rceil ceil0. Qed.
Expand Down
2 changes: 1 addition & 1 deletion theories/measurable_realfun.v
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Expand Up @@ -1720,7 +1720,7 @@ have badn' k : exists n, mu (E k n) < ((eps / 2) / (2 ^ k.+1)%:R)%:E.
pose badn k := projT1 (cid (badn' k)); exists (\bigcup_k E k (badn k)); split.
- exact: bigcup_measurable.
- apply: (@le_lt_trans _ _ (eps / 2)%:E); first last.
by rewrite lte_fin ltr_pdivrMr // ltr_pMr // Rint_ltr_addr1 // Rint1.
by rewrite lte_fin ltr_pdivrMr // ltr_pMr // ltr1n.
apply: le_trans.
apply: (measure_sigma_subadditive _ (fun k => mE k (badn k)) _ _) => //.
exact: bigcup_measurable.
Expand Down
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