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Add a RealsE multirule #1836

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Add a RealsE multirule
proux01 Feb 4, 2026
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R{0,1}E from InfoTheo
affeldt-aist Feb 6, 2026
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6 changes: 6 additions & 0 deletions CHANGELOG_UNRELEASED.md
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Expand Up @@ -6,9 +6,15 @@
- in set_interval.v
+ definitions `itv_is_closed_unbounded`, `itv_is_cc`, `itv_closed_ends`

- in `Rstruct.v`:
+ multirule `RealsE` to convert from Stdlib reals to Analysis ones

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

- in `Rstruct.v`:
+ lemmas `R1E`, `R0E`

### Changed
- in set_interval.v
+ `itv_is_open_unbounded`, `itv_is_oo`, `itv_open_ends` (Prop to bool)
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10 changes: 10 additions & 0 deletions reals_stdlib/Rstruct.v
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Expand Up @@ -539,6 +539,16 @@ Qed.
Lemma factE n : fact n = n`!.
Proof. by elim: n => //= n ih; rewrite factS mulSn ih. Qed.

Lemma R0E : Rdefinitions.IZR BinNums.Z0 = 0.
Proof. by []. Qed.

Lemma R1E : Rdefinitions.IZR (BinNums.Zpos BinNums.xH) = 1.
Proof. by []. Qed.

Definition RealsE := (R0E, R1E, RplusE, RminusE, RmultE, RoppE, RinvE, RdivE,
INRE, Pos_to_natE, IZRposE, RsqrtE, RpowE, RmaxE, RminE, RabsE, RdistE,
sum_f_R0E, factE).

Section bigmaxr.
Context {R : realDomainType}.

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