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pi8027 committed Jul 8, 2024
1 parent 31e0216 commit 2bd4d2b
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions theories/xmathcomp/algR.v
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From HB Require Import structures.
From mathcomp Require Import all_ssreflect all_fingroup all_algebra.
From mathcomp Require Import all_ssreflect all_fingroup all_algebra archimedean.
From mathcomp Require Import all_solvable all_field.
From Abel Require Import various.

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Definition algR_archiFieldMixin : Num.archimedean_axiom algR.
Proof.
move=> /= x; have /andP[/= _] := floorC_itv (valP `|x|).
set n := floorC _; have [n_lt0|n_ge0] := ltP n 0.
move=> /= x; have /andP[/= _] := real_floor_itv (valP `|x|).

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set n := Num.floor _; have [n_lt0|n_ge0] := ltP n 0.
move=> /(@lt_le_trans _ _ _ _ 0); rewrite lerz0 lezD1.
by move=> /(_ n_lt0); rewrite normr_lt0.
move=> x_lt; exists (`|(n + 1)%R|%N); apply: lt_le_trans x_lt _.
by rewrite /= rmorphMn/= pmulrn gez0_abs// addr_ge0.
Qed.
HB.instance Definition _ := Num.RealField_isArchimedean.Build algR
HB.instance Definition _ := Num.NumDomain_bounded_isArchimedean.Build algR
algR_archiFieldMixin.

Definition algRpfactor (x : algC) : {poly algR} :=
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