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Require Import Reals List Coquelicot.Coquelicot. | ||
Open Scope R. | ||
Theorem putnam_1979_b6 | ||
(n: nat) | ||
(l: list C) | ||
(hl : length l = n) | ||
(sum1 := fold_left (fun acc x => Cplus acc (Cmult x x)) l 0) | ||
(sum2 := fold_left (fun acc x => Re x) l 0) | ||
: sqrt (Re sum1) <= sum2. | ||
Proof. Admitted. | ||
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From mathcomp Require Import all_algebra all_ssreflect. | ||
From mathcomp Require Import reals complex. | ||
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About Rcomplex. | ||
Set Implicit Arguments. | ||
Unset Strict Implicit. | ||
Unset Printing Implicit Defensive. | ||
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Local Open Scope ring_scope. | ||
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Variable R : realType. | ||
Theorem putnam_1979_b6 | ||
(l : seq R[i]) | ||
: `|Re (sqrtc (\sum_(z <- l) (z ^+ 2)))| <= \sum_(z <- l) `|Re z|. | ||
Proof. Admitted. |