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Removed unnecessary lines.
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GeorgeTsoukalas committed Aug 27, 2024
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9 changes: 0 additions & 9 deletions coq/src/putnam_1979_a2.v
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@@ -1,10 +1,3 @@
(* Require Import Basics Reals Coquelicot.Coquelicot.
Definition putnam_1979_a2_solution (k : R) := k >= 0.
Theorem putnam_1979_a2
: forall (k: R), (exists (f: R -> R), continuity f /\ forall x, (compose f f) x = k * pow x 9)
<-> putnam_1979_a2_solution k.
Proof. Admitted. *)

From mathcomp Require Import all_algebra all_ssreflect.
From mathcomp Require Import reals topology sequences derive normedtype realfun real_interval.
From mathcomp Require Import classical_sets.
Expand All @@ -18,8 +11,6 @@ Local Open Scope classical_set_scope.

Import numFieldNormedType.Exports.

About continuous.

Variable R : realType.
Definition putnam_1979_a2_solution : set R := [set x : R | x >= 0].
Theorem putnam_1979_a2
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24 changes: 11 additions & 13 deletions coq/src/putnam_1979_b6.v
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@@ -1,16 +1,14 @@
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.


From mathcomp Require Import all_algebra all_ssreflect.
From mathcomp Require Import reals complex.

About Rcomplex.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.

Local Open Scope ring_scope.

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.

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