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# Proof with convex sets

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A Theorem states: Convex Sets are closed under convex combinations. That is, if C is a convex set, and if x1,x2,...,xm belongs to C then for all non-negative real numbers %1,%2,...,%m are non-negative real numbers such that \$1+\$2+....+\$m=1, we have
\$1x1 + \$2x2 + ... + \$mxm belonging to C.

Furthermore, I want to prove that if x1,x2,x3,x4 are in the convex set C, and if \$1,\$2,\$3,%4 are non-negative real numbers such that \$1+\$2+\$3+\$4=1 then \$1x1+\$2x2+\$3x3+\$4x4 belonging to C