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Simplify equations

• To: mathgroup at smc.vnet.net
• Subject: [mg99260] Simplify equations
• From: openpursuit at gmail.com
• Date: Fri, 1 May 2009 05:22:37 -0400 (EDT)

Why mathematica does not simplify this simple system?
Simplify[  C[1] \[Element] Integers &&   (x == 7 C[1] || x == 14 C
[1]) ]

I would like that it say "hey...buy if x is a multiple of 7 ,it is
also a multiple of 14 so the second equivalence is always verified if
x verify the first".