A formal proof of the Chip Model Channel Separation Property - A variant of the Channel Separation Property

A variant of the Channel Separation Property

	┌──────┐
     ───┤ chip ├──►
        └──────┘

      ┌─────────┐   ┌─────────┐
   ┌─►┤ pick 1  ├──►┤  chip   ├──┐
   │  └─────────┘   └─────────┘  │
   │  ┌─────────┐   ┌─────────┐  │
───┼─►┤ pick 2  ├──►┤  chip   ├──┼──►
   │  └─────────┘   └─────────┘  │
   │      ...          ...       │
   │  ┌─────────┐   ┌─────────┐  │
   └─►┤ pick n  ├──►┤  chip   ├──┘
      └─────────┘   └─────────┘

Processing all channels in one chip is the same as having one chip per channel.