Consumption Protocol Formula Derivation

Assume:

Bancor Price Protocol (same CW)

Use the same CW value on both ends of the connectors:

Applying formula 2 and formula 3 into formula 1:

Token consumption protocol

From the Bancor price protocol, we know:

From formula 2, we have:

Applying formula 3, formula 4 and formula 5 into formula 1:

Applying formula 6 into formula 5:

Result:

Bancor based utility-enhanced token protocol: https://github.com/Dappub/tokendapppub/blob/master/Bancor%20based%20utility-enhanced%20token%20protocol.pdf

Bancor WhitePaper: https://storage.googleapis.com/website-bancor/2018/04/01ba8253-bancor_protocol_whitepaper_en.pdf