Note, the concept of "valid" is application dependent, as defined by the customer's business logic. The transition rules, as defined by the Exchange itself, are unknown to the application's smart contract. The smart contract is aware only of a succinct commitment to the state. Any specific state transition is dependent on the executed transactions (which are not transmitted on-chain to enhance scalability).
C_0
to C_1
if there is knowledge of:S_0
such that C_0
is its commitment.S_1
such that C_1
is its commitment.t_0, t_1, ..., t_k
executable (one after the other) on S_0
(implying valid state transitions – as defined by the application rules), such that the resulting state is S_1
.