- Assume that two different sequences of FCs exist within the algebraic space that have the same runtime address, i.e the sequence of trios leading to the two FCs are same.
- Denote the two sequences as Seq1 and Seq2, and their runtime addresses as Addr1 and Addr2, respectively.
- Since Addr1 and Addr2 are the same, it implies that the last FC in Seq1 and the last FC in Seq2 are the same FC.
- According to the design-time constraint, each object can have only one particular intention leading to a specific FC. Therefore, if the last FC in Seq1 and Seq2 is the same, it means that the object and intention pairs leading to that FC must be the same.
- Let's denote the object and intention pair leading to the last FC in Seq1 and Seq2 as (Object1, Intention1) and (Object2, Intention2), respectively.
- Since (Object1, Intention1) and (Object2, Intention2) are the same, it means that both the object and intention in each pair must be the same.
- However, this contradicts the assumption that Seq1 and Seq2 are different sequences, as they have the same object and intention pair leading to the last FC.
- Therefore, we can conclude that if two different sequences of FCs exist, they must have different runtime addresses in the algebraic space, determined by the unique combination of object and intention pairs.