In discrete mathematics, the proof sequence of a proposition refers to a process consisting of a series of logical reasoning steps, which is used to derive the truth value of a proposition. When the proposition is true, the proof sequence is verifiable evidence. When there are multiple propositions to prove, it is necessary to combine all the proof sequences to generate a complete proof sequence, which is called the construction of proof sequence.

In the construction of proof sequence, it is necessary to express its composition and logical relationship with symbols corresponding to propositions, and deduce the results through various logical rules and theorems. These symbols and rules constitute the language and deductive rules for establishing proof sequences, which are called logical systems.

Taking discrete proof as an example, the reasoning construction process of a proof sequence can include the following steps:

First, determine what the proposition needs to prove, and what is the prerequisite of this proposition.

Determine the reasoning rules and logical language of the proof sequence.

Use logical reasoning to gradually decompose a proposition into simpler propositions until it is a basic proposition (that is, a proposition with known truth value) or disproof, and stop decomposition.

Each proposition obtained by decomposition is synthesized into more complex propositions by using inference rules and theorems until the target proposition is finally deduced.

The process of reasoning is expressed in the form of proof sequence, that is, step list, and each step is followed by its corresponding logical statement and reasoning rules, thus constructing the whole proof sequence.

Finally, it is necessary to check whether each step of the proof sequence is correct, so as to ensure the correctness of the derivation step and the credibility of the proof.

Through the above steps, we can construct a proof sequence through reasoning, prove the truth value of a proposition and verify its correctness.