1. Principle of truth of premise: the conclusion of proof must be based on the real premise. The premise is a known fact, definition, theorem or axiom, and its correctness and applicability need to be guaranteed.

2. Principle of validity of reasoning: the reasoning process must conform to logical rules to ensure that every step of reasoning is effective. Common logical laws include law of excluded middle, the law of contradiction and the law of identity.

3. Integrity principle of argumentation: The proof process must be complete, and no necessary steps or information can be omitted. Every step of derivation must be clear and definite.

4. The principle of argument coherence: the proof process needs to be consistent, and each step of derivation must have a clear causal relationship or logical relationship. There can be no jumping reasoning, and there can be no irrelevant insertion.

5. Principle of reduction to absurdity: When it is difficult to prove directly, it can be proved by reduction to absurdity. The reduction to absurdity proves the truth of the original proposition through the negation of the hypothetical proposition, and then deduces the contradiction.

6. Principle of mathematical induction: When a proposition about natural numbers needs to be proved, it can be proved by mathematical induction. Mathematical induction proves that the proposition is valid for all natural numbers by proving the basic situation and recursive relationship.

7. Comprehensive application principle: When solving mathematical proof problems, it is often necessary to comprehensively apply different logical reasoning principles and skills. Flexible use of various methods, combined with the characteristics of the topic to choose the appropriate strategy.

In a word, the principle of logical reasoning is the basis to ensure the correctness and integrity of the proof process when solving mathematical proof problems. Following these principles can improve the accuracy of solving problems and the rigor of thinking.