If dialectical logic is satisfied by below:

1) Defined in individual domain D, and its true-valued function is valued on closed interval [-1,+1];

2) For any individual variable a and b, and their true-valued function T(a), T(b), define three operators: conjunction operator /\, excuse me where restricted to can not use standard symbols and as same as below, disjunction operator \/, and negation operator #, make

T(a)/\T(b)=min{T(a),T(b)}

T(a)\/T(b)=max{T(a),T(b)}

#T(a)=#(v+,v+-1)=(1-v+,-v+)

3) If results oeprated by the three operators above is included in [-1,+1], then we call dialectical logic as self-completed.

Obviously dialectical logic is a Boolean-operated algebra.

Lemma1. Dialectical logic is self-completed.

Theorem: If a subset S of dialectical logic is self-completed, then this subset must be a Boolean-operated algebra.

Especially when this subset is valued on {0,1}, then it is just the Boolean algebra. Therefor we have the conclusion: Boolean algebra is a special case of dialectical logic.

Is the proof above true?