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This paper introduces each step with Branford is a geometric proof-flow occurs in the present, and the proof, as explained in Branford look at the problems that overlooked when divided into three phases. First, the intuitive proof is a proven and universal generalization, mathematical proof deals with abstract math concepts through manipulation of mathematical symbols. But this seems excessive leap that takes place between the two will have. Second, the student can prove in an intuitive level but there did not reach the level of mathematical proof, if the student is able to use their certification process to a logical and rational verbal proof enough to convince others, there is the problem of whether the student to see the level of intuitive proof. In this paper, through the intuitive proof and mathematical proof as a way to compensate for this problem, termed as' intuitive mathematical proof, and the proof is intended to refine the three-phase theory of Branford geometric theory proved to step 4.