A Class of Geometry Statements of Constructive Type and Geometry TheoremProving

This paper is a technical extension of our previous work not published fully. It describes how to generate non-degenerate conditions in geometric form for a class of geometry statements of constructive type, called Class C, using Wu''s method. We reemphasize a mathematical theorem found by us stating that in the irreducible case, the non-degenerate conditions generated by our method are sufficient for a geometry statement in Class C to be valid metric geometry. We prove a new theorem: if an irreducible statement in Class C is confirmed to be generally true, then that statement is valid under the geometric non-degenerate conditions generated by our method. As a direct consequence, most of the geometry theorems proved (to be generally true) by our technique based on the Grobner basis method are valid under those geometric non-degenerate conditions. We also find subclasses of Class C and prove a theorem that the non-degenerate conditions generated by our method are sufficient for a statement in those subclasses to be valid in Euclidean geometry.