let A, B be Point of (TOP-REAL 2); :: thesis: the_midpoint_of_the_segment (A,B) in LSeg (A,B)
consider C being Point of (TOP-REAL 2) such that
A1: C in LSeg (A,B) and
A2: C = the_midpoint_of_the_segment (A,B) and
|.(A - C).| = half_length (A,B) by Def1;
thus the_midpoint_of_the_segment (A,B) in LSeg (A,B) by A1, A2; :: thesis: verum