theorem Th61:
  A,B,C is_a_triangle implies median(A,B,C) is being_line
  proof
    assume
A1: A,B,C is_a_triangle;
A2: A,B,C are_mutually_distinct by A1,EUCLID_6:20;
    assume not median(A,B,C) is being_line;
    then consider x such that
A3: median(A,B,C)={x} by Th6;
    set D = the_midpoint_of_the_segment(B,C);
    A in median(A,B,C) & D in median(A,B,C) by EUCLID_4:41;
    then A = x & D = x by A3,TARSKI:def 1;
    then A in LSeg(B,C) & LSeg(B,C) c= Line(B,C) by Th21,RLTOPSP1:73;
    hence contradiction by A1,A2,MENELAUS:13;
  end;
