reserve G for IncProjStr;
reserve a,a1,a2,b,b1,b2,c,d,p,q,r for POINT of G;
reserve A,B,C,D,M,N,P,Q,R for LINE of G;

theorem Th17:
  (ex a,b,c st a,b,c is_a_triangle) & (for p,q ex M st {p,q} on M)
  implies ex p,P st p|'P
proof
  assume that
A1: ex a,b,c st a,b,c is_a_triangle and
A2: for p,q ex M st {p,q} on M;
  consider a,b,c such that
A3: a,b,c is_a_triangle by A1;
  consider P such that
A4: {a,b} on P by A2;
  take c,P;
  a on P & b on P by A4,INCSP_1:1;
  hence thesis by A3,Th5;
end;
