theorem Th10:
  G is configuration & {a1,a2} on A & a1<>a2 & b|'A implies a1,a2,
  b is_a_triangle
proof
  assume that
A1: G is configuration and
A2: {a1,a2} on A and
A3: a1<>a2 & b|'A and
A4: a1,a2,b are_collinear;
A5: a1 on A & a2 on A by A2,INCSP_1:1;
  ex P st a1 on P & a2 on P & b on P by A4,Th5;
  hence contradiction by A1,A3,A5;
end;
