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 Th14:
  G is configuration & {a1,a2} on A & {b1,b2} on B & a1,a2|'B & b1
  ,b2|'A & a1<>a2 & b1<>b2 implies a1,a2,b1,b2 is_a_quadrangle
proof
  assume that
A1: G is configuration and
A2: {a1,a2} on A and
A3: {b1,b2} on B and
A4: a1,a2|'B and
A5: b1,b2|'A and
A6: a1<>a2 and
A7: b1<>b2;
  b1|'A by A5;
  then
A8: a1,a2,b1 is_a_triangle by A1,A2,A6,Th10;
  b2|'A by A5;
  then a1,a2,b2 is_a_triangle by A1,A2,A6,Th10;
  then
A9: b2,a1,a2 is_a_triangle by Th11;
  a2|'B by A4;
  then b1,b2,a2 is_a_triangle by A1,A3,A7,Th10;
  then
A10: a2,b1,b2 is_a_triangle by Th11;
  a1|'B by A4;
  then b1,b2,a1 is_a_triangle by A1,A3,A7,Th10;
  hence thesis by A8,A10,A9;
end;
