Definition sqrt3 := PythF 1 (PythF 1 1).

Lemma field_prop_1 : forall a b c, ~ b =F= 0 -> a/b =F= c -> a=F=c*b.
Ltac decompose_coordinates :=
repeat
match goal with
H: _ |- context[ (coordinates_of_point_F ?X) ] =>
let fx := fresh X "x" in
let fy := fresh X "y" in
destruct (coordinates_of_point_F X) as [[fx fy] _]
end.