
theorem F815:
for F1 being Field,
    F2 being F1-monomorphic F1-homomorphic Field
for h being Monomorphism of F1,F2
for p being Element of the carrier of Polynom-Ring F1
holds (PolyHom h).(-p) = -(PolyHom h).p
proof
let F1 be Field, F2 be F1-monomorphic F1-homomorphic Field;
let h be Monomorphism of F1,F2;
let p be Element of the carrier of Polynom-Ring F1;
(PolyHom h).p + (PolyHom h).(-p)
  = (PolyHom h).(p + -p) by FIELD_1:24
 .= (PolyHom h).(0.(Polynom-Ring F1)) by RLVECT_1:5
 .= (PolyHom h).(0_.F1) by POLYNOM3:def 10
 .= 0_.F2 by FIELD_1:22
 .= 0.(Polynom-Ring F2) by POLYNOM3:def 10;
hence thesis by RLVECT_1:6;
end;
