
theorem str11:
for F being Field
for E1,E2 being FieldExtension of F st E1 == E2 holds deg(E1,F) = deg(E2,F)
proof
let F be Field, E1,E2 be FieldExtension of F;
set V1 = VecSp(E1,F), V2 = VecSp(E2,F);
assume E1 == E2; then AS: V1 = V2 by str12;
per cases;
suppose F: V1 is finite-dimensional;
  hence deg(E1,F) = dim V2 by AS,FIELD_4:def 7
                 .= deg(E2,F) by AS,F,FIELD_4:def 7;
  end;
suppose F: not V1 is finite-dimensional;
  hence deg(E1,F) = -1 by FIELD_4:def 7
                 .= deg(E2,F) by AS,F,FIELD_4:def 7;
  end;
end;
