
theorem str1a:
for F being Field
for E being FieldExtension of F holds deg(E,F) = 1 iff E == F
proof
let F be Field; let E be FieldExtension of F;
now assume deg(E,F) = 1;
   then A: the carrier of E = the carrier of F by quah1;
   F is Subfield of E by FIELD_4:7; then
   the carrier of F c= the carrier of E &
   the addF of F = (the addF of E) || the carrier of F &
   the multF of F = (the multF of E) || the carrier of F &
   1.F = 1.E & 0.F = 0.E by EC_PF_1:def 1;
   hence E == F by A;
   end;
hence thesis by quah1;
end;
