
theorem lemug1:
for F being Field holds the doubleLoopStr of F == F
proof
let F be Field;
set G = the doubleLoopStr of F;
the addF of F = (the addF of G) || the carrier of F &
the multF of F = (the multF of G) || the carrier of F &
1.F = 1.G & 0.F = 0.G;
then F is Subfield of G & G is Subfield of F by EC_PF_1:def 1;
hence thesis by FIELD_7:def 2;
end;
