
theorem
for L be Abelian add-associative right_zeroed right_complementable
         well-unital associative distributive commutative
         almost_left_invertible domRing-like non trivial doubleLoopStr
holds NF 1._(L) = 1._(L)
proof
let L be Abelian add-associative right_zeroed right_complementable
         well-unital associative distributive commutative
         almost_left_invertible domRing-like non trivial doubleLoopStr;
set z = 1._(L);
A1: NF z = NormRatF z by Lm4
       .= [(1.L / LC(z`2)) * z`1, (1.L / LC(z`2)) * z`2];
z`2 is normalized by Def11;
then A2: LC(z`2) = 1.L;
A3: 1.L / LC(z`2) = (LC(z`2))"*LC(z`2) by A2
       .= 1.L by VECTSP_1:def 10;
hence NF z = [z`1, (1.L / LC(z`2)) * z`2] by A1,POLYNOM5:27
          .= [z`1, z`2] by A3,POLYNOM5:27
          .= z;
end;
