 reserve x,y,X,Y for set;
reserve G for non empty multMagma,
  D for set,
  a,b,c,r,l for Element of G;
reserve M for non empty multLoopStr;
reserve H for non empty SubStr of G,
  N for non empty MonoidalSubStr of G;

theorem Th74:
  the multF of GFuncs X = (X-composition)||Funcs(X,X)
proof
A1: carr(GFuncs X) = Funcs(X,X) by Def40;
  op(GFuncs X) c= op(GPFuncs X) & dom op(GFuncs X) = [:carr(GFuncs X),
  carr( GFuncs X):] by Def23,FUNCT_2:def 1;
  hence thesis by A1,GRFUNC_1:23;
end;
