 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
  x is Element of GPFuncs X iff x is PartFunc of X,X
proof
  carr(GPFuncs X) = PFuncs(X,X) by Def37;
  hence thesis by PARTFUN1:45,46;
end;
