reserve x,y,X,Y for set;
reserve C for non empty set;
reserve c for Element of C;
reserve f,f1,f2,f3,g,g1 for PartFunc of C,COMPLEX;
reserve r1,r2,p1 for Real;
reserve r,q,cr1,cr2 for Complex;

theorem
  (f/g)/(f1/g1) = (f(#)(g1|dom(g1^)))/(g(#)f1)
proof
  thus (f/g)/(f1/g1) = (f/g)(#)((f1/g1)^) by Th38
    .= (f/g)(#)(((g1|dom(g1^)))/f1) by Th42
    .= (f(#)(g1|dom(g1^)))/(g(#)f1) by Th41;
end;
