Bx=S(Kx)

Iota

S(Kx)yz = Kxz(yz) = x(yz)なので、
BxとしているところはS(Kx)とできる。

よって、Dの場合なら、
D = BB = S(KB)

また、addの場合なら、
add = BSD = BS(BB) = S(KS)(S(KB))

iで書き直すと
add = i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))))(i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))))(i(i(i(i)))))));

従来版
add = i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))))(i(i(i(i))))(i(i(i(i(i)))))(i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))))(i(i(i(i))))(i(i(i(i(i))))(i(i(i(i)))(i(i(i(i(i))))))(i(i(i(i))))));