560 ページ

$$Ω=χ_0(0)$$

$$I=χ_1(0)$$

$$Λ_0=ψ_{χ_M(0)}(0)$$

## 2行

 (0)(1,1) φ(1,0) (0)(1,1)(2,1) φ(2,0) (0)(1,1)(2,1)(2,1) φ(3,0) (0)(1,1)(2,1)(3,1) φ(1,0,0)$$=Ψ^0_Ω(0)$$ (0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1) φ(1,0,1)$$=Ψ^0_Ω(1)$$ (0)(1,1)(2,1)(3,1)(2,1) φ(1,1,0)Ψ^0_Ω(Ω) (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1) φ(1,0,φ(1,1,0)+1)$$=Ψ^0_Ω(Ψ^0_Ω(Ω))$$ (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1) φ(1,0,φ(1,1,0)+2)$$Ψ^0_Ω(Ψ^0_Ω(Ω)+1)$$ (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1) φ(1,1,1)$$=Ψ^0_Ω(Ω+1)$$ (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1) φ(1,0,φ(1,1,1)+1)$$Ψ^0_Ω(Ψ^0_Ω(Ω+1))$$ (0)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1) φ(1,1,2)$$=Ψ^0_Ω(Ω+2)$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1) φ(1,2,0)$$=Ψ^0_Ω(Ω\cdot2)$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(1,1)(2,1)(3,1) φ(1,0,φ(1,2,0)+1)$$=Ψ^0_Ω(Ψ^0_Ω(Ω\cdot2))$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(1,1)(2,1)(3,1)(2,1) φ(1,1,φ(1,2,0)+1)$$=Ψ^0_Ω(Ω+Ψ^0_Ω(Ω\cdot2))$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1) φ(1,0,φ(1,1,φ(1,2,0)+1)+1)$$=Ψ_Ω(Ψ^0_Ω(Ω+Ψ^0_Ω(Ω\cdot2)))$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(1,1)(2,1)(3,1)(2,1)(1,1)(2,1)(3,1)(2,1) φ(1,1,φ(1,2,0)+2)$$=Ψ^0_Ω(Ω+Ψ^0_Ω(Ω\cdot2)+1)$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(1,1)(2,1)(3,1)(2,1)(2,1) φ(1,2,1)$$=Ψ^0_Ω(Ω\cdot2+1)$$ (0)(1,1)(2,1)(3,1)(2,1)(2,1)(2,1) φ(1,3,0)$$=Ψ^0_Ω(Ω\cdot3)$$ (0)(1,1)(2,1)(3,1)(2,1)(3,1) φ(2,0,0)$$=Ψ^0_Ω(Ω^2)$$

## 3行 ψ_Ω(Λ_0)まで

 (0)(1,1,1) $$ψ_Ω(χ_0(ω))\\Ψ^0_Ω(Ω_ω)\\=\text{PTO}(Π^1_1-\text{CA}_0)$$ (0)(1,1,1)(1,1,1) $$ψ_Ω(χ_0(ω)\cdot2)$$ (0)(1,1,1)(2,1) $$ψ_Ω(χ_0(ω)\cdotχ_0(0))$$ (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1) $$ψ_Ω(χ_0(ω)\cdotχ_0(0)+ψ_{χ_0(1)}(χ_0(ω)\cdotχ_0(0)))$$ (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,1)(4,2,1)(5,1) $$ψ_Ω(χ_0(ω)\cdotχ_0(0)+ψ_{χ_0(1)}\\(χ_0(ω)\cdotχ_0(0)+ψ_{χ_0(1)}(χ_0(ω)\cdotχ_0(0))))$$ (0)(1,1,1)(2,1)(1,1)(2,2,1)(3,1)(2,2)(3,2) $$ψ_Ω(χ_0(ω)\cdotχ_0(0)+χ_0(1))$$ (0)(1,1,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_1(0))\\=Ψ^0_Ω(Ψ^0_{Ξ(1)}(2))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1) $$ψ_Ω(Φ_1(ω))\\=Ψ^0_Ω(Ψ^0_{Ξ(1)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_2(0))\\=Ψ^0_Ω(Ξ(1))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_2(0)\cdot2)\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ξ(1)))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_2(0)^2)\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ξ(1))^2)$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(Φ_1(Φ_2(0)+1))\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ψ^0_{Ξ(1)}(Ξ(1))))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2)(4,2,1) $$ψ_Ω(Φ_1(Φ_2(0)+ω))\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ψ^0_{Ξ(1)}(Ξ(1))+ω))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2)(4,2,1)(5,2)(4) $$ψ_Ω(Φ_2(1))\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ξ(1)+1))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1,1) $$ψ_Ω(Φ_2(ω))\\=Ψ^0_Ω(Ξ(1)+Ψ^0_{Ξ(1)}(Ξ(1)+ω))$$ (0)(1,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_3(0))\\=Ψ^0_Ω(Ξ(1)\cdot2)$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(1,1,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_{Φ_1(0)}(0))\\=Ψ^0_Ω(Ξ(1)\cdotΨ^0_{Ξ(1)}(0))$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(1,1,1)(2,1,1)(3,1)(3,1)(1,1,1)(2,1,1)(3,1)(2) $$ψ_Ω(Φ_{Φ_{Φ_1(0)}(0)}(0))\\=Ψ^0_Ω(Ξ(1)\cdotΨ^0_{Ξ(1)}(Ξ(1)\cdotΨ^0_{Ξ(1)}(0)))$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(2) $$ψ_Ω(ψ_I(0))\\=Ψ^0(Ξ(1)^2)$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(2,1)(1,1,1)(2,1,1)(3,1)(3,1)(2) $$ψ_Ω(ψ_I(0)^2)\\=Ψ^0(Ξ(1)^2+Ψ^0_{Ξ(1)}(Ξ(1)^2)^2)$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(2,1,1) $$ψ_Ω(ψ_I(ω))\\=Ψ^0(Ξ(1)^2+Ψ^0_{Ξ(1)}(Ξ(1)^2+ω))$$ (0)(1,1,1)(2,1,1)(3,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(I)\\=Ψ^0(Ξ(1)^2+Ξ(1))$$ (0)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5) $$ψ_Ω(Φ_1(I+1))\\=Ψ^0_Ω(Ψ^0_{Ξ(2)}(3))$$ (0)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5,2)(6,3,1)(7,3,1)(8,3)(7) $$ψ_Ω(Φ_1(I+2))\\=Ψ^0_Ω(Ψ^0_{Ψ^1_{Ξ(2)}(3)}(4))$$ (0)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5,2,1) $$ψ_Ω(Φ_1(I+ω))\\=Ψ^0_Ω(Ψ^0_{Ψ^1_{Ξ(2)}(3)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)(5,2,1)(6,2)(5) $$ψ_Ω(Φ_2(I+1))\\=Ψ^0_Ω(Ψ^1_{Ξ(2)}(3))$$ (0)(1,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_1(ω))\\=Ψ^0_Ω(Ψ^0_{Ξ(2)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_I(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_I(χ_1(ω))^2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2)(4,2)(5,2)(4,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2)(4,2)(5,2)(4,1)(3,2)(4,2)(5,2)(4,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)\\+ψ_I(χ_1(ω))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2)(4,2)(5,2)(4,2) $$ψ_Ω(χ_1(ω)+χ_0(ψ_I(χ_1(ω))+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1) $$ψ_Ω(χ_1(ω)+χ_0(ψ_I(χ_1(ω))+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2)(5,2)(4) $$ψ_Ω(χ_1(ω)+ψ_I(χ_1(ω)+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2)(5,2)(4,2,1)(5,2)(4) $$ψ_Ω(χ_1(ω)+I)$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2)(4,2)(5,2)(4,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2)(4,2)(5,2)(4,2) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)+χ_0(ψ_I(χ_1(ω))+1)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)+χ_0(ψ_I(χ_1(ω))+ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(2,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)\\+ψ_{χ_0(I+1)}(χ_1(ω)))\cdotψ_I(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_{χ_0(ψ_I(χ_1(ω))+1)}(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω)))^2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(3,2)(4,2)(5,2)(4,2) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+χ_0(ψ_I(χ_1(ω))+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+χ_0(ψ_I(χ_1(ω))+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_I(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(2,1,1) $$ψ_Ω(χ_1(ω)+ψ_{χ_0(I+1)}(χ_1(ω))\cdotω)$$ (0)(1,1,1)(2,1,1)(3,1,1)(1,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_1(ω)\cdot2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1)(3,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(Φ_1(χ_1(ω)+1))\\=Ψ^0_Ω(Ψ^0_{Ψ^1_{Ξ(2)}(ω)}(ω+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(ψ_{χ_1(0)}(χ_1(ω))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2) $$ψ_Ω(χ_1(χ_1(0)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2) $$ψ_Ω(χ_1(χ_1(0))+ψ_I(χ_1(χ_1(0))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2)(4,2)(5,2)(4,1)(3,2)(4,2)(5,2)(4,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(ψ_I(χ_1(χ_1(0)))+1)}(χ_1(χ_1(0))\\+ψ_{χ_1(0)}(χ_1(χ_1(0)))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2)(4,2)(5,2)(4,2) $$ψ_Ω(χ_1(χ_1(0))+χ_0(ψ_I(χ_1(χ_1(0)))+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2,1)(4,2,1)(5,2)(5,2)(4) $$ψ_Ω(χ_1(χ_1(0))+ψ_I(χ_1(χ_1(0))+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3,1) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(ω))\\+ψ_I(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(ω))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(ω)\cdot2))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(3,2,1)(4,2,1)(5,2)(6,3,1)(7,3,1)(8,3,1)(7,3,1)(8,2)(4) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(χ_1(0))))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(2,1,1) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(χ_1(0)))\cdotω)$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(4,2,1) $$ψ_Ω(χ_1(χ_1(0))+ψ_{χ_0(I+1)}(χ_1(χ_1(0))\\+χ_0(χ_1(χ_1(0))+ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1)(4,2,1)(5,2,1)(6,2,1) $$ψ_Ω(χ_1(χ_1(0))+χ_1(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2) $$ψ_Ω(χ_1(χ_0(χ_1(0)+1)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2)(4,2,1)(5,2,1)(6,2)(7,3,1)(8,3,1)(9,3,1)(8,3,1)(9,2)(5) $$ψ_Ω(χ_1(χ_1(1)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(1,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_1(χ_1(ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2) $$ψ_Ω(ψ_{χ_2(0)}(0))\\=Ψ^0_Ω(Ξ(2))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2) $$ψ_Ω(ψ_{χ_2(0)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ξ(2)}(Ξ(2)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(Φ_1(ψ_{χ_2(0)}(0)+1))\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2))+1}}(Ψ^0_{Ψ^1_{Ξ(2)}(Ψ^0_{Ξ(2)}(Ξ(2)))}\\(Ψ^0_{Ξ(2)}(Ξ(2))+1)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(ψ_{χ_2(0)}(0)+ω))\\=Ψ^0_Ω(Ξ(2)\\+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2))+1}}(Ψ^0_{Ξ(2)}(Ψ^0_{Ξ(2)}(Ξ(2))+ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(ψ_{χ_2(0)}(1))\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2))+1}}(Ξ(2)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(4)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(ψ_{χ_2(0)}(1)\cdot2)\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2))}(Ξ(2)+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1,1) $$ψ_Ω(ψ_{χ_2(0)}(ω))\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2))}(Ξ(2)+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1)(2,1,1)(3,1)(2) $$ψ_Ω(χ_2(0))\\=Ψ^0_Ω(Ξ(2)+Ψ^1_{Ξ(2)}(Ξ(2)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_2(ω))\\=Ψ^0_Ω(Ξ(2)+Ψ^0_{Ξ(2)}(Ξ(2)+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_3(ω))\\=Ψ^0_Ω(Ξ(2)\cdot2+Ψ^0_{Ξ(2)}(Ξ(2)\cdot2+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3) $$ψ_Ω(ψ_{χ_ω(0)}(0))\\=Ψ^0_Ω(Ξ(2)\cdotω)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(1,1,1)(2,1,1)(3,1,1)(3) $$ψ_Ω(ψ_{χ_ω(0)}(0)\cdot2)\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ξ(2)}(Ξ(2)\cdotω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(1,1,1)(2,1,1)(3,1,1)(3) $$ψ_Ω(ψ_{χ_ω(0)}(0)^2)\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)^2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(Φ_1(ψ_{χ_ω(0)}(0)+1))\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+1}}\\(Ψ^0_{Ψ^1_{Ξ(2)}(Ψ^0_{Ξ(2)}(Ξ(2)\cdotω))}(Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+1)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_1(ψ_{χ_ω(0)}(0)+ω))\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+1}}\\(Ψ^0_{Ξ(2)}(Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+ω)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2)(4) $$ψ_Ω(ψ_{χ_2(ψ_{χ_ω(0)}(0)+1)}(0))\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+1}}(Ξ(2)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_2(ψ_{χ_ω(0)}(0)+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1)(5) $$ψ_Ω(ψ_{χ_ω(0)}(1))\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^0_{Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+1}}(Ξ(2)\cdotω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1)(5)(3,2,1) $$Ψ^0_Ω(Ξ(2)\cdotω\\+Ω_{Ψ^0_{Ξ(2)}(Ξ(2)\cdotω)+ω})$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1)(3,2,1)(4,2,1)(5,2,1)(5)(3,2,1)(4,2,1)(5,2,1)(5) $$Ψ^0_Ω(Ξ(2)\cdotω\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotω)}(Ξ(2)\cdotω+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1) $$ψ_Ω(ψ_{χ_ω(0)}(ω))\\=Ψ^0_Ω(Ξ(2)\cdotω\\+Ψ^0_{Ψ^1_{Ξ(2)}(Ξ(2)\cdotω)}(Ξ(2)\cdotω+ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2) $$ψ_Ω(χ_ω(0))\\=Ψ^0_Ω(Ξ(2)\cdotω+Ψ^1_{Ξ(2)}(Ξ(2)\cdotω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2) $$ψ_Ω(χ_ω(0)+ψ_{χ_ω(0)}(χ_ω(0)))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5) $$ψ_Ω(χ_ω(0)+ψ_{χ_ω(0)}(χ_ω(0)+1))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5)(4,2,1)(5,2)(4) $$ψ_Ω(χ_ω(0)\cdot2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1)(2,1,1) $$ψ_Ω(χ_ω(0)\cdotω)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1,1) $$ψ_Ω(χ_ω(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1,1)(2,1,1)(3,1,1) $$ψ_Ω(χ_{ω+1}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3)(2,1,1)(3,1,1)(3) $$ψ_Ω(ψ_{χ_{ω\cdot2}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1) $$ψ_Ω(ψ_{χ_{χ_0(0)}(0)}(0))\\=Ψ^0_Ω(Ξ(2)\cdotΩ)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)(3,2,1) $$ψ_Ω(ψ_{χ_{χ_0(0)}(0)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)(3,2,1)(4,2)(3) $$ψ_Ω(χ_{χ_0(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)(3,2,1)(4,2,1) $$ψ_Ω(χ_{χ_0(0)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)(3,2,1)(4,2,1)(3,2,1)(4,2,1) $$ψ_Ω(χ_{χ_0(0)+1}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,1)(3,2,1)(4,2,1)(4,1) $$ψ_Ω(ψ_{χ_{χ_0(0)\cdot2}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1)(2,2,1)(3,2,1)(4,2,1)(4,2) $$ψ_Ω(ψ_{χ_{χ_0(1)}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1) $$ψ_Ω(ψ_{χ_{χ_0(ω)}(0)}(0))\\=Ψ^0_Ω(Ξ(2)\cdotΩ_ω)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(1,1,1) $$ψ_Ω(ψ_{χ_{χ_0(ω)}(0)}(0)\cdot2)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1) $$ψ_Ω(ψ_{χ_{χ_0(ω)}(0)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2)(4) $$ψ_Ω(χ_{χ_0(ω)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_{χ_0(ω)}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1)(4,2,1)(5,2,1) $$ψ_Ω(χ_{χ_0(ω)+1}(ω))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,1)(4,2,1)(5,2,1)(5,1)(1,1,1) $$ψ_Ω(ψ_{χ_{χ_0(ω)\cdot2}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1)(3,2,1)(4,2,1)(5,2,1)(5,2)(3,2,1) $$ψ_Ω(ψ_{χ_{χ_0(ω\cdot2)}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1,1) $$ψ_Ω(ψ_{χ_{χ_0(ω^2)}(0))}(0)$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1,1)(3,1,1) $$ψ_Ω(ψ_{χ_{χ_1(ω)}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(1,1,1)(2,1,1)(3,1,1)(3,1) $$ψ_Ω(ψ_{χ_{χ_{χ_0(0)}(0)}(0)}(0))$$ (0)(1,1,1)(2,1,1)(3,1,1)(3,1)(2) $$ψ_Ω(Λ_0)\\=Ψ^0_Ω(Ξ(2)^2)$$

\begin{array}&=&\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2)&=&Ψ^0_Ω(Ξ(3))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2)(1,1,1)(2,1,1)\\(3,1,1)(3,1,1)(2,1,1)(3,1)(2)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ξ(3)}(Ξ(3)))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2)(4)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^1_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3)))}(Ξ(3)+1))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2)(6,3,1)(7,3,1)(8,3)(7)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^2_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3)))}(Ξ(3)+1))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2)(6,3,1)(7,3,1)(8,3)(7,3)\\(8,4,1)(9,4,1)(10,4)(9)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^1_{Ψ^2_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3)))}(Ξ(3)+1)}(Ξ(3)+2))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2,1)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^2_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3)))}(Ξ(3)+ω))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2,1)(4,2,1)(5,2)(4)&=&Ψ^0_Ω(Ξ(3)+Ψ^2_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3))))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2,1)(5,2,1)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ξ(3)}(Ψ^0_{Ξ(3)}(Ξ(3))+ω))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1)(3,2,1)(4,2,1)\\(5,2,1)(5,2,1)(4,2,1)(5,2)(4)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^1_{Ξ(3)}(Ξ(3))}(Ξ(3)+1))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1,1)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^1_{Ξ(3)}(Ξ(3))}(Ξ(3)+ω))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(2,1,1)(3,1)(2)&=&Ψ^0_Ω(Ξ(3)+Ψ^1_{Ξ(3)}(Ξ(3)))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)\\(5)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^2_{Ξ(3)}(Ψ^1_{Ξ(3)}(Ξ(3)))}(Ξ(3)+1))\\(0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)\\(2,1,1)(3,1)(4,2,1)(5,2,1)(6,2)\\(5,2)(6,3,1)(7,3,1)(8,3)(7)&=&Ψ^0_Ω(Ξ(3)+Ψ^0_{Ψ^1_{Ψ^2_{Ξ(3)}(Ψ^1_{Ξ(3)}(Ξ(3)))}(Ξ(3)+1)}(Ξ(3)+2))\\ \\(0)(1,1,1)(2,1,1)(3,1,1)(4,1)\\(2)&=&Ψ^0_Ω(K)\\(0)(1,1,1)(2,1,1)(3,1,1)(4,1)\\(5,2)&=&Ψ^0_Ω(φ_1(K+1))\\(0)(1,1,1)(2,2)&=&\text{pDAN}\\(0)(1,1,1)(2,2,1)(2,2)&=&\text{sDAN}\\(0)(1,1,1)(2,2,1)(3)&=&\text{DAN}\end{array}