| ∀ x0 : ι → ι → (ι → ι → ι) → ι . (∀ x1 . SNo x1 ⟶ ∀ x2 . SNo x2 ⟶ ∀ x3 x4 : ι → ι → ι . (∀ x5 . x5 ∈ SNoS_ (SNoLev x1) ⟶ ∀ x6 . SNo x6 ⟶ x3 x5 x6 = x4 x5 x6) ⟶ (∀ x5 . x5 ∈ SNoS_ (SNoLev x2) ⟶ x3 x1 x5 = x4 x1 x5) ⟶ x0 x1 x2 x3 = x0 x1 x2 x4) ⟶ ∀ x1 . SNo x1 ⟶ ∀ x2 : ι → ι → ι . ∀ x3 . SNo x3 ⟶ SNo_rec_i (λ x5 . λ x6 : ι → ι . x0 x1 x5 (λ x7 x8 . If_i (x7 = x1) (x6 x8) (x2 x7 x8))) x3 = x0 x1 x3 (λ x5 x6 . If_i (x5 = x1) (SNo_rec_i (λ x7 . λ x8 : ι → ι . x0 x1 x7 (λ x9 x10 . If_i (x9 = x1) (x8 x10) (x2 x9 x10))) x6) (x2 x5 x6)) |
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