Let x0 of type ι → ι be given.

Assume H0: ∀ x1 . 1eb0a.. x1 ⟶ and (SNo (x0 x1)) (∃ x2 . and (SNo x2) (∃ x3 . and (SNo x3) (∃ x4 . and (SNo x4) (∃ x5 . and (SNo x5) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (∃ x8 . and (SNo x8) (x1 = bbc71.. (x0 x1) x2 x3 x4 x5 x6 x7 x8)))))))).

Assume H1: ∀ x1 . 1eb0a.. x1 ⟶ SNo (x0 x1).

Let x1 of type ι → ι be given.

Assume H2: ∀ x2 . 1eb0a.. x2 ⟶ and (SNo (x1 x2)) (∃ x3 . and (SNo x3) (∃ x4 . and (SNo x4) (∃ x5 . and (SNo x5) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (∃ x8 . and (SNo x8) (x2 = bbc71.. (x0 x2) (x1 x2) x3 x4 x5 x6 x7 x8))))))).

Assume H3: ∀ x2 . 1eb0a.. x2 ⟶ SNo (x1 x2).

Let x2 of type ι → ι be given.

Assume H4: ∀ x3 . 1eb0a.. x3 ⟶ and (SNo (x2 x3)) (∃ x4 . and (SNo x4) (∃ x5 . and (SNo x5) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (∃ x8 . and (SNo x8) (x3 = bbc71.. (x0 x3) (x1 x3) (x2 x3) x4 x5 x6 x7 x8)))))).

Assume H5: ∀ x3 . 1eb0a.. x3 ⟶ SNo (x2 x3).

Let x3 of type ι → ι be given.

Assume H6: ∀ x4 . 1eb0a.. x4 ⟶ and (SNo (x3 x4)) (∃ x5 . and (SNo x5) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (∃ x8 . and (SNo x8) (x4 = bbc71.. (x0 x4) (x1 x4) (x2 x4) (x3 x4) x5 x6 x7 x8))))).

Assume H7: ∀ x4 . 1eb0a.. x4 ⟶ SNo (x3 x4).

Let x4 of type ι → ι be given.

Assume H8: ∀ x5 . 1eb0a.. x5 ⟶ and (SNo (x4 x5)) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (∃ x8 . and (SNo x8) (x5 = bbc71.. (x0 x5) (x1 x5) (x2 x5) (x3 x5) (x4 x5) x6 x7 x8)))).

Let x5 of type ι be given.

Assume H9: 1eb0a.. x5.

Apply unknownprop_247af2b11bc65375389236e2f87b5d88dba18cbcd741fa8d933f377169c29afe with x0, x1, x2, x3, x4, x5, SNo (28f5a.. x0 x1 x2 x3 x4 x5) leaving 11 subgoals.

The subproof is completed by applying H0.

The subproof is completed by applying H1.

The subproof is completed by applying H2.

The subproof is completed by applying H3.

The subproof is completed by applying H4.

...

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Proofgold Proof