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))))).

Let x4 of type ι be given.

Assume H7: 1eb0a.. x4.

Apply unknownprop_6885b34a909c57357a9371c8f632d305bcfee5a7dda52ca2bf191272f9ad5d31 with x0, x1, x2, x3, x4, SNo (41ec1.. x0 x1 x2 x3 x4) leaving 9 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.

The subproof is completed by applying H5.

The subproof is completed by applying H6.

The subproof is completed by applying H7.

Assume H8: SNo (41ec1.. x0 x1 x2 x3 x4).

Assume H9: ∃ x5 . and (SNo x5) (∃ x6 . and (SNo x6) (∃ x7 . and (SNo x7) (x4 = bbc71.. (x0 x4) (x1 x4) (x2 x4) (x3 x4) (41ec1.. x0 x1 x2 x3 x4) x5 x6 x7))).

The subproof is completed by applying H8.

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Proofgold Proof