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 be given.

Let x4 of type ι be given.

Let x5 of type ι be given.

Let x6 of type ι be given.

Let x7 of type ι be given.

Let x8 of type ι be given.

Let x9 of type ι be given.

Let x10 of type ι be given.

Assume H6: SNo x3.

Assume H7: SNo x4.

Assume H8: SNo x5.

Assume H9: SNo x6.

Assume H10: SNo x7.

Assume H11: SNo x8.

Assume H12: SNo x9.

Assume H13: SNo x10.

Apply unknownprop_8229c3616e9e41610bc79f2f56a50fda9fdf97a5060d19a39ffc03f0fce0477f with x0, x1, x2, bbc71.. x3 x4 x5 x6 x7 x8 x9 x10, 8d7df.. x0 x1 x2 (bbc71.. x3 x4 x5 x6 x7 x8 x9 x10) = x6 leaving 7 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.

Apply unknownprop_ecb826179418a88ca9938db10e4512d4b2d75d8190777ac7689e0335cc07481b with x3, x4, x5, x6, x7, x8, x9, x10 leaving 8 subgoals.

The subproof is completed by applying H6.

The subproof is completed by applying H7.

The subproof is completed by applying H8.

The subproof is completed by applying H9.

The subproof is completed by applying H10.

The subproof is completed by applying H11.

The subproof is completed by applying H12.

The subproof is completed by applying H13.

Assume H14: SNo (8d7df.. x0 x1 x2 (bbc71.. x3 x4 x5 x6 x7 x8 x9 x10)).

Assume H15: ∃ x11 . and (SNo x11) (∃ x12 . and (SNo x12) (∃ x13 . and (SNo x13) (∃ x14 . and (SNo x14) (bbc71.. x3 x4 x5 x6 x7 x8 x9 ... = ...)))).

...

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Proofgold Proof