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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
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.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Assume H5: SNo x5.
Assume H6: SNo x6.
Assume H7: SNo x7.
Apply unknownprop_14a4ee8538d143fe8dc45eb2eb967d12f82b99130422357962aa2d0a55ab88f9 with bbc71.. x0 x1 x2 x3 x4 x5 x6 x7, 8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7) = x0 leaving 2 subgoals.
Apply unknownprop_ecb826179418a88ca9938db10e4512d4b2d75d8190777ac7689e0335cc07481b with x0, x1, x2, x3, x4, x5, x6, x7 leaving 8 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 (8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7)).
Assume H9: ∃ x8 . and (SNo x8) (∃ x9 . and (SNo x9) (∃ x10 . and (SNo x10) (∃ x11 . and (SNo x11) (∃ x12 . and (SNo x12) (∃ x13 . and (SNo x13) (∃ x14 . and (SNo x14) (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7 = bbc71.. (8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7)) x8 x9 x10 x11 x12 x13 x14))))))).
Apply H9 with 8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7) = x0.
Let x8 of type ι be given.
Assume H10: (λ x9 . and (SNo x9) (∃ x10 . and (SNo x10) (∃ x11 . and (SNo x11) (∃ x12 . and (SNo x12) (∃ x13 . and (SNo x13) (∃ x14 . and (SNo x14) (∃ x15 . and (SNo x15) (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7 = bbc71.. (8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7)) x9 x10 x11 x12 x13 x14 x15)))))))) x8.
Apply H10 with 8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7) = x0.
Assume H11: SNo x8.
Assume H12: ∃ x9 . and (SNo x9) (∃ x10 . and (SNo x10) (∃ x11 . and (SNo x11) (∃ x12 . and (SNo x12) (∃ x13 . and (SNo x13) (∃ x14 . and (SNo x14) (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7 = bbc71.. (8dd2c.. (bbc71.. x0 x1 x2 x3 x4 x5 x6 x7)) x8 x9 x10 x11 x12 ... ...)))))).
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