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Proofgold Proof

pf
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 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.
Let x8 of type ι be given.
Assume H2: SNo x1.
Assume H3: SNo x2.
Assume H4: SNo x3.
Assume H5: SNo x4.
Assume H6: SNo x5.
Assume H7: SNo x6.
Assume H8: SNo x7.
Assume H9: SNo x8.
Apply unknownprop_35aad255a0ebc1a79b9cd24e9634a038476cfcc2bcb07410ad3e7bec2e8f5a27 with x0, bbc71.. x1 x2 x3 x4 x5 x6 x7 x8, d4639.. x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8) = x2 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_ecb826179418a88ca9938db10e4512d4b2d75d8190777ac7689e0335cc07481b with x1, x2, x3, x4, x5, x6, x7, x8 leaving 8 subgoals.
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.
The subproof is completed by applying H8.
The subproof is completed by applying H9.
Assume H10: SNo (d4639.. x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8)).
Assume H11: ∃ 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.. x1 x2 x3 x4 x5 x6 x7 x8 = bbc71.. (x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8)) (d4639.. x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8)) x9 x10 x11 x12 x13 x14)))))).
Apply H11 with d4639.. x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8) = x2.
Let x9 of type ι be given.
Assume H12: (λ 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.. x1 x2 x3 x4 x5 x6 x7 x8 = bbc71.. (x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8)) (d4639.. x0 (bbc71.. x1 x2 x3 x4 x5 x6 x7 x8)) x10 ... ... ... ... ...))))))) ....
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