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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.
Let x8 of type ι be given.
Let x9 of type ι be given.
Let x10 of type ι be given.
Let x11 of type ι be given.
Let x12 of type ι be given.
Let x13 of type ι be given.
Let x14 of type ι be given.
Let x15 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.
Assume H8: SNo x8.
Assume H9: SNo x9.
Assume H10: SNo x10.
Assume H11: SNo x11.
Assume H12: SNo x12.
Assume H13: SNo x13.
Assume H14: SNo x14.
Assume H15: SNo x15.
Assume H16: SNoLt 0 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x15))))))).
Assume H17: SNoLe x8 (add_SNo x0 (minus_SNo x1)).
Assume H18: SNoLe x9 (add_SNo x1 (minus_SNo x2)).
Assume H19: SNoLe x10 (add_SNo x2 (minus_SNo x3)).
Assume H20: SNoLe x11 (add_SNo x3 (minus_SNo x4)).
Assume H21: SNoLe x12 (add_SNo x4 (minus_SNo x5)).
Assume H22: SNoLe x13 (add_SNo x5 (minus_SNo x6)).
Assume H23: SNoLe x14 (add_SNo x6 (minus_SNo x7)).
Assume H24: SNoLe x15 (add_SNo x7 (minus_SNo x0)).
Claim L25: ...
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Claim L26: ...
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Claim L27: ...
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Claim L28: ...
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Claim L29: ...
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Claim L30: ...
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Claim L31: ...
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Claim L32: ...
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Apply idl_negcycle_8 with x0, x1, x2, x3, x4, x5, x6, x7, minus_SNo x8, minus_SNo x9, minus_SNo x10, minus_SNo x11, minus_SNo x12, minus_SNo x13, minus_SNo x14, minus_SNo x15 leaving 25 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.
The subproof is completed by applying L25.
The subproof is completed by applying L26.
The subproof is completed by applying L27.
The subproof is completed by applying L28.
The subproof is completed by applying L29.
The subproof is completed by applying L30.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
Apply minus_SNo_Lt_contra3 with 0, add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (minus_SNo x15))))))) leaving 3 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_add_SNo_8 with minus_SNo x8, minus_SNo x9, minus_SNo x10, minus_SNo x11, minus_SNo x12, minus_SNo x13, minus_SNo x14, minus_SNo x15 leaving 8 subgoals.
The subproof is completed by applying L25.
The subproof is completed by applying L26.
The subproof is completed by applying L27.
The subproof is completed by applying L28.
The subproof is completed by applying L29.
The subproof is completed by applying L30.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
Apply minus_SNo_0 with λ x16 x17 . SNoLt x17 (minus_SNo (add_SNo (minus_SNo x8) (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (minus_SNo x15))))))))).
Apply minus_add_SNo_distr_m_7 with x8, x9, x10, x11, x12, x13, x14, minus_SNo x15, λ x16 x17 . SNoLt 0 x17 leaving 9 subgoals.
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.
The subproof is completed by applying H14.
The subproof is completed by applying L32.
Apply minus_SNo_invol with x15, λ x16 x17 . SNoLt 0 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x17))))))) leaving 2 subgoals.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
Apply minus_SNo_Le_swap with x8, x0, x1 leaving 4 subgoals.
The subproof is completed by applying H8.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H17.
Apply minus_SNo_Le_swap with x9, x1, x2 leaving 4 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H18.
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