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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.
Let x16 of type ι be given.
Let x17 of type ι be given.
Let x18 of type ι be given.
Let x19 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: SNo x16.
Assume H17: SNo x17.
Assume H18: SNo x18.
Assume H19: SNo x19.
Assume H20: SNoLt 0 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 x19))))))))).
Assume H21: SNoLe x10 (add_SNo x0 (minus_SNo x1)).
Assume H22: SNoLe x11 (add_SNo x1 (minus_SNo x2)).
Assume H23: SNoLe x12 (add_SNo x2 (minus_SNo x3)).
Assume H24: SNoLe x13 (add_SNo x3 (minus_SNo x4)).
Assume H25: SNoLe x14 (add_SNo x4 (minus_SNo x5)).
Assume H26: SNoLe x15 (add_SNo x5 (minus_SNo x6)).
Assume H27: SNoLe x16 (add_SNo x6 (minus_SNo x7)).
Assume H28: SNoLe x17 (add_SNo x7 (minus_SNo x8)).
Assume H29: SNoLe x18 (add_SNo x8 (minus_SNo x9)).
Assume H30: SNoLe x19 (add_SNo x9 (minus_SNo x0)).
Claim L31: ...
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Claim L32: ...
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Claim L33: ...
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Claim L34: ...
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Claim L35: ...
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Claim L36: ...
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Claim L37: ...
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Claim L38: ...
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Claim L39: ...
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Claim L40: ...
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Apply idl_negcycle_10 with x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, minus_SNo x10, minus_SNo x11, minus_SNo x12, minus_SNo x13, minus_SNo x14, minus_SNo x15, minus_SNo x16, minus_SNo x17, minus_SNo x18, minus_SNo x19 leaving 31 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 H8.
The subproof is completed by applying H9.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
The subproof is completed by applying L33.
The subproof is completed by applying L34.
The subproof is completed by applying L35.
The subproof is completed by applying L36.
The subproof is completed by applying L37.
The subproof is completed by applying L38.
The subproof is completed by applying L39.
The subproof is completed by applying L40.
Apply minus_SNo_Lt_contra3 with 0, 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) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (add_SNo (minus_SNo x17) (add_SNo (minus_SNo x18) (minus_SNo x19))))))))) leaving 3 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_add_SNo_10 with minus_SNo x10, minus_SNo x11, minus_SNo x12, minus_SNo x13, minus_SNo x14, minus_SNo x15, minus_SNo x16, minus_SNo x17, minus_SNo x18, minus_SNo x19 leaving 10 subgoals.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
The subproof is completed by applying L33.
The subproof is completed by applying L34.
The subproof is completed by applying L35.
The subproof is completed by applying L36.
The subproof is completed by applying L37.
The subproof is completed by applying L38.
The subproof is completed by applying L39.
The subproof is completed by applying L40.
Apply minus_SNo_0 with λ x20 x21 . SNoLt x21 (minus_SNo (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) (add_SNo (minus_SNo x15) (add_SNo ... ...)))))))).
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