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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.
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.
Claim L12: ...
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Claim L13: ...
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Claim L14: ...
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Claim L15: ...
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Claim L16: ...
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Claim L17: ...
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Claim L18: ...
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Claim L19: ...
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Claim L20: ...
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Claim L21: ...
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Claim L22: ...
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Claim L23: ...
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Claim L24: ...
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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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Assume H32: SNoLt (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11))))) 0.
Assume H33: SNoLe (add_SNo x1 (minus_SNo x0)) x6.
Assume H34: SNoLe (add_SNo x2 (minus_SNo x1)) x7.
Assume H35: SNoLe (add_SNo x3 (minus_SNo x2)) x8.
Assume H36: SNoLe (add_SNo x4 (minus_SNo x3)) x9.
Assume H37: SNoLe (add_SNo x5 (minus_SNo x4)) x10.
Assume H38: SNoLe (add_SNo x0 (minus_SNo x5)) x11.
Apply idl_negcycle_5 with x0, x1, x2, x3, add_SNo x4 x5, x6, x7, x8, add_SNo x9 x5, add_SNo x11 (minus_SNo x4) leaving 16 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.
Apply SNo_add_SNo with x4, x5 leaving 2 subgoals.
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.
Apply SNo_add_SNo with x9, x5 leaving 2 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H5.
Apply SNo_add_SNo with x11, minus_SNo x4 leaving 2 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying L16.
Apply add_SNo_com with x11, minus_SNo x4, λ x12 x13 . SNoLt (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo (add_SNo x9 x5) x13)))) 0 leaving 3 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying L16.
Apply add_SNo_assoc with x9, x5, add_SNo (minus_SNo x4) x11, λ x12 x13 . SNoLt (add_SNo x6 (add_SNo x7 (add_SNo x8 x12))) 0 leaving 4 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying H5.
Apply SNo_add_SNo with minus_SNo x4, x11 leaving 2 subgoals.
The subproof is completed by applying L16.
The subproof is completed by applying H11.
Apply add_SNo_assoc with x5, minus_SNo x4, x11, λ x12 x13 . SNoLt (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 x13)))) 0 leaving 4 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying L16.
The subproof is completed by applying H11.
Apply SNoLeLt_tra with add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo (add_SNo x5 (minus_SNo x4)) x11)))), add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11)))), 0 leaving 5 subgoals.
Apply L27 with add_SNo x5 (minus_SNo x4).
The subproof is completed by applying L18.
The subproof is completed by applying L31.
The subproof is completed by applying SNo_0.
Apply add_SNo_Le2 with x6, add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo (add_SNo x5 (minus_SNo x4)) x11))), add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x11))) leaving 4 subgoals.
The subproof is completed by applying H6.
Apply L26 with add_SNo x5 (minus_SNo x4).
The subproof is completed by applying L18.
The subproof is completed by applying L30.
Apply add_SNo_Le2 with x7, add_SNo x8 (add_SNo x9 (add_SNo (add_SNo x5 (minus_SNo x4)) x11)), add_SNo x8 (add_SNo x9 (add_SNo x10 x11)) leaving 4 subgoals.
The subproof is completed by applying H7.
Apply L25 with add_SNo x5 (minus_SNo x4).
The subproof is completed by applying L18.
The subproof is completed by applying L29.
Apply add_SNo_Le2 with x8, add_SNo x9 (add_SNo (add_SNo x5 ...) ...), ... leaving 4 subgoals.
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