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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.
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 L30: ...
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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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Claim L41: ...
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Claim L42: ...
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Claim L43: ...
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Assume H44: SNoLt (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x15))))))) 0.
Assume H45: SNoLe (add_SNo x1 (minus_SNo x0)) x8.
Assume H46: SNoLe (add_SNo x2 (minus_SNo x1)) x9.
Assume H47: SNoLe (add_SNo x3 (minus_SNo x2)) x10.
Assume H48: SNoLe (add_SNo x4 (minus_SNo x3)) x11.
Assume H49: SNoLe (add_SNo x5 (minus_SNo x4)) x12.
Assume H50: SNoLe (add_SNo x6 (minus_SNo x5)) x13.
Assume H51: SNoLe (add_SNo x7 (minus_SNo x6)) x14.
Assume H52: SNoLe (add_SNo x0 (minus_SNo x7)) x15.
Apply idl_negcycle_7 with x0, x1, x2, x3, x4, x5, add_SNo x6 x7, x8, x9, x10, x11, x12, add_SNo x13 x7, add_SNo x15 (minus_SNo x6) leaving 22 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.
Apply SNo_add_SNo with x6, x7 leaving 2 subgoals.
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 H10.
The subproof is completed by applying H11.
The subproof is completed by applying H12.
Apply SNo_add_SNo with x13, x7 leaving 2 subgoals.
The subproof is completed by applying H13.
The subproof is completed by applying H7.
Apply SNo_add_SNo with x15, minus_SNo x6 leaving 2 subgoals.
The subproof is completed by applying H15.
The subproof is completed by applying L22.
Apply add_SNo_com with x15, minus_SNo x6, λ x16 x17 . SNoLt (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo (add_SNo x13 x7) x17)))))) 0 leaving 3 subgoals.
The subproof is completed by applying H15.
The subproof is completed by applying L22.
Apply add_SNo_assoc with x13, x7, add_SNo (minus_SNo x6) x15, λ x16 x17 . SNoLt (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x16))))) 0 leaving 4 subgoals.
The subproof is completed by applying H13.
The subproof is completed by applying H7.
Apply SNo_add_SNo with minus_SNo x6, x15 leaving 2 subgoals.
The subproof is completed by applying L22.
The subproof is completed by applying H15.
Apply add_SNo_assoc with x7, minus_SNo x6, x15, λ x16 x17 . SNoLt (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 x17)))))) 0 leaving 4 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying L22.
The subproof is completed by applying H15.
Apply SNoLeLt_tra with add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo (add_SNo x7 (minus_SNo x6)) x15)))))), add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 x15)))))), 0 leaving 5 subgoals.
Apply L37 with add_SNo x7 (minus_SNo x6).
The subproof is completed by applying L24.
The subproof is completed by applying L43.
The subproof is completed by applying SNo_0.
Apply add_SNo_Le2 with x8, add_SNo ... ..., ... leaving 4 subgoals.
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