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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.
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.
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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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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Assume H38: SNoLt (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x13)))))) 0.
Assume H39: SNoLe (add_SNo x1 (minus_SNo x0)) x7.
Assume H40: SNoLe (add_SNo x2 (minus_SNo x1)) x8.
Assume H41: SNoLe (add_SNo x3 (minus_SNo x2)) x9.
Assume H42: SNoLe (add_SNo x4 (minus_SNo x3)) x10.
Assume H43: SNoLe (add_SNo x5 (minus_SNo x4)) x11.
Assume H44: SNoLe (add_SNo x6 (minus_SNo x5)) x12.
Assume H45: SNoLe (add_SNo x0 (minus_SNo x6)) x13.
Apply idl_negcycle_6 with x0, x1, x2, x3, x4, add_SNo x5 x6, x7, x8, x9, x10, add_SNo x11 x6, add_SNo x13 (minus_SNo x5) leaving 19 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.
Apply SNo_add_SNo with x5, x6 leaving 2 subgoals.
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 H10.
Apply SNo_add_SNo with x11, x6 leaving 2 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H6.
Apply SNo_add_SNo with x13, minus_SNo x5 leaving 2 subgoals.
The subproof is completed by applying H13.
The subproof is completed by applying L19.
Apply add_SNo_com with x13, minus_SNo x5, λ x14 x15 . SNoLt (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo (add_SNo x11 x6) x15))))) 0 leaving 3 subgoals.
The subproof is completed by applying H13.
The subproof is completed by applying L19.
Apply add_SNo_assoc with x11, x6, add_SNo (minus_SNo x5) x13, λ x14 x15 . SNoLt (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 x14)))) 0 leaving 4 subgoals.
The subproof is completed by applying H11.
The subproof is completed by applying H6.
Apply SNo_add_SNo with minus_SNo x5, x13 leaving 2 subgoals.
The subproof is completed by applying L19.
The subproof is completed by applying H13.
Apply add_SNo_assoc with x6, minus_SNo x5, x13, λ x14 x15 . SNoLt (add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 x15))))) 0 leaving 4 subgoals.
The subproof is completed by applying H6.
The subproof is completed by applying L19.
The subproof is completed by applying H13.
Apply SNoLeLt_tra with add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo (add_SNo x6 (minus_SNo x5)) x13))))), add_SNo x7 (add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x13))))), 0 leaving 5 subgoals.
Apply L32 with add_SNo x6 (minus_SNo x5).
The subproof is completed by applying L21.
The subproof is completed by applying L37.
The subproof is completed by applying SNo_0.
Apply add_SNo_Le2 with x7, add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo (add_SNo x6 (minus_SNo x5)) x13)))), add_SNo x8 (add_SNo x9 (add_SNo x10 (add_SNo x11 (add_SNo x12 x13)))) leaving 4 subgoals.
The subproof is completed by applying H7.
Apply L31 with add_SNo x6 ....
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