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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.
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.
Claim L10: ...
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Claim L11: ...
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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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Assume H26: SNoLt (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 x9)))) 0.
Assume H27: SNoLe (add_SNo x1 (minus_SNo x0)) x5.
Assume H28: SNoLe (add_SNo x2 (minus_SNo x1)) x6.
Assume H29: SNoLe (add_SNo x3 (minus_SNo x2)) x7.
Assume H30: SNoLe (add_SNo x4 (minus_SNo x3)) x8.
Assume H31: SNoLe (add_SNo x0 (minus_SNo x4)) x9.
Apply idl_negcycle_4 with x0, x1, x2, add_SNo x3 x4, x5, x6, add_SNo x7 x4, add_SNo x9 (minus_SNo x3) leaving 13 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply SNo_add_SNo with x3, x4 leaving 2 subgoals.
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.
Apply SNo_add_SNo with x7, x4 leaving 2 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H4.
Apply SNo_add_SNo with x9, minus_SNo x3 leaving 2 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying L13.
Apply add_SNo_com with x9, minus_SNo x3, λ x10 x11 . SNoLt (add_SNo x5 (add_SNo x6 (add_SNo (add_SNo x7 x4) x11))) 0 leaving 3 subgoals.
The subproof is completed by applying H9.
The subproof is completed by applying L13.
Apply add_SNo_assoc with x7, x4, add_SNo (minus_SNo x3) x9, λ x10 x11 . SNoLt (add_SNo x5 (add_SNo x6 x10)) 0 leaving 4 subgoals.
The subproof is completed by applying H7.
The subproof is completed by applying H4.
Apply SNo_add_SNo with minus_SNo x3, x9 leaving 2 subgoals.
The subproof is completed by applying L13.
The subproof is completed by applying H9.
Apply add_SNo_assoc with x4, minus_SNo x3, x9, λ x10 x11 . SNoLt (add_SNo x5 (add_SNo x6 (add_SNo x7 x11))) 0 leaving 4 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying L13.
The subproof is completed by applying H9.
Apply SNoLeLt_tra with add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo (add_SNo x4 (minus_SNo x3)) x9))), add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 x9))), 0 leaving 5 subgoals.
Apply L22 with add_SNo x4 (minus_SNo x3).
The subproof is completed by applying L15.
The subproof is completed by applying L25.
The subproof is completed by applying SNo_0.
Apply add_SNo_Le2 with x5, add_SNo x6 (add_SNo x7 (add_SNo (add_SNo x4 (minus_SNo x3)) x9)), add_SNo x6 (add_SNo x7 (add_SNo x8 x9)) leaving 4 subgoals.
The subproof is completed by applying H5.
Apply L21 with add_SNo x4 (minus_SNo x3).
The subproof is completed by applying L15.
The subproof is completed by applying L24.
Apply add_SNo_Le2 with x6, add_SNo x7 (add_SNo (add_SNo x4 (minus_SNo x3)) x9), add_SNo x7 (add_SNo x8 x9) leaving 4 subgoals.
The subproof is completed by applying H6.
Apply L20 with add_SNo x4 (minus_SNo x3).
The subproof is completed by applying L15.
The subproof is completed by applying L23.
Apply add_SNo_Le2 with x7, add_SNo (add_SNo x4 (minus_SNo x3)) x9, add_SNo x8 x9 leaving 4 subgoals.
The subproof is completed by applying H7.
Apply SNo_add_SNo with add_SNo x4 (minus_SNo x3), x9 leaving 2 subgoals.
The subproof is completed by applying L15.
The subproof is completed by applying H9.
The subproof is completed by applying L16.
Apply add_SNo_Le1 with add_SNo x4 (minus_SNo x3), x9, x8 leaving 4 subgoals.
The subproof is completed by applying L15.
The subproof is completed by applying H9.
The subproof is completed by applying H8.
The subproof is completed by applying H30.
The subproof is completed by applying H26.
The subproof is completed by applying H27.
The subproof is completed by applying H28.
Apply add_SNo_com_3b_1_2 with x3, x4, minus_SNo x2, λ x10 x11 . SNoLe x11 (add_SNo x7 x4) leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying L12.
Apply add_SNo_Le1 with add_SNo x3 (minus_SNo x2), x4, x7 leaving 4 subgoals.
Apply SNo_add_SNo with x3, ... leaving 2 subgoals.
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