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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.
Let x20 of type ι be given.
Let x21 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: SNo x20.
Assume H21: SNo x21.
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Assume H62: SNoLt (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo x19 (add_SNo x20 x21)))))))))) 0.
Assume H63: SNoLe (add_SNo x1 (minus_SNo x0)) x11.
Assume H64: SNoLe (add_SNo x2 (minus_SNo x1)) x12.
Assume H65: SNoLe (add_SNo x3 (minus_SNo x2)) x13.
Assume H66: SNoLe (add_SNo x4 (minus_SNo x3)) x14.
Assume H67: SNoLe (add_SNo x5 (minus_SNo x4)) x15.
Assume H68: SNoLe (add_SNo x6 (minus_SNo x5)) x16.
Assume H69: SNoLe (add_SNo x7 (minus_SNo x6)) x17.
Assume H70: SNoLe (add_SNo x8 (minus_SNo x7)) x18.
Assume H71: SNoLe (add_SNo x9 (minus_SNo x8)) x19.
Assume H72: SNoLe (add_SNo x10 (minus_SNo x9)) x20.
Assume H73: SNoLe (add_SNo x0 (minus_SNo x10)) x21.
Apply idl_negcycle_10 with x0, x1, x2, x3, x4, x5, x6, x7, x8, add_SNo x9 x10, x11, x12, x13, x14, x15, x16, x17, x18, add_SNo x19 x10, add_SNo x21 (minus_SNo x9) 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.
Apply SNo_add_SNo with x9, x10 leaving 2 subgoals.
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.
The subproof is completed by applying H13.
The subproof is completed by applying H14.
The subproof is completed by applying H15.
The subproof is completed by applying H16.
The subproof is completed by applying H17.
The subproof is completed by applying H18.
Apply SNo_add_SNo with x19, x10 leaving 2 subgoals.
The subproof is completed by applying H19.
The subproof is completed by applying H10.
Apply SNo_add_SNo with x21, minus_SNo x9 leaving 2 subgoals.
The subproof is completed by applying H21.
The subproof is completed by applying L31.
Apply add_SNo_com with x21, minus_SNo x9, λ x22 x23 . SNoLt (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 (add_SNo (add_SNo x19 x10) x23))))))))) 0 leaving 3 subgoals.
The subproof is completed by applying H21.
The subproof is completed by applying L31.
Apply add_SNo_assoc with x19, x10, add_SNo (minus_SNo x9) x21, λ x22 x23 . SNoLt (add_SNo x11 (add_SNo x12 (add_SNo x13 (add_SNo x14 (add_SNo x15 (add_SNo x16 (add_SNo x17 (add_SNo x18 x22)))))))) 0 leaving 4 subgoals.
The subproof is completed by applying H19.
The subproof is completed by applying H10.
Apply SNo_add_SNo with minus_SNo x9, ... leaving 2 subgoals.
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