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.
Apply idl_negcycle_9 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
minus_SNo x9,
minus_SNo x10,
minus_SNo x11,
minus_SNo x12,
minus_SNo x13,
minus_SNo x14,
minus_SNo x15,
minus_SNo x16,
minus_SNo x17 leaving 28 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.
The subproof is completed by applying L28.
The subproof is completed by applying L29.
The subproof is completed by applying L30.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
The subproof is completed by applying L33.
The subproof is completed by applying L34.
The subproof is completed by applying L35.
The subproof is completed by applying L36.
Apply minus_SNo_Lt_contra3 with
0,
add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (minus_SNo x17)))))))) leaving 3 subgoals.
The subproof is completed by applying SNo_0.
Apply SNo_add_SNo_9 with
minus_SNo x9,
minus_SNo x10,
minus_SNo x11,
minus_SNo x12,
minus_SNo x13,
minus_SNo x14,
minus_SNo x15,
minus_SNo x16,
minus_SNo x17 leaving 9 subgoals.
The subproof is completed by applying L28.
The subproof is completed by applying L29.
The subproof is completed by applying L30.
The subproof is completed by applying L31.
The subproof is completed by applying L32.
The subproof is completed by applying L33.
The subproof is completed by applying L34.
The subproof is completed by applying L35.
The subproof is completed by applying L36.
Apply minus_SNo_0 with
λ x18 x19 . SNoLt x19 (minus_SNo (add_SNo (minus_SNo x9) (add_SNo (minus_SNo x10) (add_SNo (minus_SNo x11) (add_SNo (minus_SNo x12) (add_SNo (minus_SNo x13) (add_SNo (minus_SNo x14) (add_SNo (minus_SNo x15) (add_SNo (minus_SNo x16) (minus_SNo x17)))))))))).
Apply minus_add_SNo_distr_m_8 with
x9,
x10,
x11,
x12,
x13,
x14,
x15,
x16,
minus_SNo x17,
λ x18 x19 . SNoLt 0 x19 leaving 10 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 L36.
Apply minus_SNo_invol with
x17,
... leaving 2 subgoals.