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.
Apply minus_add_SNo_distr_m_9 with
x0,
x1,
x2,
x3,
x4,
x5,
x6,
x7,
x8,
add_SNo (minus_SNo x9) x10,
λ x11 x12 . x12 = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (add_SNo x5 (add_SNo x6 (add_SNo x7 (add_SNo x8 (add_SNo x9 (minus_SNo x10)))))))))) leaving 11 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
minus_SNo x9,
x10 leaving 2 subgoals.
Apply SNo_minus_SNo with
x9.
The subproof is completed by applying H9.
The subproof is completed by applying H10.