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.
Apply minus_add_SNo_distr_m_4 with
x0,
x1,
x2,
x3,
add_SNo (minus_SNo x4) x5,
λ x6 x7 . x7 = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (minus_SNo x5))))) leaving 6 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.
Apply SNo_add_SNo with
minus_SNo x4,
x5 leaving 2 subgoals.
Apply SNo_minus_SNo with
x4.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply minus_add_SNo_distr_m with
x4,
x5,
λ x6 x7 . add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 x7))) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (add_SNo x4 (minus_SNo x5))))) leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying H6.