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.
Apply minus_add_SNo_distr_m_3 with
x0,
x1,
x2,
add_SNo (minus_SNo x3) x4,
λ x5 x6 . x6 = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (minus_SNo x4)))) leaving 5 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
minus_SNo x3,
x4 leaving 2 subgoals.
Apply SNo_minus_SNo with
x3.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply minus_add_SNo_distr_m with
x3,
x4,
λ x5 x6 . add_SNo x0 (add_SNo x1 (add_SNo x2 x6)) = add_SNo x0 (add_SNo x1 (add_SNo x2 (add_SNo x3 (minus_SNo x4)))) leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H5.