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.
Apply minus_add_SNo_distr_m_2 with
x0,
x1,
add_SNo (minus_SNo x2) x3,
λ x4 x5 . x5 = add_SNo x0 (add_SNo x1 (add_SNo x2 (minus_SNo x3))) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_add_SNo with
minus_SNo x2,
x3 leaving 2 subgoals.
Apply SNo_minus_SNo with
x2.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply minus_add_SNo_distr_m with
x2,
x3,
λ x4 x5 . add_SNo x0 (add_SNo x1 x5) = add_SNo x0 (add_SNo x1 (add_SNo x2 (minus_SNo x3))) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying H4.