Let x0 of type ι be given.
Let x1 of type ι be given.
Apply add_SNo_com with
minus_SNo x0,
add_SNo x0 x1,
λ x2 x3 . x3 = x1 leaving 3 subgoals.
Apply SNo_minus_SNo with
x0.
The subproof is completed by applying H0.
Apply SNo_add_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_com with
x0,
x1,
λ x2 x3 . add_SNo x3 (minus_SNo x0) = x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_minus_R2 with
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.