Let x0 of type ι be given.
Apply mul_SNo_distrL with
eps_ 1,
x0,
x0,
λ x1 x2 . x0 = x2 leaving 4 subgoals.
Apply SNo_eps_ with
1.
Apply nat_p_omega with
1.
The subproof is completed by applying nat_1.
The subproof is completed by applying H0.
The subproof is completed by applying H0.
Let x1 of type ι → ι → ο be given.
Apply eps_1_split_eq with
x0,
λ x2 x3 . x1 x3 x2.
The subproof is completed by applying H0.