Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply SNo_add_SNo with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply mul_SNo_nonzero_cancel with
2,
x0,
mul_SNo (eps_ 1) (add_SNo x1 x2) leaving 5 subgoals.
The subproof is completed by applying SNo_2.
The subproof is completed by applying neq_2_0.
The subproof is completed by applying H0.
Apply SNo_mul_SNo with
eps_ 1,
add_SNo x1 x2 leaving 2 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 L4.
Apply mul_SNo_assoc with
2,
eps_ 1,
add_SNo x1 x2,
λ x3 x4 . mul_SNo 2 x0 = x4 leaving 4 subgoals.
The subproof is completed by applying SNo_2.
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 L4.
Apply eps_1_half_eq2 with
λ x3 x4 . mul_SNo 2 x0 = mul_SNo x4 (add_SNo x1 x2).
Apply mul_SNo_oneL with
add_SNo x1 x2,
λ x3 x4 . mul_SNo 2 x0 = x4 leaving 2 subgoals.
The subproof is completed by applying L4.
Apply add_SNo_1_1_2 with
λ x3 x4 . mul_SNo x3 x0 = add_SNo x1 x2.
Apply mul_SNo_distrR with
1,
1,
x0,
λ x3 x4 . x4 = add_SNo x1 x2 leaving 4 subgoals.
The subproof is completed by applying SNo_1.
The subproof is completed by applying SNo_1.
The subproof is completed by applying H0.
Apply mul_SNo_oneL with
x0,
λ x3 x4 . add_SNo x4 x4 = add_SNo x1 x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.