Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoS_E2 with
omega,
x0,
mul_CSNo x0 x1 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H0.
Apply SNoS_E2 with
omega,
x1,
mul_CSNo x0 x1 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H1.
Apply unknownprop_e8fe572c395c46aa7a6d67f7a8cd850bf647261d6b3677aecbf3b7ddfa5a7193 with
x0,
x1,
λ x2 x3 . x2 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H8.
Apply mul_SNo_SNoS_omega with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.