Let x0 of type ι be given.
Let x1 of type ι be given.
Apply nat_p_omega with
add_CSNo x0 x1.
Apply unknownprop_43cb5a76d994a313182eba8f3a42eede331e54ecc8fc62c4c505222670320894 with
x0,
x1 leaving 2 subgoals.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.
Apply omega_nat_p with
x1.
The subproof is completed by applying H1.