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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNoLt 1 x0.
Apply add_SNo_1_1_2 with λ x1 x2 . SNoLt (add_SNo x0 1) (mul_SNo x1 x0).
Apply mul_SNo_distrR with 1, 1, x0, λ x1 x2 . SNoLt (add_SNo x0 1) 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 x1 x2 . SNoLt (add_SNo x0 1) (add_SNo x2 x2) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply add_SNo_Lt2 with x0, 1, x0 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_1.
The subproof is completed by applying H0.
The subproof is completed by applying H1.