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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNoLe x0 0.
Assume H3: SNoLe 0 x1.
Apply SNoLeE with 0, x1, SNoLe (mul_SNo x0 x1) 0 leaving 5 subgoals.
The subproof is completed by applying SNo_0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply mul_SNo_nonpos_pos with x0, x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Assume H4: 0 = x1.
Apply H4 with λ x2 x3 . SNoLe (mul_SNo x0 x2) 0.
Apply mul_SNo_zeroR with x0, λ x2 x3 . SNoLe x3 0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying SNoLe_ref with 0.