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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: SNo x0.
Assume H1: x0 = 0∀ x1 : ο . x1.
Apply mul_SNo_com with recip_SNo x0, x0, λ x1 x2 . x2 = 1 leaving 3 subgoals.
Apply SNo_recip_SNo with x0.
The subproof is completed by applying H0.
The subproof is completed by applying H0.
Apply recip_SNo_invR with x0 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.