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Proofgold Proof

pf
Apply CD_conj_mul with Sing 2, SNo, minus_SNo, λ x0 . x0, add_SNo, mul_SNo leaving 14 subgoals.
The subproof is completed by applying complex_tag_fresh.
The subproof is completed by applying SNo_minus_SNo.
Let x0 of type ι be given.
Assume H0: SNo x0.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_add_SNo.
The subproof is completed by applying SNo_mul_SNo.
The subproof is completed by applying minus_SNo_invol.
Let x0 of type ι be given.
Assume H0: SNo x0.
Let x1 of type ιιο be given.
Assume H1: x1 x0 x0.
The subproof is completed by applying H1.
Let x0 of type ι be given.
Assume H0: SNo x0.
Let x1 of type ιιο be given.
Assume H1: x1 (minus_SNo x0) (minus_SNo x0).
The subproof is completed by applying H1.
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Let x2 of type ιιο be given.
Assume H2: x2 (add_SNo x0 x1) (add_SNo x0 x1).
The subproof is completed by applying H2.
The subproof is completed by applying minus_add_SNo_distr.
The subproof is completed by applying add_SNo_com.
The subproof is completed by applying mul_SNo_com.
The subproof is completed by applying mul_SNo_minus_distrR.
The subproof is completed by applying mul_SNo_minus_distrL.