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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.
Apply add_SNo_com with minus_SNo x0, add_SNo x0 x1, λ x2 x3 . x3 = x1 leaving 3 subgoals.
Apply SNo_minus_SNo with x0.
The subproof is completed by applying H0.
Apply SNo_add_SNo with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_com with x0, x1, λ x2 x3 . add_SNo x3 (minus_SNo x0) = x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_minus_R2 with x1, x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.