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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Apply add_SNo_com with x3, minus_SNo x2, λ x4 x5 . add_SNo (add_SNo x0 (add_SNo x1 x2)) x5 = add_SNo x0 (add_SNo x1 x3) leaving 3 subgoals.
The subproof is completed by applying H3.
Apply SNo_minus_SNo with x2.
The subproof is completed by applying H2.
Apply add_SNo_minus_SNo_prop3 with x0, x1, x2, x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.