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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.
Assume H4: add_SNo x0 x1 = add_SNo x3 x2.
Apply add_SNo_assoc with x0, x1, minus_SNo x2, λ x4 x5 . x5 = x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with x2.
The subproof is completed by applying H2.
Apply H4 with λ x4 x5 . add_SNo x5 (minus_SNo x2) = x3.
Apply add_SNo_minus_R2 with x3, x2 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H2.