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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: SNoLe (add_SNo x0 x1) (add_SNo x3 x2).
Apply add_SNo_assoc with x0, x1, minus_SNo x2, λ x4 x5 . SNoLe 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 add_SNo_minus_Le1b with add_SNo x0 x1, x2, x3 leaving 4 subgoals.
Apply SNo_add_SNo with x0, x1 leaving 2 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.
The subproof is completed by applying H4.