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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.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H0: SNo x0.
Assume H1: SNo x1.
Assume H2: SNo x2.
Assume H3: SNo x3.
Assume H4: SNo x4.
Assume H5: SNo x5.
Assume H6: SNoLt x0 x3.
Assume H7: SNoLt x1 x4.
Assume H8: SNoLt x2 x5.
Apply add_SNo_Lt3 with x0, add_SNo x1 x2, x3, add_SNo x4 x5 leaving 6 subgoals.
The subproof is completed by applying H0.
Apply SNo_add_SNo with x1, x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply SNo_add_SNo with x4, x5 leaving 2 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Apply add_SNo_Lt3 with x1, x2, x4, x5 leaving 6 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
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