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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.
Let x6 of type ι be given.
Let x7 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: SNo x6.
Assume H7: SNo x7.
Assume H8: SNoLe x0 x4.
Assume H9: SNoLe x1 x5.
Assume H10: SNoLe x2 x6.
Assume H11: SNoLe x3 x7.
Apply add_SNo_Le3 with x0, add_SNo x1 (add_SNo x2 x3), x4, add_SNo x5 (add_SNo x6 x7) leaving 6 subgoals.
The subproof is completed by applying H0.
Apply SNo_add_SNo_3 with x1, x2, x3 leaving 3 subgoals.
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.
Apply SNo_add_SNo_3 with x5, x6, x7 leaving 3 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.
Apply unknownprop_c65c101ade85bfa060331a47af562cb2e92a7682259cab9d1c17312979426654 with x1, x2, x3, x5, x6, x7 leaving 9 subgoals.
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 H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H9.
The subproof is completed by applying H10.
The subproof is completed by applying H11.
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