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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 (add_SNo x0 (add_SNo x1 x5)) (add_SNo x3 (add_SNo x4 x2)).
Apply add_SNo_minus_Lt1b3 with x0, x1, x2, add_SNo x3 (add_SNo x4 (minus_SNo x5)) leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply SNo_add_SNo_3 with x3, x4, minus_SNo x5 leaving 3 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply SNo_minus_SNo with x5.
The subproof is completed by applying H5.
Apply add_SNo_assoc with x3, x4, minus_SNo x5, λ x6 x7 . SNoLt (add_SNo x0 x1) (add_SNo x7 x2) leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply SNo_minus_SNo with x5.
The subproof is completed by applying H5.
Apply add_SNo_com_3b_1_2 with add_SNo x3 x4, minus_SNo x5, x2, λ x6 x7 . SNoLt (add_SNo x0 x1) x7 leaving 4 subgoals.
Apply SNo_add_SNo with x3, x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply SNo_minus_SNo with x5.
The subproof is completed by applying H5.
The subproof is completed by applying H2.
Apply add_SNo_minus_Lt2b with add_SNo (add_SNo x3 x4) x2, x5, add_SNo x0 x1 leaving 4 subgoals.
Apply SNo_add_SNo with add_SNo x3 x4, x2 leaving 2 subgoals.
Apply SNo_add_SNo with x3, x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
Apply SNo_add_SNo with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_assoc with x0, x1, x5, λ x6 x7 . SNoLt x6 (add_SNo (add_SNo x3 x4) x2) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H5.
Apply add_SNo_assoc with x3, x4, x2, λ x6 x7 . SNoLt (add_SNo x0 (add_SNo x1 x5)) x6 leaving 4 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
The subproof is completed by applying H6.
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