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.
Apply add_SNo_rotate_3_1 with
x0,
x4,
x1,
λ x5 x6 . SNoLt x6 (add_SNo x2 (add_SNo x3 x4)) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
Apply add_SNo_3_3_3_Lt1 with
x1,
x0,
x2,
x3,
x4 leaving 6 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.