Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply H3 with
λ x3 x4 . SNoLt x4 0.
Apply add_SNo_com with
minus_SNo x0,
x2,
λ x3 x4 . SNoLt x4 0 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply add_SNo_minus_Lt1b with
x2,
x0,
0 leaving 4 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H0.
The subproof is completed by applying SNo_0.
Apply add_SNo_0L with
x0,
λ x3 x4 . SNoLt x2 x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H5.