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_assoc with
x0,
x1,
x4,
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 H1.
The subproof is completed by applying H4.
Apply add_SNo_assoc with
x2,
x3,
x4,
λ x5 x6 . SNoLt (add_SNo (add_SNo x0 x1) x4) x6 leaving 4 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply add_SNo_Lt1 with
add_SNo x0 x1,
x4,
add_SNo x2 x3 leaving 4 subgoals.
Apply SNo_add_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H4.
Apply SNo_add_SNo with
x2,
x3 leaving 2 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H5.