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.
Apply add_SNo_assoc with
x0,
x1,
minus_SNo x2,
λ x4 x5 . SNoLt x5 x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with
x2.
The subproof is completed by applying H2.
Apply add_SNo_minus_Lt1b with
add_SNo x0 x1,
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 H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.