Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply add_SNo_com with
x0,
x1,
λ x3 x4 . SNoLt x4 (add_SNo x0 x2) ⟶ SNoLt x1 x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_SNo_com with
x0,
x2,
λ x3 x4 . SNoLt (add_SNo x1 x0) x4 ⟶ SNoLt x1 x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Apply add_SNo_Lt1_cancel with
x1,
x0,
x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H2.