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
x1,
x0,
λ x3 x4 . x4 = add_SNo x1 x2 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply add_SNo_com with
x1,
x2,
λ x3 x4 . add_SNo x0 x1 = x4 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply add_SNo_cancel_L with
x1,
x0,
x2 leaving 4 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 L4.