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_com with
x2,
x3,
λ x4 x5 . add_SNo (add_SNo x0 x1) x5 = add_SNo (add_SNo x0 x3) (add_SNo x1 x2) leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply add_SNo_com_4_inner_mid with
x0,
x1,
x3,
x2 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H2.