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_rotate_3_1 with
x1,
x2,
x3,
λ x4 x5 . add_SNo x0 x5 = add_SNo x3 (add_SNo x0 (add_SNo x1 x2)) leaving 4 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_com_3_0_1 with
x0,
x3,
add_SNo x1 x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply SNo_add_SNo with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.