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.
Let x4 of type ι be given.
Apply add_SNo_rotate_4_1 with
x1,
x2,
x3,
x4,
λ x5 x6 . add_SNo x0 x6 = add_SNo x4 (add_SNo x0 (add_SNo x1 (add_SNo x2 x3))) leaving 5 subgoals.
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.
Apply add_SNo_com_3_0_1 with
x0,
x4,
add_SNo x1 (add_SNo x2 x3) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
Apply SNo_add_SNo_3 with
x1,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.