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_CSNo_assoc with
add_CSNo x0 x1,
x2,
x3,
λ x4 x5 . x4 = add_CSNo (add_CSNo x0 x2) (add_CSNo x1 x3) leaving 4 subgoals.
Apply CSNo_add_CSNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply add_CSNo_com_3b_1_2 with
x0,
x1,
x2,
λ x4 x5 . add_CSNo x5 x3 = add_CSNo (add_CSNo x0 x2) (add_CSNo x1 x3) leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply add_CSNo_assoc with
add_CSNo x0 x2,
x1,
x3 leaving 3 subgoals.
Apply CSNo_add_CSNo with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H1.
The subproof is completed by applying H3.