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_assoc with
add_SNo x0 x1,
x2,
x3,
λ x4 x5 . x5 = add_SNo (add_SNo x0 x2) (add_SNo x1 x3) leaving 4 subgoals.
Apply SNo_add_SNo 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_SNo_com_3b_1_2 with
x0,
x1,
x2,
λ x4 x5 . add_SNo x5 x3 = add_SNo (add_SNo x0 x2) (add_SNo 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.
Let x4 of type ι → ι → ο be given.
Apply add_SNo_assoc with
add_SNo x0 x2,
x1,
x3,
λ x5 x6 . x4 x6 x5 leaving 3 subgoals.
Apply SNo_add_SNo 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.