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_com with
add_SNo x0 (add_SNo x1 x2),
add_SNo x3 x4,
λ x5 x6 . x6 = add_SNo (add_SNo x4 (add_SNo x1 x2)) (add_SNo x3 x0) leaving 3 subgoals.
Apply SNo_add_SNo_3 with
x0,
x1,
x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply SNo_add_SNo with
x3,
x4 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
Apply add_SNo_com_4_inner_mid with
x3,
x4,
x0,
add_SNo x1 x2,
λ x5 x6 . x6 = add_SNo (add_SNo x4 (add_SNo x1 x2)) (add_SNo x3 x0) leaving 5 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H0.
Apply SNo_add_SNo with
x1,
x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply add_SNo_com with
add_SNo x3 x0,
add_SNo x4 (add_SNo x1 x2) leaving 2 subgoals.
Apply SNo_add_SNo with
x3,
x0 leaving 2 subgoals.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
Apply SNo_add_SNo_3 with
x4,
x1,
x2 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H2.