Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply add_SNo_com with
x2,
minus_SNo x1,
λ x3 x4 . divides_int x0 x4 leaving 3 subgoals.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with
x1.
The subproof is completed by applying H0.
Apply minus_SNo_invol with
x2,
λ x3 x4 . divides_int x0 (add_SNo (minus_SNo x1) x3) leaving 2 subgoals.
The subproof is completed by applying H1.
Apply minus_add_SNo_distr with
x1,
minus_SNo x2,
λ x3 x4 . divides_int x0 x3 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply SNo_minus_SNo with
x2.
The subproof is completed by applying H1.
Apply divides_int_minus_SNo with
x0,
add_SNo x1 (minus_SNo x2).
The subproof is completed by applying H2.