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_3_0_1 with
x1,
x3,
x4,
λ x5 x6 . divides_int x0 x6 ⟶ divides_int x0 (add_SNo x1 (add_SNo x2 x4)) leaving 4 subgoals.
Apply int_SNo with
x1.
The subproof is completed by applying H0.
Apply int_SNo with
x3.
The subproof is completed by applying H2.
Apply int_SNo with
x4.
The subproof is completed by applying H3.
Apply add_SNo_com_3_0_1 with
x1,
x2,
x4,
λ x5 x6 . divides_int x0 (add_SNo x3 (add_SNo x1 x4)) ⟶ divides_int x0 x6 leaving 4 subgoals.
Apply int_SNo with
x1.
The subproof is completed by applying H0.
Apply int_SNo with
x2.
The subproof is completed by applying H1.
Apply int_SNo with
x4.
The subproof is completed by applying H3.
Apply unknownprop_82d8b16cbabe15f33566315da037f391b292861be9631cc7d9815c42bac38696 with
x0,
x2,
x3,
add_SNo x1 x4 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply int_add_SNo with
x1,
x4 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
The subproof is completed by applying H4.