Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply setminusE with
omega,
Sing 0,
x0,
divides_int x0 (add_SNo x1 (minus_SNo x2)) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply nat_p_trans with
x0,
96eca.. x0 x1 leaving 2 subgoals.
Apply omega_nat_p with
x0.
The subproof is completed by applying H4.
Apply unknownprop_b8495c15b713ede179e55ace8614d7c473b63e6d664fda42134df335ee990bdf with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_99a3c86e262d57a15068e53f2903d0677a958c45db7b2862850c06494aa7d66e with
x1,
96eca.. x0 x1,
minus_SNo x2,
λ x3 x4 . divides_int x0 x3 leaving 4 subgoals.
Apply nat_p_SNo with
x1.
The subproof is completed by applying H1.
Apply nat_p_SNo with
96eca.. x0 x1.
The subproof is completed by applying L6.
Apply SNo_minus_SNo with
x2.
Apply nat_p_SNo with
x2.
The subproof is completed by applying H2.
Apply divides_int_add_SNo with
x0,
add_SNo x1 (minus_SNo (96eca.. x0 x1)),
add_SNo (96eca.. x0 x1) (minus_SNo x2) leaving 2 subgoals.
Apply unknownprop_de46f3f56305affec6d4587c784b63a18d38e7b33818071c678730ea3a326a68 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply divides_int_diff_SNo_rev with
x0,
x2,
96eca.. x0 x1 leaving 3 subgoals.
Apply nat_p_int with
x2.
The subproof is completed by applying H2.
Apply nat_p_int with
96eca.. x0 x1.
The subproof is completed by applying L6.
Apply H3 with
λ x3 x4 . divides_int x0 (add_SNo x2 (minus_SNo x4)).
Apply unknownprop_de46f3f56305affec6d4587c784b63a18d38e7b33818071c678730ea3a326a68 with
x0,
x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.