Let x0 of type ι be given.
Apply H0 with
x0 = 2.
Apply H2 with
(∀ x1 . x1 ∈ omega ⟶ divides_nat x1 x0 ⟶ or (x1 = 1) (x1 = x0)) ⟶ x0 = 2.
Assume H4: 1 ∈ x0.
Apply unknownprop_08fb078d795c0975d950898a1224977eb8db97682ff225342ef66a3071181f64 with
x0.
The subproof is completed by applying H1.
Apply H5 with
2,
x0 = 2 leaving 4 subgoals.
Apply nat_p_omega with
2.
The subproof is completed by applying nat_2.
The subproof is completed by applying L6.
Assume H7: 2 = 1.
Apply FalseE with
x0 = 2.
Apply neq_2_1.
The subproof is completed by applying H7.
Assume H7: 2 = x0.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H7 with λ x2 x3 . x1 x3 x2.