Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Assume H0:
∀ x2 . x1 x2 ⟶ ∀ x3 . x3 ∈ x2 ⟶ nIn x0 x3.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H1: x1 x2.
Assume H2: x1 x3.
Assume H3: x1 x4.
Assume H4: x1 x5.
Apply set_ext with
x3,
x5 leaving 2 subgoals.
Apply pair_tag_prop_2_Subq with
x0,
x1,
x2,
x3,
x4,
x5 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
Apply pair_tag_prop_2_Subq with
x0,
x1,
x4,
x5,
x2,
x3 leaving 5 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H4.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying H5 with λ x7 x8 . x6 x8 x7.