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 x4.
Apply set_ext with
x2,
x4 leaving 2 subgoals.
Apply pair_tag_prop_1_Subq with
x0,
x1,
x2,
x3,
x4,
x5 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Apply pair_tag_prop_1_Subq with
x0,
x1,
x4,
x5,
x2,
x3 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying H3 with λ x7 x8 . x6 x8 x7.