Let x0 of type ι be given.
Let x1 of type ι → ι → ο be given.
Let x2 of type ι be given.
Apply H0 with
λ x3 . x3 = pack_r_e x0 x1 x2 ⟶ x2 ∈ x0 leaving 2 subgoals.
Let x3 of type ι be given.
Let x4 of type ι → ι → ο be given.
Let x5 of type ι be given.
Assume H1: x5 ∈ x3.
Apply pack_r_e_inj with
x3,
x0,
x4,
x1,
x5,
x2,
x2 ∈ x0 leaving 2 subgoals.
The subproof is completed by applying H2.
Assume H3:
and (x3 = x0) (∀ x6 . x6 ∈ x3 ⟶ ∀ x7 . x7 ∈ x3 ⟶ x4 x6 x7 = x1 x6 x7).
Apply H3 with
x5 = x2 ⟶ x2 ∈ x0.
Assume H4: x3 = x0.
Assume H5: ∀ x6 . x6 ∈ x3 ⟶ ∀ x7 . x7 ∈ x3 ⟶ x4 x6 x7 = x1 x6 x7.
Assume H6: x5 = x2.
Apply H4 with
λ x6 x7 . x2 ∈ x6.
Apply H6 with
λ x6 x7 . x6 ∈ x3.
The subproof is completed by applying H1.
Let x3 of type ι → ι → ο be given.
The subproof is completed by applying H1.